Dual reciprocity hybrid boundary node method for free vibration analysis

As a truly meshless method of boundary-type, the hybrid boundary node method (HBNM) has the advantages of both boundary element method (BEM) and meshless method. The main problem is that it is only suitable for the homogeneous problems. Now, the dual reciprocity method (DRM) is introduced into HBNM to deal with the integral for the inhomogeneous terms of the governing equations, and the rigid body motion approach is employed to solve the hyper-singular integrations. A new meshless method named dual reciprocity hybrid boundary node method (DRHBNM) is proposed and applied to solve free vibration problems. In this method, the solution composes into two parts, i.e., the general solution and the particular solution. The general solution is solved by HBNM and the particular one is obtained by DRM. DRHBNM is a true boundary-type meshless method. It does not require the ‘boundary element mesh’, either for the purpose of interpolation of the variables, or for the integration of ‘energy’. The points in the domain are only used to interpolate particular solution by the radial basis function. Finally, the boundary variables are interpolated by the independent smooth boundary segments. The Q–R algorithm and Householder algorithm are applied to solve the eigenvalues and eigenvectors of the transformed matrix. cal examples for free vibration problems show that a good convergence with mesh refinement is achievable and the computational results for the natural circular frequencies and free vibration modes are very accurate. Furthermore, the computation parameters have little influence on the results and can be chosen in a wide range. It is shown that the present method is effective and can be widely applied in practical engineering.