Nonlinear vibration suppression of laminated composite conical shells on elastic foundations with magnetostrictive layers

Abstract

Abstract Nonlinear vibration control of laminated composite conical shells surrounded by elastic foundations through magnetostrictive layers is presented in this paper. The shell modeled via the consideration of the effects of shear deformation and rotary inertia while von Karman theory of nonlinearity is also employed. In order to suppress the nonlinear vibration, velocity feedback control method is adopted. Modified Galerkin method is exerted to obtain the nonlinear ordinary differential equation of the system from equations obtained via Hamilton principle. The results of this study are acquired with a combination of modal analysis and multiple scales method. The asymptotical stability of the system around zero equilibrium point is investigated based on Lyapunov’s indirect method. The results for damping coefficients of nonlinear system and fundamental linear frequency as well as the curves of amplitude versus nonlinear frequency and nonlinear frequency ratio are obtained for different values of several parameters.