Anomalous Nonlinear Dynamics Behavior of Fractional Viscoelastic Beams
Abstract
Fractional models and their parameters are sensitive to intrinsic microstructural changes in anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of mechanical systems. In particular, we study the vibration of a fractional, geometrically nonlinear viscoelastic cantilever beam, under base excitation and free vibration, where the viscoelasticity is described by a distributed-order fractional model. We employ Hamilton's principle to obtain the equation of motion with the choice of specific material distribution functions that recover a fractional Kelvin–Voigt viscoelastic model of order α. Through spectral decomposition in space, the resulting time-fractional partial differential equation reduces to a nonlinear time-fractional ordinary differential equation, where the linear counterpart is numerically integrated through a direct L1-difference scheme. We further develop a semi-analytical scheme to solve the nonlinear system through a method of multiple scales, yielding a cubic algebraic equation in terms of the frequency. Our numerical results suggest a set of α-dependent anomalous dynamic qualities, such as far-from-equilibrium power-law decay rates, amplitude super-sensitivity at free vibration, and bifurcation in steady-state amplitude at primary resonance.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 22, 2021
- Source ID
- 10.1115/1.4052286
Entities
People
- Ehsan Kharazmi
- Jorge L. Suzuki
- Maryam Naghibolhosseini
- Mohsen Zayernouri
- Pegah Varghaei
Organizations
- Army Research Office
- Brown University
- Michigan State University
- National Institutes of Health
- National Science Foundation Directorate for Mathematical & Physical Sciences