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Description
The computation of the fundamental mode in structural moment frames provides valuable insight into the physical response of the frame to dynamic or time-varying loads. In standard practice, it is not necessary to solve for all n mode shapes in a structural system; it is therefore practical to limit the system to some determined number of r significant mode shapes. Current building codes, such as the American Society of Civil Engineers (ASCE), require certain class of structures to obtain 90% effective mass participation as a way to estimate the accuracy of a solution for base shear motion. A parametric study was performed from the collected data obtained by the analysis of a large number of framed structures. The purpose of this study was the development of rules for the required number of r significant modes to meet the ASCE code requirements. The study was based on the implementation of an algorithm and a computer program developed in the past. The algorithm is based on Householders Transformations, QR Factorization, and Inverse Iteration and it extracts a requested s (s<< n) number of predominate mode shapes and periods. Only the first r (r < s) of these modes are accurate. To verify the accuracy of the algorithm a variety of building frames have been analyzed using the commercially available structural software (RISA 3D) as a benchmark. The salient features of the algorithm are presented briefly in this study.
ContributorsGrantham, Jonathan (Author) / Fafitis, Apostolos (Thesis advisor) / Attard, Thomas (Committee member) / Houston, Sandra (Committee member) / Hjelmstad, Keith (Committee member) / Arizona State University (Publisher)
Created2014
Description
As more and more stadia structures nowadays are being built by making use of new high strength building materials which tend to be lighter than the "old" ones, composite systems and also the fact that engineers, contractors and clients want their structures as optimized as possible, in terms of minimal materials used, there is an inevitable side effect that comes with this. The result is that structures are more flexible, and thus they become susceptible to undergone vibration problems due to the action of dynamic loading. Pop/rock concerts, exhibitions, boxing matches, and so forth are staged to supplement the football/sport seasons. Consequently, stadia structures must resist not only static loading, but also dynamic loading, such as the human induced loads from various activities of the spectators which include, standing, jumping, stamping, clapping and dancing, particularly in response to touchdowns (in football matches) or musical beats (during concerts). Active and passive models of humans are studied to see how they influence the response in TCF Bank Stadium for different ranges in excitation frequencies, by performing dynamic analyses and comparing the results with the ones obtained from static analysis. Parameter estimation and system identification in mechanical sciences and structural engineering have become increasingly important areas of research in the last three decades. Many nondestructive testing methods are based on the concepts of system identification and parameter estimation. In this document, two parameter estimation algorithms are studied, namely the Equation Error Estimator and the Output Error Estimator, through the simulation of modal data obtained from a computer structural analysis program and comparisons of their results are presented so that future researchers are better informed about the two and therefore can decide which one would give the best results for their application.
ContributorsAldaco Lopez, Manuel (Author) / Hjelmstad, Keith D. (Thesis advisor) / Rajan, Subramaniam D. (Committee member) / Fafitis, Apostolos (Committee member) / Arizona State University (Publisher)
Created2014
Description
Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) of the F-16 have provided good support to the long-standing hypothesis that this phenomenon involves a nonlinear structural damping. A potential mechanism for the appearance of nonlinearity in the damping are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is first on extending nonlinear reduced order modeling (ROM) methods to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An identification approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software.
The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.
The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.
