Bifurcation and Nonlinear Dynamic Analysis of a Moving Viscoelastic Sandwich Beam under Parametric Excitation
In this paper, transverse vibrations of an axially accelerated viscoelastic sandwich beam subjected to principal parametric resonances resulting from harmonically varying tension and velocity simultaneously in the presence of 3:1 internal resonance between first two modes are investigated. Applying the direct method of multiple scales to the governing equation, the Eigen functions and natural frequency of the system are obtained and a set of first-order ordinary differential equations and associated boundary conditions are derived. Considering the solvability condition, the frequency response and their stability and bifurcation are studied. Different equilibrium solutions curves are numerically simulated from the modulated differential equation which helps to investigate various types of bifurcations such as saddle node bifurcation, sub-critical and super-critical Hopf and pitchfork bifurcations. Keywords - Axially Accelerating Viscoelastic Sandwich Beam, Internal Resonance, Parametric Resonance, Bifurcation, Stability.