Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


2018_MS_Thesis_BAG_final.pdf (5.44 MB)

ETD Abstract Container

Abstract Header

Analytical Modeling and Impedance Characterization of Nonlinear, Steady-State Structural Dynamics in Thermomechanical Loading Environments

Goodpaster, Benjamin A.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1524063139635613

Abstract Details

2018, Master of Science, Ohio State University, Mechanical Engineering.
This research advances the state-of-the-art of analytical techniques to study the steady-state nonlinear dynamics of multi-degree-of-freedom, multistable structures subjected to harmonic excitations. A recently formulated analytical methodology, validated by numerical and experimental evidence, has been shown to accurately predict the steady-state dynamics of a discrete, multistable structure. Yet, the analysis is limited to lumped-parameter systems and cannot account for multiphysics phenomena, such as thermomechanical effects. Additionally, the analysis is challenged by an inefficient solution procedure, since the completeness of the dynamic predictions is highly dependent upon the generation of initial conditions. This research develops an enhanced solution procedure and normalization scheme to rectify these limitations, providing a robust and efficient analytical tool in the process. The analytical formulation is then extended to encompass distributed-parameter structures that exhibit global nonlinear coupling among all degrees-of-freedom in a form typical of reduced order models. In the process, assumptions inherent to traditional analyses, such as considering only single-degree-of-freedom systems or systems exhibiting weak nonlinear response, are overcome. Comparisons between the analytical and computational results indicate that the generalized analysis accurately characterizes the nonlinear dynamics of such multistable structures at speeds over two orders of magnitude faster than numerical simulation. Furthermore, the analysis is extended to encompass two-way coupling between thermal and mechanical domains, overcoming limitations of previous thermomechanical analyses. The thermomechanical analysis is capable of predicting the pre- and post-buckled nonlinear dynamics of a distributed-parameter beam model, the efficacy of which is verified with experimental evidence. In the process of developing these advancements to the analytical formulation, the analysis is leveraged to deliver significant, new insight into various aspects of nonlinear structural dynamics. The normalized analytical procedure enables the application of standard modal analysis techniques to structures that exhibit nonlinear deformation. A built-up structure of linearly coupled Duffing oscillators is studied, through which it is revealed that the characteristic displacement response of a single bistable Duffing oscillator is preserved in the higher degree-of-freedom composition by way of the fundamental equivalent nonlinear mode. The thermomechanical analysis is utilized in order to newly characterize the impedance of a distributed parameter structure exhibiting nonlinear dynamics. Furthermore, a measure of thermomechanical impedance that relates the temperature gradient to the velocity response of a structure is proposed and characterized. Both mechanical and thermomechanical impedances are observed to exhibit distinguishing trends that may be utilized to forecast dynamic bifurcations that have various positive or negative ramifications based on the application. All together, the results of this research may be used to study the nonlinear steady-state dynamics of a broad range of multi-degree-of-freedom structures undergoing harmonic excitations in thermomechanical loading environments.
Ryan Harne (Advisor)
Jack McNamara (Committee Member)
78 p.
Mechanical Engineering; Mechanics
analysis; nonlinear dynamics; thermomechanical coupling; multi-degree-of-freedom structure; impedance; mechanical impedance; thermomechanical impedance; dynamic bifurcation; snap-through; lumped-parameter; distributed-parameter; equivalent linearization;

Recommended Citations

Citations

  • Goodpaster, B. A. (2018). Analytical Modeling and Impedance Characterization of Nonlinear, Steady-State Structural Dynamics in Thermomechanical Loading Environments [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524063139635613

    APA Style (7th edition)

  • Goodpaster, Benjamin. Analytical Modeling and Impedance Characterization of Nonlinear, Steady-State Structural Dynamics in Thermomechanical Loading Environments. 2018. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1524063139635613.

    MLA Style (8th edition)

  • Goodpaster, Benjamin. "Analytical Modeling and Impedance Characterization of Nonlinear, Steady-State Structural Dynamics in Thermomechanical Loading Environments." Master's thesis, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524063139635613

    Chicago Manual of Style (17th edition)

osu1524063139635613
446
© 2018, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.