A NEW SYMMETRIC AND POSITIVE DEFINITE BOUNDARY ELEMENT FORMULATION FOR LATERAL VIBRATIONS OF PLATES

Abstract

A new symmetric and positive definite boundary element method in the time domain is presented for the dynamic analysis of thin elastic plates. The governing equations of the problem are obtained from a variational principle in which a hybrid modified functional is employed. The functional is expressed in terms of the domain and boundary basic variables in plate bending, assumed to be independent of each other. In the discretized model the boundary variables are expressed by nodal values, whereas the internal displacement field is modelled by a superposition of static fundamental solutions. The equations of motion are deduced from the functional stationarity conditions and they constitute a linear system of ordinary differential equations expressed in terms of nodal displacements. The structural operators are frequency independent and preserve the symmetry and definiteness properties of the continuum. Moreover these operators are calculated by performing boundary integrations of regular kernels only. Some applications to free vibrations and self-excited vibrations under aerodynamic loads have been worked out to test the accuracy of the proposed method. The numerical results have been found in very good agreement with those obtained by using other solution techniques by which the accuracy of the present boundary element model is demonstrated.