Vibration Analysis of Geometrically Nonlinear and Fractional Viscoelastic Cantilever Beams

Anomalous Nonlinear Dynamics Behavior of Fractional Viscoelastic Structures

Fractional models and their parameters are sensitive to changes in the intrinsic micro-structures of anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of mechanical systems. In particular, we analyze the vibration of a fractional, geometrically nonlinear viscoelastic cantilever beam, under base excitation and free vibration, where the viscoelastic response is general through a distributed-order fractional model. We employ Hamilton's principle to obtain the corresponding equation of motion with the choice of …

非线性弹性杆中快速和慢动态的研究

Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations

本文提出描述此类材料纵向振动的物理模型，并开发数值策略求解演化方程，通过耦合不同时间尺度的过程来研究材料动态特性。

抽象动态问题的时间离散化与能量守恒及其在固体力学中的应用

Energy-conserving time-discretisation of abstract dynamic problems with applications in continuum mechanics of solids

本文提出了一种时间离散化方法，用于保持能量守恒，应用于固体力学中的振动和波传播问题，包括粘弹性材料的小应变情况及塑性、损伤等非弹性过程。

A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations

We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases like $\exp(-cN/\log(N))$ for $N$ quadrature points. The method is parallisable, avoids having to resolve singularities of the solution as $t\downarrow 0$, and avoids the large memory consumption that can be a challenge for time-stepping methods applied to time-fractional PDEs. The ODEs resulting from quadrature are solved using adaptive sparse spectral methods…

High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to large amplitude vibrations and uncovering of a folding point

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that the technique is directly applicable to problems discretised by the finite element method. Two nonlinear mappings, respectively related to displacement and velocity, are introduced, and the link between the two is made explicit at arbitrary order of expansion. The same development is performed on the reduced-order dynamics which is computed at generic order f…