ContributorsSong, Pengchao (Author) / Mignolet, Marc P (Thesis advisor) / Chattopadhyay, Aditi (Committee member) / Oswald, Jay (Committee member) / Arizona State University (Publisher)
Created2015
Description
This paper addresses some aspects of the development of fully coupled thermal-structural reduced order modeling of planned hypersonic vehicles. A general framework for the construction of the structural and thermal basis is presented and demonstrated on a representative panel considered in prior investigations. The thermal reduced order model is first developed using basis functions derived from appropriate conduction eigenvalue problems. The modal amplitudes are the solution of the governing equation, which is nonlinear due to the presence of radiation and temperature dependent capacitance and conductance matrices, and the predicted displacement field is validated using published data. A structural reduced order model was developed by first selecting normal modes of the system and then constructing associated dual modes for the capturing of nonlinear inplane displacements. This isothermal model was validated by comparison with full finite element results (Nastran) in static and dynamic loading environments. The coupling of this nonlinear structural reduced order model with the thermal reduced order model is next considered. Displacement-induced thermal modes are constructed in order to account for the effect that structural deflections will have on the thermal problem. This coupling also requires the enrichment of the structural basis to model the elastic deformations that may be produced consistently with the thermal reduced order model. The validation of the combined structural-thermal reduced order model is carried out with pure mechanical loads, pure thermal loads, and combined mechanical-thermal excitations. Such comparisons are performed here on static solutions with temperature increases up to 2200F and pressures up to 3 psi for which the maximum displacements are of the order of 3 thicknesses. The reduced order model predicted results agree well with the full order finite element predictions in all of these various cases. A fully coupled analysis was performed in which the solution of the structural-thermal-aerodynamic reduced order model was carried out for 300 seconds and validated against a full order model. Finally, a reduced order model of a thin, aluminum beam is extended to include linear variations with local temperature of the elasticity tensor and coefficients of thermal expansion.
ContributorsMatney, Andrew (Author) / Mignolet, Marc P (Thesis advisor) / Arizona State University (Publisher)
Created2014
Description
This thesis focuses on the continued extension, validation, and application of combined thermal-structural reduced order models for nonlinear geometric problems. The first part of the thesis focuses on the determination of the temperature distribution and structural response induced by an oscillating flux on the top surface of a flat panel. This flux is introduced here as a simplified representation of the thermal effects of an oscillating shock on a panel of a supersonic/hypersonic vehicle. Accordingly, a random acoustic excitation is also considered to act on the panel and the level of the thermo-acoustic excitation is assumed to be large enough to induce a nonlinear geometric response of the panel. Both temperature distribution and structural response are determined using recently proposed reduced order models and a complete one way, thermal-structural, coupling is enforced. A steady-state analysis of the thermal problem is first carried out that is then utilized in the structural reduced order model governing equations with and without the acoustic excitation. A detailed validation of the reduced order models is carried out by comparison with a few full finite element (Nastran) computations. The computational expedience of the reduced order models allows a detailed parametric study of the response as a function of the frequency of the oscillating flux. The nature of the corresponding structural ROM equations is seen to be of a Mathieu-type with Duffing nonlinearity (originating from the nonlinear geometric effects) with external harmonic excitation (associated with the thermal moments terms on the panel). A dominant resonance is observed and explained. The second part of the thesis is focused on extending the formulation of the combined thermal-structural reduced order modeling method to include temperature dependent structural properties, more specifically of the elasticity tensor and the coefficient of thermal expansion. These properties were assumed to vary linearly with local temperature and it was found that the linear stiffness coefficients and the "thermal moment" terms then are cubic functions of the temperature generalized coordinates while the quadratic and cubic stiffness coefficients were only linear functions of these coordinates. A first validation of this reduced order modeling strategy was successfully carried out.
ContributorsMatney, Andrew (Author) / Mignolet, Marc (Thesis advisor) / Jiang, Hanqing (Committee member) / Spottswood, Stephen (Committee member) / Arizona State University (Publisher)
Created2011
Description
This investigation focuses on the development of uncertainty modeling methods applicable to both the structural and thermal models of heated structures as part of an effort to enable the design under uncertainty of hypersonic vehicles. The maximum entropy-based nonparametric stochastic modeling approach is used within the context of coupled structural-thermal Reduced Order Models (ROMs). Not only does this strategy allow for a computationally efficient generation of samples of the structural and thermal responses but the maximum entropy approach allows to introduce both aleatoric and some epistemic uncertainty into the system.
While the nonparametric approach has a long history of applications to structural models, the present investigation was the first one to consider it for the heat conduction problem. In this process, it was recognized that the nonparametric approach had to be modified to maintain the localization of the temperature near the heat source, which was successfully achieved.
