Vibration analysis of rotating cross-ply laminated cylindrical, conical and spherical shells by using weak-form differential quadrature method

In this article, the weak-form differential quadrature method is adopted to analyze the vibration characteristics of rotating laminated thin shells with arbitrary boundary conditions. Firstly, based on the Reissner–Naghdi’s linear shell theory, the energy expression of rotating laminated cylindrical, conical and spherical shells is established. The arbitrary boundary conditions are simulated equivalently by introducing the boundary spring. According to the energy method, the numerical differentiation and numerical integration techniques of the differential quadrature method are combined into the Ritz method, where the admissible function is not introduced in the whole solution process, so to obtain the displacement of any point in the element, it is necessary to use the polynomial to approximate the admissible function of shell. In this paper, the Lagrangian interpolation polynomials are used. The correctness of the current solution model is fully proved by a series of numerical examples. On this basis, the vibration characteristics of rotating cross-ply laminated cylindrical, conical and spherical shells under elastic boundary conditions are further studied.