Browsing by Author "Heyliger, Paul, advisor"

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Open Access
Disruptive packing of binary mixtures
(Colorado State University. Libraries, 2016) Zou, Shuai, author; Heyliger, Paul, advisor; Bareither, Christopher, committee member; Shuler, Scott, committee member
Granular materials are common in many areas such as civil engineering, food industry,and chemistry. The discrete element method has been demonstrated to be an eectivemethod to study the particle dynamics of such materials over the past several decades. Thepacking of monosized spherical particles has been well studied from both numerical andexperimental perspectives. However, the study of packings of a binary mixture that containsparticles of two dierent sizes has been limited because of the numerous variables that aectthe packing structure.The potential variables for packing of binary mixtures of spherical particles blended bygeometric disruptors in a gravity loaded ramp are evaluated in this thesis. The complexity ofthe disruptor geometry was used as the primary variable to study the resulting packing of twodierent-sized particles. The nal packing structure was quantied by coordination number,radial distribution function, packing density, and vertical position of the smaller-diameterparticles. Based on the analysis conducted in this thesis, the mean coordination number ofall particles, larger particles and smaller particles, generally increases with the complexity ofdisruptor geometry. The mean vertical position of smaller particles decrease with an increasein the complexity of the disruptor geometry. The radial distribution function of each type ofparticle in a binary mixture has the same characteristics of the radial distribution functionof mono-size particle packing. The methodology presented in this thesis can be eective toanalyze binary mixtures of spherical particles.
Open Access
Effective properties of magneto-electro-elastic two-dimensional cellular solids
(Colorado State University. Libraries, 2016) Khattab, Mustafa M., author; Heyliger, Paul, advisor; Ellingwood, Bruce, committee member; Puttlitz, Christian, committee member
Two-dimensional cellular solids composed of magneto-electro-elastic (MEE) materials were studied using the finite element method (FEM). A MATLAB code was written to implement field models to determine the effective properties for this cellular solid including elastic, piezoelectric, piezomagnetic, thermal, pyroelectric and pyromagnetic effective properties as a function of the relative density. Results obtained for purely elastic properties were compared with results from other studies and showed good agreement. Varying microstructures of the cellular solids including square, equilateral triangle and hexagonal systems, were considered and comparisons between the results of all the geometries were established. The triangular cellular solid was the stiffest among all shapes, and the regular hexagon cellular solid showed the highest effective coupling constants for the piezoelectric, piezomagnetic, pyroelectric and pyromagnetic coefficients. The thermal expansion coefficient was found to be independent from the relative density and was constant for all the MEE cellular solid shapes. A set of simple equations are proposed to approximate the effective properties for these low density MEE solids.
Open Access
Effects of explosive pressure on cadaveric ovine auditory tissue
(Colorado State University. Libraries, 2018) McCann, Amanda, author; Heyliger, Paul, advisor; Mahmoud, Hussam, committee member; McGilvray, Kirk, committee member
The focus of this research centered around two main goals: 1) determine the allowable pressures that people can be exposed to in non-life-threatening situations and 2) determine the pressure required to rupture a sheep eardrum as a representative sample for human ears. For the first goal, blast pressure tests were conducted at a local football stadium using Composition 1 (C1) plastic explosive, 50-grain detonation cord, and the game cannon firing 75% strength shells. The results for each explosive were put into units of TNT equivalency to provide a common unit between explosive types. Based on the recorded pressures, spectators and staff in the vicinity of the game cannon are not at risk of severe ear damage, but should still take precautions and wear hearing protection when in the vicinity. The second goal, which forms the bulk of this thesis, was investigated through conducting two series of explosive tests on dissected sheep heads and sheep ears as a representative sample for human ears. Through these experiments, the author developed a refined process for preparing and analyzing the eardrum samples under blast conditions. From these two blast tests, eight eardrums were ruptured when exposed to varying explosive pressures and this damage was used to estimate the threshold pressure at which severe damage initially occurs. The threshold pressure for these experiments is within the range of 34 kPa (4.9psi) to 42 kPa (6.1psi), which is substantially refined compared to the range of 8 kPa (1.2psi) to 104 kPa (15.1 psi) listed in other published literature. At this time, this result is only accurate for deceased sheep eardrum ruptures, but further testing could verify that this is applicable to humans.
