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Anomalous Nonlinear Dynamics Behavior of Fractional Viscoelastic Beams
- Source :
- J Comput Nonlinear Dyn
- Publication Year :
- 2021
- Publisher :
- American Society of Mechanical Engineers, 2021.
-
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.
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- J Comput Nonlinear Dyn
- Accession number :
- edsair.doi.dedup.....3410a8ef10bb67a2d9fdc2d0e574b34c