Matching Items (5)
Filtering by
- All Subjects: Structural Dynamics
- Creators: Mignolet, Marc P
- Creators: Liu, Yongming
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 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
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
Description
Over the past few decades there has been significant interest in the design and construction of hypersonic vehicles. Such vehicles exhibit strongly coupled aerodynamics, acoustics, heat transfer, and structural deformations, which can take significant computational efforts to simulate using standard finite element and computational fluid dynamics techniques. This situation has lead to development of various reduced order modelling (ROM) methods which reduce the parameter space of these simulations so they can be run more quickly. The planned hypersonic vehicles will be constructed by assembling a series of sub-structures, such as panels and stiffeners, that will be welded together creating built-up structures.In this light, the focus of the present investigation is on the formulation and validation of nonlinear reduced order models (NLROMs) of built-up structures that include nonlinear geometric effects induced by the large loads/large response. Moreover, it is recognized that gaps between sub-structures could result from the these intense loadings can thus the inclusion of the nonlinearity introduced by contact separation will also be addressed. These efforts, application to built-up structures and inclusion of contact nonlinearity, represent novel developments of existing NLROM strategies. A hat stiffened panel is selected as a representative example of built-up structure and a compact NRLOM is successfully constructed for this structure which exhibited a potential internal resonance. For the investigation of contact nonlinearity, two structural models were used: a cantilevered beam which can contact several stops and an overlapping plate model which can exhibit the opening/closing of a gap. Successful NLROMs were constructed for these structures with the basis for the plate model determined as a two-step process, i.e., considering the plate without gap first and then enriching the corresponding basis to account for opening of the gap. Adaptions were then successfully made to a Newton-Raphson solver to properly account for contact and the associated forces in static predictions by NLROMs.
ContributorsWainwright, Bret Aaron (Author) / Mignolet, Marc P (Thesis advisor) / Oswald, Jay (Committee member) / Peralta, Pedro (Committee member) / Spottswood, Stephen (Committee member) / Rajan, Subramaniam (Committee member) / Arizona State University (Publisher)
Created2021