Open Access
Elasticity-based vibrations of hollow anisotropic beams and an evaluation of the shape factor for hollow anisotropic sections
(Colorado State University. Libraries, 2012) Lebsack, Michael J., author; Heyliger, Paul, advisor; Criswell, Marvin, committee member; Puttlitz, Christian, committee member
This study considers the transverse vibrations and natural frequencies of hollow anisotropic beams free from end restraints using full three-dimensional elasticity solutions and common one-dimensional beam theory approximations. Calculations of the natural frequencies are made for a number of hollow beam dimensions using the one-dimensional Euler-Bernoulli, Rayleigh, and Timoshenko beam theories. Complete derivations of the elasticity solutions and beam theories are presented. The accuracy of the approximate methods is determined by comparison to elasticity solutions. Subsequent discussion on the limitations of each approximate beam theory in calculating natural frequencies is made. Mode shapes and cross-section deformations for the first five modes of vibration are presented. Additionally, the shape factor for the Timoshenko beam theory is analyzed for hollow-anisotropic sections.
Open Access
Failure mode analysis of a post-tension anchored dam using linear finite element analysis
(Colorado State University. Libraries, 2014) Corn, Aimee, author; Heyliger, Paul, advisor; Bareither, Chris, committee member; Glick, Scott, committee member; Lund, Guy, committee member
There are currently over 84,000 dams in the United States, and the average age of those dams is 52 years. Concrete gravity dams are the second most common dam type, with more than 3,000 in the United States. Current engineering technology and technical understanding of hydrologic and seismic events has resulted in significant increases to the required design loads for most dams; therefore, many older dams do not have adequate safety for extreme loading events. Concrete gravity dams designed and constructed in the early 20th century did not consider uplift pressures beneath the dam, which reduces the effective weight of the structure. One method that has been used to enhance the stability of older concrete gravity dams includes the post-tension anchor (PTA) system. Post-tensioning infers modifying cured concrete and using self-equilibrating elements to increase the weight of the section, which provides added stability. There is a lack of historical evidence regarding the potential failure mechanisms for PTA concrete gravity dams. Of particular interest, is how these systems behave during large seismic events. The objective of this thesis is to develop a method by which the potential failure modes during a seismic event for a PTA dam can be evaluated using the linear elastic finite element method of analysis. The most likely potential failure modes (PFM) for PTA designs are due to tensile failure and shear failure. A numerical model of a hypothetical project was developed to simulate PTAs in the dam. The model was subjected to acceleration time-history motions that simulated the seismic loads. The results were used to evaluate the likelihood of tendon failure due to both tension and shear. The results from the analysis indicated that the PTA load increased during the seismic event; however, the peak load in the tendons was less than the gross ultimate tensile strength (GUTS) and would not be expected to result in tensile failure at the assumed project. The analysis also indicated there was a potential for permanent horizontal displacement along the dam/foundation interface. The horizontal movement was not considered large enough to develop a shear failure of the tendons at the project. The results from this study indicate demand to capacity ratios (DCR) of 0.79 for the anchor head, 0.75 for the tendon, and 0.63 for the foundation cone failure, and a potential displacement of 0.33 inches, which is not large enough to shear the tendon. The methods developed are appropriate for the evaluation of the tensile and shear failure modes for the PTA tendons. Based on the results, it would appear that shear failure of the tendon is a more likely failure mechanism. Thus, shear failure of the tendon should be a focus of seismic evaluations.
Open Access
Flow-generated displacement of reinforced granular slopes using the discrete element method
(Colorado State University. Libraries, 2017) Dalaeli, Mozhdeh, author; Heyliger, Paul, advisor; Bareither, Christopher, committee member; Puttlitz, Christian, committee member
The Discrete Element Method (DEM) has been used by researchers to study the behavior of granular material. It is based on the discrete nature of the granular media and tracks the displacements of individual particles and their interactions at every time-step of the simulation. This approach was used in this study to investigate the flow-generated displacement of spring-reinforced planar granular slopes. A Discrete Element (DE) code was created using MATLAB and FORTRAN to carry out the simulations. The code was validated by comparison of simulation results with analytical solutions. Granular slopes with particle radii ranging from 5 to 10 mm and various initial slopes were generated. Reinforced slopes were created by adding reinforcement, in the form of linear springs restraining surface particles, to the original geometry. The surface of both the original and the reinforced slopes was exposed to flow-generated drag forces. Various reinforcement patterns were modeled and the resulting flow-generated displacements were measured and studied. It was found that slope reinforcing can either delay or prevent flow-generated movements and the effectiveness of the reinforcing depends on the slope of the packing, size of the drag force and the pattern of the reinforcing.
