Steady-State Response of Axially Moving Viscoelastic Beams With Pulsating Speed:

Abstract Principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed. A nonlinear partial-differential equation governing the transverse vibration is derived from the dynamical, constitutive, and geometrical relations. Under certain assumption, the partial-differential reduces to an integro-partialdifferential equation for transverse vibration of axially accelerating viscoelastic nonlinear beams. The method of multiple scales is applied to two equations to calculate the steady-state response. Closed form solutions for the amplitude of the vibration are derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by use of the Lyapunov linearized stability theory. Numerical examples are presented to highlight the effects of speed pulsation, viscoelascity, and nonlinearity and to compare results obtained from two equations

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Vibrations of axially travelling CNT reinforced beams with clamped-clamped boundary condition and an elastic support

Vibrational analysis in engineering systems of axially travelling beams has attracted noticeable attention due to the many applications, such as in robotic manipulators, cable tramways, textile fibres, and in general when there is the axial mass transport of a continuous structure. This article studies the vibrational response of axially-travelling, functionally-graded, carbon nanotube-(CNT)-reinforced beam structures, by investigating linear gyroscopic aspects, such as Argand diagrams. The distribution of CNT fibres is assumed to vary along the thickness of the beam. The Hamilton principle is employed to obtain the coupled axial and transverse behaviour of the beam, subjected to clamped-clamped boundary condition and additionally supported by a spring. These equations of motion are then solved using the modal decomposition technique for the Coriolis-dependent axial and transverse frequencies. For verification, the results are compared to the simplified case in the literature for CNT strengthened beams with zero axial velocity, the dynamics of axially travelling beams, studies of the clamped-clamped boundary condition, and the effects on the Argand diagrams, which have been performed. The Argand diagrams are plotted to examine the effects of varying axial speed on the different linear characteristics of vibration. Variation of the volume fraction of the CNT and the spring support, has also been considered, to understand its effects on the vibration characteristics. Results produced in this article are important in assisting in the future design of engineering devices involving axially travelling systems.Moaz Sibtain, Saxon Smith, Alireza Yeganehmehr, Oscar Zi Shao Ong, Mergen H. Ghayes