Frontiers in Built Environment (Sep 2018)
A Meshless Solution to the Vibration Problem of Cylindrical Shell Panels
Abstract
The Meshless Analog Equation Method (MAEM) is a purely mesh-free method for solving partial differential equations (PDEs). In the present study, the method is applied to the dynamic analysis of cylindrical shell structures. Based on the principle of the analog equation, MAEM converts the three governing partial differential equations in terms of displacements into three uncoupled substitute equations, two of 2nd order (Poisson's) and one of 4th order (biharmonic), with fictitious sources. The fictitious sources are represented by series of Radial Basis Functions (RBFs) of multiquadric (MQ) type, and the substitute equations are integrated. The integration allows the representation of the displacements by new RBFs, which approximate the displacements accurately and also their derivatives involved in the governing equations. By inserting the approximate solution in the governing differential equations and taking into account the boundary and initial conditions and collocating at a predefined set of mesh-free nodal points, we obtain a system of ordinary differential equations of motion. The solution of the system gives the unknown time-dependent series coefficients and the solution to the original problem. Several shell panels are analyzed using the method, and the numerical results demonstrate its efficiency and accuracy.
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