Open Access
Geometrically and materially nonlinear analysis using material point method
(Colorado State University. Libraries, 2022) Asiri, Abdullah N., author; Heyliger, Paul, advisor; van de Lindt, John, committee member; Chen, Suren, committee member; Cheney, Margaret, committee member
Computational engineering has become an effective tool for different engineering aspects. It provides suitable simulation models for complex problems. Also, the computational models are strongly recommended as alternatives to experiments due to the consumed cost and time. In addition, because this field has gotten attention earlier, the accuracy of computational models has been improved. The finite element method (FEM) is one of the famous computer simulations that has been adopted widely in scientific and technical fields. It considers an excellent tool for different engineering analyses; however, for the large deformation behavior, the FEM cannot withstand due to the finite discretization of the systems in which the accuracy would be lost as a result of the large distortion that occurred for the model. Thereby, the mesh-less methods are appropriate models for such problems. The material point method (MPM) is one of the improved mesh-less methods, which is an extension of the Particle In Cell (PIC) method used for fluid mechanics modeling. Both static and dynamic applications are intended to simulate the two-dimensional material point method model. The main objective here is to simulate and validate the material point method with the analytical solutions for different solid mechanics applications. Further, to examine the formulation of the nonlinear behavior using the MPM. The research can be achieved by studying two hypotheses: 1) Beam mechanics analysis using the material point method and 2) Damage mechanics analysis using the material point method. Both hypotheses consider different assumptions of the geometry and material constants. Material point simulation of the two hypotheses will be conducted through RMACC Summit Supercomputer using FORTRAN and MATLAB languages.
Open Access
Ipe: evaluation of orthotropic elastic properties and its application in roadside barriers
(Colorado State University. Libraries, 2016) Lankford, Robert, author; Heyliger, Paul, advisor; Atadero, Rebecca, committee member; Glick, Scott, committee member
Roadside barriers are the primary structural safety device on surface roads. They can be made from any material as long as they can absorb the energy involved in an impact scenario. One material that has that potential is Ipe. Ipe is a hardwood material that has relatively high strength compared to common structural woods. Despite its high strength, the 9 independent material properties for Ipe has not studied in the literature. In this paper, those material properties are determined with various tests. With the material properties, dynamic finite element analyses were done with seven different roadside barrier configurations and were then compared to the performance of the commonly used steel W-beam barrier. Ipe showed great potential with certain configurations, but with a much higher cost. Realistic implementation of Ipe in roadside barriers would be more beneficial for roads with lower speed limits, thus lowering that cost.
Open Access
Mechanics of extendable wind turbine blades
(Colorado State University. Libraries, 2015) John, Jeswin, author; Heyliger, Paul, advisor; Atadero, Rebecca, committee member; Radford, Donald, committee member
This research aims at understanding the reductions in deflection, stress, and natural frequency of extendable wind turbine blades. For that purpose, a comparative study of these properties for the extendable turbine blade compared with those of a conventional turbine blade was completed. Wind turbine blades have seen extensive growth in application, and extendable turbine blades are a novel advancement over conventional blades. They can be more efficient in extracting energy from wind and are much more practical for transportation purposes. Lengths of the turbine blade have been increasing every year, and the next logical step is to consider making them extendable. In this research, a basic model of the blade was created and then a three-dimensional linear elasticity model was used and studied using the finite element method for analyzing the crucial parameters. In addition to this, two different load cases and six different retracted blade positions were analyzed for in-depth study of the blade behavior. As far as loading is considered, an initial analysis was completed using the wind load alone to give a basic idea of how the model behaves under standard parked conditions. In the second case, both wind and dead load were considered to help understand the blade behavior from a more practical perspective. Overall, the research gives estimates of the reductions in stress, displacement, and natural frequency when the blades are extendable and gives better understanding into the design parameters of these novel structures.
