A Lumped Mass Meshfree Collocation Method with Frequency Error Estimates for Free Vibration Analysis of Elastic Solids

A meshfree collocation method with particular reference to the lumped mass formulation is presented for the free vibration analysis of elastic solids. The lumped mass formulation leads to a simple unit entry for the collocation mass matrix. With the aid of the consistency conditions of meshfree approximation, a systematic theoretical investigation is provided to measure the frequency error of lumped mass meshfree collocation analysis of elastic solids, where both the pressure and shear waves are considered in the frequency accuracy order estimation. It is proven that the lumped mass meshfree collocation method yields similar convergence rates as those given by the consistent mass formulation, i.e., for a [Formula: see text]th degree basis function, the frequency accuracy order is [Formula: see text] for even basis degree and [Formula: see text] for odd basis degree, respectively. In addition, it is shown that the lumped mass collocation approach using interpolatory meshfree shape functions is free of spurious modes. Numerical results consistently validate the proposed theoretical frequency error estimates for the free vibration analysis of elastic solids.