Analysis of Free and Forced Vibrations Problems Using the Dual Reciprocity Boundary Element Method Based on Inverse Multiquadric Radial Basis Functions

This paper presents a new boundary element formulation for free and forced vibration analysis of 2D elastic domains. The main idea of the present formulation is to approximate the inertia terms using the inverse multiquadric radial basis functions (IMQ RBFs). The dual reciprocity method (DRM) with the static-type fundamental solution is reconsidered by using the proposed RBFs. The fictitious particular solution kernels of inverse multiquadric RBFs corresponding to displacement and traction, a few terms of which are singular, are explicitly derived. Therefore, a simple mathematical trick is employed to resolve the singularity problem. In addition, the limiting values of the particular solution kernels are evaluated. Several examples are studied to demonstrate the validity and the accuracy of the proposed formulation. The results are compared to the obtained analytical and other RBFs available in the literature.