Open Access
Modelling the effective properties of magneto-electro-elastic three-dimensional cellular solids
(Colorado State University. Libraries, 2020) Kannan, Sandhya, author; Heyliger, Paul, advisor; Chen, Suren, committee member; Puttlitz, Christian, committee member
Cellular solid foams are increasingly used in various industries right from disposable coffee cups to crash padding of an aircraft cockpit. Hence it is important to understand the structure and properties of cellular solids and the ways their properties can be utilized in engineering design. Using the method of Finite Element analysis three-dimensional cellular solids made up of Magneto-Electro-Elastic (MEE) materials were studied. A FORTRAN code was written to implement the models in order to determine the effective mechanical properties for the solid under study. Computational model was created and properties such as elastic, piezoelectric and piezomagnetic and permittivity were studied as a function of relative density. Result obtained for purely elastic properties were plotted against the relative density. Different thickness of the three-dimensional foam under consideration was studied by varying the Poisson's ratio. The obtained results of the jack packed cellular foam analysis gave a similar behavior of other foam structures thus verifying the accuracy of the model.
Open Access
Natural frequencies of twisted cables: a numerical and experimental study
(Colorado State University. Libraries, 2021) Alkharisi, Mohammed K., author; Heyliger, Paul, advisor; van de Lindt, John, committee member; Chen, Suren, committee member; Stright, Lisa, committee member
As the uses of cables have increased in different engineering applications, a better understating of their mechanical and dynamical behavior becomes more critical. Over the past several decades, many analytical, experimental, and finite element models have been developed to investigate vibrations of the cable structure. This attention explains the importance of such a structure, where it is more challenging than many ordinary structures because of the nonlinearity of the geometry and other combined effects. In addition, the twist along cable length leads to coupling behavior on the various kinematic variables of the cable system. This work is aimed at predicting and investigating the natural frequencies and the translations and rotations mode shapes occurring stimulatingly for both horizontal and inclined sagged cables, using both numerical and experimental methods. An efficient numerical procedure using elasticity-based finite elements is presented to generate the primary elastic stiffness coefficients of single-layered six-wire strands where the cables are subjected to axial and torsional loads in three-dimensional space. Cable models with lay angles varying from 5 to 30 degrees are then compared to eight different one-dimensional analytical models for the same range of angles. The finite element model gives stiffness coefficients that are in good agreement with the analytical models for angles below the maximum angle of the cable. The free vibration behavior of untwisted and twisted cables is then analyzed using the derived stiffness and mass matrices. When discretized over the horizontal span, the sagged cable is represented using transformed axial, coupling, and torsional characteristics where the resulting two-node cable element has three translational and three rotational degrees of freedom. A similar computational approach is used for inclined cables using inclination angles from 10 to 60 degrees. The natural frequencies and modal shapes are found to be in very good agreement in comparison with the results obtained using extensive experimental tests for identical cable geometries and materials. Where a harmonically time-varying support motion is employed, undergo different conditions. The acceleration and angular velocity time histories are then collected by sensors mounted on the mid and quarter span of the cables. In addition to the experimental results, the frequency spectrum and the translational and rotational mode shapes are analyzed and compared with the limited analytical model available from the literature and the computer finite element software ABAQUS. Practical examples are used to demonstrate the validity and applicability of the finite element model for untwisted and twisted cables. Then, the influence of the principal and microstructural parameters variation on the dynamics of the cable is investigated. This study shows that the elasticity, twist coupling, initial sag, inclination angle, and self-weight of the cable play a considerable role in the frequency and modal coupling behavior. It further suggests that some of the simple models available may not be adequate to fully understand the significant levels of modal coupling in the cable's dynamic behavior. The methods used in this study are finally extended to experimentally find the internal damping ratios and the reduction in the in-plane peak motions when a damper is used.
