A nonlinear analytical formula for forced vibration analysis of the hard-coating cylindrical shell based on the strain energy density principle

Abstract

In this paper, a nonlinear analytical formulation of the forced vibration of the hard-coating cylindrical shell is developed to investigate the nonlinear resonant characteristics of the shell. The strain dependence of hard coating and the elastic constraint with continuous variable stiffness are considered in the formulation. In order to fully introduce the effects of the strain dependence of hard coating on the resonant characteristics with base excitation, a novel analytical method is presented to determine the equivalent strain of hard coating according to the principle of equal strain energy density. The nonlinear governing equations of motion and the admissible displacement function are derived based on the Love's first approximation theory and the Gram-Schmidt orthogonalization process. A unified Newton-Raphson iterative solution method is employed to solve the nonlinear resonant frequency and response of the shell. As an example to demonstrate the feasibility of the developed analytical model, the forced vibration of the cylindrical shell coated with NiCoCrAlY + YSZ hard coating is implemented numerically and experimentally. Moreover, the influences of the storage modulus, loss modulus and thickness of hard coating on the forced vibration characteristics of the hard-coating cylindrical shell are analyzed in detail.