A Meshless Solution to the Vibration Problem of Cylindrical Shell Panels - Yiotis, Aristophanes J.; Katsikadelis, John T. (Frontiers in Built Environment, 2018)
Abstract. The MAEM (Meshless Analog Equation Method), a purely mesh-free method, is applied to the dynamic analysis of cylindrical shell panels. The method is based on the principle of the analog equation, which converts the three governing partial differential equations in terms of displacements into three uncoupled substitute equations, two of second order and one of fourth order, with fictitious sources. The fictitious sources are represented by series of RBFs (Radial Basis Functions) of MQ (multiquadric) type and the substitute equations are integrated. This integration allows the representation of the displacements by new RBFs, which approximate accurately not only the displacements but also their derivatives involved in the governing equations. Then, inserting the approximate solution in the governing differential equations as well as in the associated boundary and initial conditions and collocating at a predefined set of mesh-free nodal points, a system of ordinary differential equations of motion results, the solution of which gives the unknown time dependent series coefficients and thus the displacements. The method is illustrated by analyzing several shell panels. The studied examples demonstrate the efficiency and the accuracy of the presented method. Keywords: Meshless Analog Equation Method (MAEM), Dynamic Analysis, Cylindrical Shells, Radial Basis Functions (RBFs), Partial Differential Equations.