Open Access
Nonlinear free vibration of beams by one-dimensional and elasticity solutions
(Colorado State University. Libraries, 2018) Asiri, Abdullah N., author; Heyliger, Paul, advisor; Chen, Suren, committee member; O’Reilly, Mike, committee member
In this research, linear and nonlinear free vibration are examined. A three-dimensional rectangular parallelepiped free–free beam is studied based on the Ritz method. The equation of motion is derived depending on Hamilton's principle. A validation of the Ritz method formulation has been conducted by comparison with the Euler–Bernoulli beam theory. The impact of three-dimensional beam length has been investigated as well. In terms of nonlinear analysis, a two-dimensional clamped–clamped beam was studied. Total Lagrange formulation is adopted for the elasticity method based on the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. The outcomes of the approximated method have been compared by using the nonlinear Euler–Bernoulli theory depending on the Hermite and Lagrange interpolations. The solutions of both theories are computed according to the direct iteration method. Poisson's ratio effect is studied with two assumptions, as well as the impact of the Gauss evaluations.
Open Access
Numerical and experimental evaluation of the erodibility of particle packings with surface treatments and spring reinforcements using the discrete element method
(Colorado State University. Libraries, 2019) Peterson, Kirsten LaRhea, author; Heyliger, Paul, advisor; Bareither, Christopher, advisor; Atadero, Rebecca, committee member; Kampf, Stephanie, committee member
Chapter 4. The erodibility of homogeneous two-dimensional spherical particle packings subjected to added mass surface treatments was explored using a combination of physical flume experiments and the discrete element method (DEM). Packings composed of spherical glass particles, with and without surface treatments and angled at two different slopes, were tested experimentally and simulated numerically under surficial flow conditions. The surface treatments acted to add mass to the surface of the particle packings. Particle erosion was quantified by tracking eroded particles as a function of fluid velocity. DEM simulations and flume experiments were first performed with a layer of steel particles that served as an extreme case of surface treatment. Similar trends were observed between the simulations and experiments, whereby the number of eroded particles decreased by an average of 90% when compared to untreated cases. The results from this surface treatment suggested that if the surface treatment mass is large enough, nearly all particle erosion under surficial flow conditions can be mitigated. Additional experiments were performed with surface treatments composed of increasing application rates of wetted agricultural straw. The particle erosion rates were dominated by piecewise linear behavior as a function of eroded mass versus fluid velocity. This behavior indicated a) an initial resistance to flow based on gravity, followed by b) a surface treatment movement that induced widespread failure or erosion at a much higher rate. Dislodgement and subsequent erosion of particles occurred at higher fluid velocities (over 50% higher for the highest straw application rate) when the surface treated cases were compared to the untreated cases. Conclusions drawn from the simulation and experiment results indicated a direct correlation between added mass on the surface of a particle packing and decreased erosion under surficial flow conditions and showed that as slope increased, erosion levels increased and began at lower surficial flow fluid velocities. Chapter 5. The erodibility of three-dimensional particle packings reinforced numerically with elastic springs and subjected to overland flow conditions was explored using the discrete element method (DEM). Particle packings at three slopes, subjected to overland flow at two fluid velocities, and four reinforcement configurations resulted in a total of 24 datasets of simulation results for comparisons to be made. The three slopes were composed of the same 2400 particles with coarse sand material properties and a uniform distribution of diameters between 1.8 and 8.0 millimeters. The elastic spring reinforcements represent a potential modeling technique for root development in a soil. The spring reinforcement technique presented here is a proof-of-concept attempt to model three-dimensional slopes at up-scaled particle sizes, root stiffness, and fluid velocities. Particle displacements were tracked and compared as functions of time, reinforcement level, and slope. The results suggest linear relationships between decreased particle movement with increased percent reinforced surface particles, increased particle movement with increased slope, and decreased sediment yields with increased percent reinforced surface particles. Also, at the lower fluid velocity, particle displacements were more dependent on incremental changes in slope; whereas at the higher fluid velocity, particle displacements were not dependent on small changes in slope. Overall, the results from the simulations and experiments showed the influence of elastic spring reinforcements on particle movements and the next step of the research would be to assess the scaling effects and apply the root model to smaller particles, more indicative of where roots are expected to grow.
