Dynamic stability of viscoelastic plates under axial flow by differential quadrature method

Abstract

Purpose Cantilever plates subject to axial flow can lose stability by flutter and properties such as viscoelasticity and laminar friction affect dynamic stability. The purpose of the present study is to investigate the dynamic stability of viscoelastic cantilever plates subject to axial flow by using the differential quadrature method. Design/methodology/approach Equation of motion of the viscoelastic plate is derived by implementing Kelvin-Voigt model of viscoelasticity and applying inverse Laplace transformation. The differential quadrature method is employed to discretize the equation of motion and the boundary conditions leading to a generalized eigenvalue problem. The solution is verified using the existing results in the literature and numerical results are given for critical flow velocities Findings It is observed that higher aspect ratios lead to imaginary part of third frequency becoming negative and causing single-mode flutter instability. It was found that flutter instability does not occur at low aspect ratios. Moreover the friction coefficient is found to affect the magnitude of critical flow velocity, however, its effect on the stability behaviour is minor. Originality/value The effects of various problem parameters on the dynamic stability of a viscoelastic plate subject to axial flow were established. It was shown that laminar friction coefficient of the flowing fluid increases the critical fluid velocity and higher aspect ratios lead to single-mode flutter instability. The effect of increasing damping of viscoelastic material on the flutter instability was quantified and it was found that increasing viscoelasticity can lead to divergence instability.