Vibration analysis of beams using meshfree methods

In this study, deflection and free vibration of elastic thin beams are analysed by using meshfree methods point interpolation (PIM) and radial point interpolation (RPIM) methods with standard Gaussian integration and a nodal integration based on the Taylor series expansion. The effects of integration schemes, support domain sizes and RPIM shape dimensionless parameters on the deflection and free vibration modes are investigated. Their results are compared with finite element method and available analytical solutions. Beams with four different boundary conditions; two ends-clamped beam, free end-cantilever beam, simply-supported beam, and supported end-cantilever beam, are solved by linear elastic materials with uniform cross-section.