Open Access
Numerical simulations of binary mixtures under gravity deposition using the discrete element method
(Colorado State University. Libraries, 2021) Jiang, Chao, author; Heyliger, Paul, advisor; Bareither, Christopher, committee member; Ellingwood, Bruce R., committee member; Venayagamoorthy, Karan, committee member; McGilvray, Kirk, committee member
Binary granular mixtures are frequently used in manufacturing, geotechnical engineering, and construction. Applications for these materials include dams, roads, and railway embankments. The mixing process requires dealing with particles with varying sizes and properties, and the complex composite nature of these mixtures can bring unpredictable results in overall performance. At present, there are no specifications for mixing these materials that can be used to quantify the levels of mixing and give estimates of the overall bulk properties. In this study, the Discrete Element Method (DEM) is used to examine the mechanics of the mixing process and give guidelines on how to achieve a well-mixed aggregate. A comprehensive non-linear visco-elastic damping collision model was developed to better represent the interactions between two dissimilar particles. A general Hertz model was applied for describing the normal force but a refined non-linear spring model was generated to imitate the friction force behavior without having to consider the entire loading history. A transition zone revealing the interactions between static and dynamic friction forces was shown in our numerical results. A moment resistance model was also added to capture the behavior of particle surface asperities and the damping force was calculated using relative motion. An alternative condition was applied to determine the end of a collision. Excellent agreement was found with well-established benchmark solutions and new results are also provided for future comparisons. Using this new DEM model, the mixing process of binary unbonded particles was studied using the effects of the number and position of geometric mixing obstacles and the number of mixing iterations. It was found that the mixing degree can be best quantified by measuring the spatial variation of the volume ratio φv. It was also found that small adjustments in the geometric position of the mixing obstacles could have a significant impact on the final mixing parameters. Surprisingly, the results indicate that two mixing iterations provided almost identical levels of mixing regardless of the number and nature of mixing obstacles. Estimates of the bulk elastic constants were provided and showed a high level of anisotropy as measured by the Poisson ratios for the horizontal versus vertical planes of the control volume. Particle crushing is a typical characteristic of many granular materials and can influence the mixing process, and it is possible to model non-particulate materials by bonding individual spheres together. The particle interactions and possibly impact with mixing barriers can result in the fracture of these solids as the allowable bond strength is exceeded. Therefore, the strength of the bond between individual particles that can be part of the mixing process is a critical parameter. The parallel bond model of Potyondy and Cundall (2004) was extended with the present DEM model was used to study the effects of bond strength on the mixing and mechanical properties of binary mixtures. Three types of particle blocks were studied for this purpose: unbonded, weakly bonded, and strongly bonded particles. The bonded particles result in a wider range of reflection angles as the particles interact with geometric mixers and simultaneously change and improve the level of mixing. Overall, these simulations serve to established specific guidelines and provide a basis for field-level mixing operations. They also provide some levels of expectation for the final mixing and bulk elastic behavior for the final aggregates.
Open Access
One-dimensional effective continuum mechanics models of braided and trapezoidal wires
(Colorado State University. Libraries, 2017) Alkharisi, Mohammed K., author; Heyliger, Paul, advisor; Chen, Suren, committee member; Weinberger, Chris, committee member
As the use of wires in different engineering applications increases, investigation into and better understanding of the wire's behavior become more important. Over the past years, heavy work has been done to study the mechanical and dynamical behavior of wires using analytical, experimental, and finite element models. This attention explains the importance of such a structure. However, studying such a structure is more challenging than with other ordinary structures, due to the nonlinearity of the geometry. In this work, the axial elastic behavior was studied using linear three-dimensional finite element Fortran 77 code. The wire was discretized, element matrices were built, and varying boundary conditions were applied to find the four elastic coefficients of the global matrix: pure tensile stiffness, two coupling terms between the tensile and torsional stiffness. Couple action appears when there is a twist in the wire, for that varying twist angles (0°, 5°, 10°, 15°, 20°, 25°, and 30°) were used to check their effect on the stiffness. To validate the model used, a simple straight wire rope (1+6) of known behavior was tested using same approach and twist angles, and then compared with 7 existing analytical models available in literature. Results showed a good agreement with the finite element model, which indicates that the approach used to solve for the trapezoidal wire was reliable and valid. The results showed that the trapezoidal wire is stiffer than the simple straight wire rope and exhibited extensional and torsional coupling behavior values, which can be critical in the design process of these structures. This model can also be used to decrease the high costs associated with experimental tests needed to determine its behavior. The method was extended, as, to evaluate the integrity of such a structure, it was essential to conduct a free vibration analysis using a one-dimensional finite element approximation for the trapezoidal wire as well as for the simple straight wire rope, which had not been done before, to investigate the extensional and torsional behavior of the motion of these wires. First, an aluminum straight bar was tested by solving the mass and stiffness matrices using 2-, 4-, 8-, and 16-element approximations, and the convergence was checked against the known exact axial and torsional frequency solutions. The 16-element approximation was applied to both the trapezoidal and the simple straight wire rope with all the lay angles considered. The coupled extensional and torsional vibration for these wires was solved using closed-form equations for the mass matrices; with these and the stiffness matrices constructed, the eigenproblem was solved to find the frequencies and the corresponding mode shapes. The two types of displacement, axial and torsional, were found in each frequency while having coupled stiffness. The simple straight wire rope behaved similarly to the trapezoidal wire, but with relatively lower frequencies. Which conclude that it is important to the design, safety, and monitoring, depending on the application for which these wires are used, that the coupled frequencies suggested be considered and studied carefully.
