Dynamic response of arbitrary double-curved shells by meridian curve digitalization - Bich, Nguyen Dang; Tung, Nguyen Hoang; Tung, Le Xuan (Vietnam Journal of Mechanics, 2023)
For the resulting equation of double-curved shells, which is formed by revolution of an arbitrary in-plane meridian curve and cannot be represented analytically, there exists no analytical approach to problem setting and solution. This paper presents the digitalization of the meridian curve in the polar coordinate system, which forms double number series. The double number series then can be approximated by an interpolation function so that calculations can be performed in a similar methodology for an explicit function. Digitalization enables the input parameters in the form of interpolation functions. Procedures for the proposed selection of solution forms, formation of the kinetic equation, and computation of coefficients for the kinetic equation from on the interpolation and explicit functions are presented in the paper. The final solution is obtained by using the program Mathematica 7.0 to solve the system of nonlinear differential equations. Assessment of the dynamic response of the double-curved shell, especially responses with chaotic motion, is also presented in the paper.