Free vibration analysis of non-axisymmetric and axisymmetric structures by the dual reciprocity BEM
The dual reciprocity boundary element method (DR/BEM) is employed for the free vibration analysis of three-dimensional non-axisymmetric and axisymmetric elastic solids. The method uses the elastostatic fundamental solution in the integral formulation of elastodynamics and as a result of that, an inertial volume integral is created in addition to the boundary ones. This volume integral is transformed into a surface integral by invoking the reciprocal theorem and expanding of the displacement field into a series involving seven different approximation functions. The approximation functions used are local radial basis functions (RBFs) and are applied in combination (or not) with global basis functions (augmentation). All these functions are compared in terms of the accuracy they provide. The axisymmetric case is efficiently treated with the aid of the fast Fourier transform (FFT) algorithm in order to provide even non-axisymmetric vibration modes. Two representative numerical examples involving the determination of natural frequencies and modal shapes of an elastic cube and an elastic cylinder serve to investigate in detail the potentiality of each of the seven approximation functions tested to provide results of high accuracy and to reach useful practical conclusions.
free vibrations dual reciprocity boundary elements elastodynamics radial basis functions augmentation fast fourier transform natural frequencies modal shapes three-dimensional solids axisymmetric solids