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This paper examines the effect of viscoelasticity on the periodic response of a lumped parameter viscoelastic von Mises truss. The viscoelastic system is described by a second-order equation that governs the mechanical motion coupled to a first-order equation that governs the time evolution of the viscoelastic forces. The viscoelastic force evolves at a much slower rate than the elastic oscillations in the system. This adds additional time scales and degrees of freedom to the system compared to its viscous counterparts. The focus of this study is on the system’s behavior under harmonic loading, which is expected to show both regular and chaotic dynamics for certain combinations of forcing frequency and amplitude. While the presence of chaos in this system has already been demonstrated, we shall concentrate only on the periodic solutions. The presence of the intrawell and interwell periodic oscillations is revealed using the Harmonic Balance method. The study also looks at the influence of parameter changes on the system’s behavior through bifurcation diagrams, which enable us to identify optimal system parameters for maximum energy dissipation. Lastly, we formulate an equivalent viscous system using an energy-based approach. We observe that a naive viscous model fails to capture the behavior accurately depending on the system and excitation parameters, as well as the type of excitation. This underscores the necessity to study the full-scale viscoelastic system.
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Model calibration of locally nonlinear dynamical systems: Extended constitutive relation error with multi-harmonic coefficients
Purpose This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process. Design/methodology/approach The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters. Findings When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system. Originality/value This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.
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- Award ID(s):
- 1633608
- PAR ID:
- 10341182
- Date Published:
- Journal Name:
- Engineering Computations
- Volume:
- 36
- Issue:
- 2
- ISSN:
- 0264-4401
- Page Range / eLocation ID:
- 466 to 490
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1108/EC-10-2017-0419
