Engineering, characterization, identification and reduced order modeling of systems with softening nonlinearities

Mojahed, Alireza

Permalink

https://hdl.handle.net/2142/112984 Copy

Description

Title

Engineering, characterization, identification and reduced order modeling of systems with softening nonlinearities

Author(s)

Mojahed, Alireza

Issue Date

2021-07-07

Director of Research (if dissertation) or Advisor (if thesis)

• Vakakis, Alexander F
• Bergman, Lawrence A

Doctoral Committee Chair(s)

Vakakis, Alexander F

Committee Member(s)

• Tawfick, Sameh H
• Wissa, Aimy

Department of Study

Mechanical Sci & Engineering

Discipline

Theoretical & Applied Mechans

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Nonlinear dynamics
• Geometric nonlinearity
• Softening nonlinearity
• Hardening nonlinearity
• Reduced-order modeling.

Abstract

Reduced-order modeling, whether statistical, physics-based, or phenomenological, is a primary component in nearly every field of science where prediction and close investigation of certain features and phenomena are concerned. The study of dynamical and oscillating mechanical systems is no exception, due to its importance in many industrial settings. Dynamical and oscillating mechanical systems are typically categorized into linear and nonlinear; the former being more convenient to study due to well-developed supporting theories, whereas the latter being often difficult to explore due to their complicated responses. However, it has been shown that, for instance, in vibration mitigation applications, nonlinear dynamical systems can yield improved performance compared to their linear counterparts. Accordingly, the first part of this thesis focuses on theoretical and experimental modeling and characterization of a new type of softening-hardening nonlinear springs. This can be successfully employed as vibration mitigation devices owning to a rather unique tunability feature. For instance, being capable of softening or hardening behavior, i.e., possessing decreasing or increasing stiffness, respectively, with increasing deformation. It will be shown that by exploiting the softening nature of such nonlinear element, one can increase the dissipative capacity of a structure that should not undergo large deformation. The second part of the thesis focuses on creating a nonlinear reduced-order computational model of the dynamics of the human brain; more specifically, the white matter tissue of the human brain. This is of great significance since traumatic brain injury (TBI) is often associated with tissue damage in the brain originating from its complex biomechanical behavior. This model is employed to first, identify possible connections between TBI and the nonlinear dynamics of the deep white matter of the human brain, and second, to explore the features of a helmet that minimizes strain in the damage-prone regions of the human brain. The final part of the thesis discusses the concept of “bandwidth”, a feature of oscillatory systems that is often overlooked due to the lack of a rigorous framework for its definition and understanding, especially when nonlinear systems are concerned. To this end, the concept of bandwidth is generalized to include nonlinear oscillatory systems, and it is shown that depending on their nonlinear characteristics they can possess a lower or higher bandwidth compared to the linear case. This results in breaking of the so-called classical time-bandwidth limit, which states that the bandwidth of a single degree of freedom (SDOF) linear time-invariant (LTI) system is the inverse of the duration that it can store energy; moreover, the break of the time-bandwidth limit in the nonlinear case can be accomplished in a way that is tunable with energy, i.e., the intensity of the applied excitation; these assertions are confirmed by theoretical and experimental studies. This key result opens the possibility of conceiving broadband and simultaneously low-loss wave-storage devices (a feature that is impossible in LTI SDOF systems), with applications such as clinical diagnostics, nanoparticle (and virus) detection and manipulation, etc. In the process of this research the lack of an accurate, robust, data-driven and versatile harmonic decomposition technique was noticed. This led to the development of a new data-driven harmonic decomposition method based on the numerical inversion of the continuous wavelet transform, without the limitation (mainly mode-mixing) of the current mode decomposition methods. The efficacy of this method in data-driven modeling of linear and nonlinear systems is demonstrated, but its capacity goes beyond the study of dynamical systems in areas such as audio analysis imaging, video processing, and structural health monitoring.

Graduation Semester

2021-08

Type of Resource

Thesis

Permalink

http://hdl.handle.net/2142/112984

Copyright and License Information

© 2021 Alireza Mojahed

Owning Collections