Open Access
Stresses and frequency shifts in fully extended and folded wind turbine blades
(Colorado State University. Libraries, 2017) Abdalrwaf, Wael, author; Heyliger, Paul, advisor; Radford, Donald, committee member; Atadero, Rebecca, committee member
Alternative methods for generating energy have grown in the application in the past few decades. The main objective of this research is to understand the changes in the displacements, stresses, and natural frequencies of fully extended and folded wind turbine blades. A comparative study of the folded blade of fitted properties with the fully extended wind turbine blade was achieved. Folded blades could be more efficient in generating electricity from the wind for turbines with small radii and could be beneficial for transportation purposes. In this study, a basic model of fully extended and folded blades was completed using three-dimensional linear elasticity model and the finite element method. Two different load cases were analyzed to study the conventional and folded blade behaviors. By using the wind load alone, an initial analysis is achieved as the wind load is applied to observe the blade behavior under standard conditions. For more practical consideration, both wind and gravity load were then applied. The study estimates the changes in stresses, displacements, and natural frequencies when the blades are folded and helps better understanding the necessary design parameters of these structures. Finally, free vibration behavior of the folded and extended blades is considered.
Open Access
Structural health monitoring MEMS sensors using elasticity-based beam vibrations
(Colorado State University. Libraries, 2012) Plankis, Alivia, author; Heyliger, Paul, advisor; Atadero, Rebecca, committee member; Leisure, Robert, committee member
The worsening problem of aging and deficient infrastructure in this nation and across the world has demonstrated the need for an improved system to monitor and maintain these structures. The field of structural health monitoring has grown in recent years to address this issue. The goal of this field is to continually monitor the condition of a structure to detect and mitigate damage that may occur. Many structural health monitoring methods have been developed and most of these require sensor systems to collect the necessary information to assess the current strength and integrity of a structure. The motivation for this thesis is a proposed new microelectromechanical systems (MEMS) sensor with applications in civil infrastructure sensing. The work required was to determine accurate estimates of the resonant frequencies for a fixed-fixed silicon bridge within the device so that further testing and development could proceed. Additional knowledge and information were essential, though, before these requested calculations could be performed confidently. First, a thorough review of current structural health monitoring concepts and methods was performed to better understand the field in which this device would be applied and what incentive existed to develop a new sensor. Second, an in-depth investigation of vibrational beam mechanics theories was completed to ensure the accuracy of the frequency results for the new MEMS sensor. This study analyzed the influence of three assumptions employed in the Euler-Bernoulli, Rayleigh, and Timoshenko beam theories by comparing their results to a three-dimensional, elasticity-based approximation for vibrational frequencies and mode shapes. The results of this study showed that all three theories are insufficient when a fixed support is involved, so the elasticity-based approximation was utilized to calculate the frequencies for the bridge component in the MEMS device. These results have been passed on to the developers so that the testing process could move forward in the hopes that the device could advance the field of structural health monitoring in the future.
