Abstract
Free and forced flexural vibrations of homogeneous, isotropic and linear elastic Kirchhoff plates and plate systems are studied numerically. The conventional direct boundary element method, which employs the dynamic fundamental solution of the problem, and the direct domain/boundary element method, which employs the static fundamental solution of the problem are employed in both the time and the frequency domain. The former is essentially associated with boundary integrals only, while the latter with boundary as well as domain integrals accommodating the inertia terms. Thus, while only a boundary discretization is necessary in the former method, a boundary as well as an interior discretization is required in the latter one. However, the latter method deals with a much simpler fundamental solution and is computationally more efficient. Transient forced vibrations are treated with the aid of a time marching scheme in the time domain or Laplace transform with respect to time, in which case a numerical inversion of the transformed solution is required to obtain the time domain response. The effect of external viscous damping or internal viscoelastic damping as well as of in-plane forces on the response is also studied. Various numerical examples are presented for illustrating the two aforementioned boundary element approaches and comparisons against the finite element method are also made to demonstrate their merits.
Published Version
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