The introduction of uncertainty in coupled structural-thermal ROMs of heated structures was addressed next. It was first recognized that the structural stiffness coefficients (linear, quadratic, and cubic) and the parameters quantifying the effects of the temperature distribution on the structural response can be regrouped into a matrix that is symmetric and positive definite. The nonparametric approach was then applied to this matrix allowing the assessment of the effects of uncertainty on the resulting temperature distributions and structural response.
The third part of this document focuses on introducing uncertainty using the Maximum Entropy Method at the level of finite element by randomizing elemental matrices, for instance, elemental stiffness, mass and conductance matrices. This approach brings some epistemic uncertainty not present in the parametric approach (e.g., by randomizing the elasticity tensor) while retaining more local character than the operation in ROM level.
The last part of this document focuses on the development of “reduced ROMs” (RROMs) which are reduced order models with small bases constructed in a data-driven process from a “full” ROM with a much larger basis. The development of the RROM methodology is motivated by the desire to optimally reduce the computational cost especially in multi-physics situations where a lack of prior understanding/knowledge of the solution typically leads to the selection of ROM bases that are excessively broad to ensure the necessary accuracy in representing the response. It is additionally emphasized that the ROM reduction process can be carried out adaptively, i.e., differently over different ranges of loading conditions.
While the nonparametric approach has a long history of applications to structural models, the present investigation was the first one to consider it for the heat conduction problem. In this process, it was recognized that the nonparametric approach had to be modified to maintain the localization of the temperature near the heat source, which was successfully achieved.
The introduction of uncertainty in coupled structural-thermal ROMs of heated structures was addressed next. It was first recognized that the structural stiffness coefficients (linear, quadratic, and cubic) and the parameters quantifying the effects of the temperature distribution on the structural response can be regrouped into a matrix that is symmetric and positive definite. The nonparametric approach was then applied to this matrix allowing the assessment of the effects of uncertainty on the resulting temperature distributions and structural response.
The third part of this document focuses on introducing uncertainty using the Maximum Entropy Method at the level of finite element by randomizing elemental matrices, for instance, elemental stiffness, mass and conductance matrices. This approach brings some epistemic uncertainty not present in the parametric approach (e.g., by randomizing the elasticity tensor) while retaining more local character than the operation in ROM level.
The last part of this document focuses on the development of “reduced ROMs” (RROMs) which are reduced order models with small bases constructed in a data-driven process from a “full” ROM with a much larger basis. The development of the RROM methodology is motivated by the desire to optimally reduce the computational cost especially in multi-physics situations where a lack of prior understanding/knowledge of the solution typically leads to the selection of ROM bases that are excessively broad to ensure the necessary accuracy in representing the response. It is additionally emphasized that the ROM reduction process can be carried out adaptively, i.e., differently over different ranges of loading conditions.
ContributorsSong, Pengchao (Author) / Mignolet, Marc P (Thesis advisor) / Smarslok, Benjamin (Committee member) / Chattopadhyay, Aditi (Committee member) / Liu, Yongming (Committee member) / Jiang, Hanqing (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2019
Description
Mistuning is defined as the blade-to-blade variation of bladed disks caused by slight changes in material or geometric properties; mistuned blades can cause significant increases in vibrational response. The primary goal of this thesis is to describe the relationship between coupling index and amplification factors of mistuned bladed disks with various sets of parameters, targeting the veering zone. At around a coupling index of 0, the amplification factors tend to stay around 1. This is due to localization of energy, where no energy is "shared" between blades, and the response of mistuned blades remain at resonance. As coupling index increases, amplification factors reach a peak between coupling indices of 0.15 and 0.2, before experiencing a downward trend towards 1. As blade-to-disk interaction increases, more energy is "shared" across blades. This results in the upward trend of amplification factor as coupling index increases, until too much energy is "shared". Additionally, a reduced order model enriching-stripping process to match natural frequencies of Nastran simulations will be discussed. This thesis is a continuation of Saurav Sahoo's Master's thesis at Arizona State University, Approximate a-priori Estimation of the Response Amplification due to Geometric and Young's Modulus Mistuning.