Open Access
The impact of non-local elasticity factors on natural frequencies of a rectangular cantilever beam
(Colorado State University. Libraries, 2020) Bouzaid, Ibrahim F., author; Heyliger, Paul, advisor; Chen, Suren, committee member; Weinberger, Chris, committee member
The natural frequencies of a structural element are important factors in attaining a safe design. Natural frequency is the frequency at which an element tends to vibrate in the absence of any driving or damping force. When an object vibrates at a frequency equivalent to its natural frequency, its vibration amplitude increases significantly, which could lead to severe damage. A safe design would thus require having a different natural frequency compared to the frequency of the vibrating element. In some cases, obtaining accurate natural frequencies is challenging. In cases in which non-local elasticity, where the stress at a point is a function of the strain at the close region around that point, provides a better solution to the mechanical problems compared to other theories, natural frequencies should be studied. The non-local elastic solution to the non-local elastic natural frequencies of a rectangular cantilever beam problem was developed using a Fortran code, and the finite elements of non-local mesh were generated using a MATLAB code. The eigenvalue problem was solved, and the mode shapes were plotted using another MATLAB code. The results indicate that the natural frequencies for the non-local solution have dropped 25–30 percent. The non-local factors, mesh size, and slenderness influenced the drop in the natural frequencies. The non-local natural frequencies tended to match the local natural frequencies up to the third frequency, then start diverged. The mode shapes are similar to the local elastic mode shapes in all cases.
Open Access
The mechanics of plastic-aluminum composite I-beams
(Colorado State University. Libraries, 2014) Peterson, Kirsten LaRhea, author; Heyliger, Paul, advisor; Atadero, Rebecca, committee member; Leisure, Robert, committee member
This thesis presents an initial investigation of the mechanics of I-beams developed with plastic-aluminum composite technology. Plastic-aluminum composites in structural beam/frame/truss elements are a relatively new concept that has seen little, if any, application in modern construction. This technology has considerable potential to add innovative choices to the array of materials currently available in the construction industry. Several new tests were designed and performed on different portions of the beams, including Push-Through and Knit-Line Pull tests, and tensile tests per ASTM D638-10. The results of these tests showed increased strength with an increase of talc filler content and also showed that the addition of a metal deactivator additive to the plastic results in a slight increase in strength. Duration of Load tests were performed per ASTM D7031-04 and none of the beams tested exhibit tertiary creep. The I-beams investigated here use an internal shear connector (deboss) which acts as a mechanical fastener between the aluminum and the flange plastic. A numerical finite element model was developed in ABAQUS to better understand the underlying physics of the deboss and was compared with a Push-Through test specimen. The results from the model closely match experimental results and the model can be used to predict within 10% the load per deboss region that can be resisted before the plastic begins to yield and extensively deform. This model can be used for differing deboss geometries and any plastic with known material properties. Overall, the results of this research support potential future research involving a more in-depth investigation of this innovative, new class of material technology for use as a structural material.
Open Access
Three-dimensional elasticity models for buckling of anisotropic and auxetic beams and plates
(Colorado State University. Libraries, 2015) Hamad, Eltigani, author; Heyliger, Paul, advisor; Atadero, Rebecca, committee member; Puttlitz, Christian, committee member
The three-dimensional elasticity model is developed to determine the critical buckling load for isotropic, anisotropic, and auxetic beams and plates. Different beam theories are studied and compared to the elasticity theory. The study was based on the assessment of those beam theories using different beam cross-sections and boundary conditions. The elasticity theory for anisotropic beams obtained well results for large slenderness ratios when it compared with Euler-Bernoulli theory which is considered in this study the main area of comparison study. For small values of slenderness ratio the elasticity theory obtained significant difference than the Euler-Bernoulli theory, which means that Euler-Bernoulli is weaker when it is used for short beams than long beams. The orientation of the anisotropy behavior is also studied and has showed how the buckling load can be changed due to the orientation of the elasticity modulus. The auxetic beams behave differently than the anisotropic behavior, it gives results higher and lower than the Euler-Bernoulli theory according to the slenderness ratio and the Poisson’s ratio values. A significant behavior was noticed in using beams with negative Poisson’s the ratio which can be useful in structure mechanics field.