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

Abstract

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.

Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

“…Besides the dynamical modeling and dynamical properties of beam structures with complex boundary conditions [19], the dynamical modeling and dynamical properties of plate structures [20][21][22][23][24], shell structures [25][26][27][28][29][30][31], and other types of structures [32][33][34] with complex boundary conditions have also been investigated [35][36][37][38][39]. For example, Xue et al [20] developed and solved a dynamics model for medium-thick composite laminates with arbitrary boundary conditions based on Mindlin's theory, Hamilton's principle, a modified Fourier series method, and the spring technique, with parametric studies on the effects of several key parameters, such as thickness-to-width ratio, number of plies, and lay-up angle between two plies.…”

Modelagem matemática e computacional de interação fluido-estrutura com elementos de casca curvilíneos tridimensionais

“…Modelos para geometrias cilíndricas e esféricas, como tubos, domos e arcos, são apresentados nos trabalhos de Chung (1980), Belytschko et al (1985a), Belytschko (1986) e Han et al (2020). Modelagens para geometrias arbitrárias, segundo diversas teorias e elementos de casca, são desenvolvidas nos trabalhos de Ahmad (1969), Olson e Lindberg (1971), Bathe (1986), Saetta e Vitaliani (1990), Basu e Ghosh (1993), e Bischoff et al (2004).…”