ContributorsLiu, Gavin (Author) / Mignolet, Marc (Thesis director) / Murthy, Raghavendra (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The present investigation is part of a long-term effort focused on the development of a methodology for the computationally efficient prediction of the dynamic response of structures with multiple joints. The first part of this thesis reports on the dynamic response of nominally identical beams with a single lap joint (“Brake-Reuss” beam). The observed impact responses at different levels clearly demonstrate the occurrence of both micro- and macro-slip, which are reflected by increased damping and a lowering of natural frequencies. Significant beam-to-beam variability of impact responses is also observed.
Based on these experimental results, a deterministic 4-parameter Iwan model of the joint was developed. These parameters were randomized following a previous investigation. The randomness in the impact response predicted from this uncertain model was assessed in a Monte Carlo format through a series of time integrations of the response and found to be consistent with the experimental results.
The availability of an uncertain computational model for the Brake-Reuss beam provides a starting point to analyze and model the response of multi-joint structures in the presence of uncertainty/variability. To this end, a 4-beam frame was designed that is composed of three identical Brake-Reuss beams and a fourth, stretched one. The response of that structure to impact was computed and several cases were identified.
The presence of uncertainty implies that an exact prediction of the response of a particular frame cannot be achieved. Rather, the response can only be predicted to lie within a band reflecting the level of uncertainty. In this perspective, the computational model adopted for the frame is only required to provide a good estimate of this uncertainty band. Equivalently, a relaxation of the model complexity, i.e., the introduction of epistemic uncertainty, can be performed as long as it does not affect significantly the uncertainty band of the predictions. Such an approach, which holds significant promise for the efficient computational of the response of structures with many uncertain joints, is assessed here by replacing some joints by linear spring elements. It is found that this simplification of the model is often acceptable at lower excitation/response levels.
Based on these experimental results, a deterministic 4-parameter Iwan model of the joint was developed. These parameters were randomized following a previous investigation. The randomness in the impact response predicted from this uncertain model was assessed in a Monte Carlo format through a series of time integrations of the response and found to be consistent with the experimental results.
The availability of an uncertain computational model for the Brake-Reuss beam provides a starting point to analyze and model the response of multi-joint structures in the presence of uncertainty/variability. To this end, a 4-beam frame was designed that is composed of three identical Brake-Reuss beams and a fourth, stretched one. The response of that structure to impact was computed and several cases were identified.
The presence of uncertainty implies that an exact prediction of the response of a particular frame cannot be achieved. Rather, the response can only be predicted to lie within a band reflecting the level of uncertainty. In this perspective, the computational model adopted for the frame is only required to provide a good estimate of this uncertainty band. Equivalently, a relaxation of the model complexity, i.e., the introduction of epistemic uncertainty, can be performed as long as it does not affect significantly the uncertainty band of the predictions. Such an approach, which holds significant promise for the efficient computational of the response of structures with many uncertain joints, is assessed here by replacing some joints by linear spring elements. It is found that this simplification of the model is often acceptable at lower excitation/response levels.
ContributorsRobertson, Brett Anthony (Author) / Mignolet, Marc P (Thesis advisor) / Brake, Matt (Committee member) / Liu, Yongming (Committee member) / Arizona State University (Publisher)
Created2016
ContributorsEvans, Bartlett R. (Conductor) / Schildkret, David (Conductor) / Glenn, Erica (Conductor) / Concert Choir (Performer) / Chamber Singers (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-16
ContributorsOwen, Ken (Conductor) / McDevitt, Mandy L. M. (Performer) / Larson, Brook (Conductor) / Wang, Lin-Yu (Performer) / Jacobs, Todd (Performer) / Morehouse, Daniel (Performer) / Magers, Kristen (Performer) / DeGrow, Gary (Performer) / DeGrow, Richard (Performer) / Women's Chorus (Performer) / Sun Devil Singers (Performer) / ASU Library. Music Library (Publisher)
Created2004-03-24