Vibration and nonlinear dynamic response of temperature-dependent FG-CNTRC laminated double curved shallow shell with positive and negative Poisson’s ratio

Abstract

This paper reports a study on natural frequency, nonlinear dynamic response and frequency amplitude relation of temperature-dependent FG-CNTRC laminated double curved shallow shell with positive and negative Poisson’s ratio. The nonlinear motion equations and the compatibility equation are retrieved from first order shear deformation theory including the effect of von Karman nonlinearity terms, elastic foundations and initial imperfection. The system of dynamic governing equations is obtained by utilizing the Airy stress function and Bubnov–Galerkin procedure. The nonlinear dynamic response is also obtained by applying the 4th-order Runge–Kutta method. The frequency–amplitude relations of the shell is determined by using the assumption of inertia caused by a rotation. Besides, the analytical method and the finite element method are proposed to calculate the vibrational frequencies. Five types of FG-CNTRC laminate shell, three types of the structures and different thermal environments with the shell’s material properties depending on the temperature are also considered in this study. The numerical results are presented, verified with available studies in the literature. Finally, the effects of elastic foundations, initial imperfection, and temperature-dependence, typing double curved shallow shell, angle of lamination against the shell x-axis on the natural frequency and nonlinear dynamic response of FG-CNTRC laminated double curved shallow shell with positive and negative Poisson’s ratio are discussed.