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Dynamic analyses of plane frames by integral equations for bars and Timoshenko beams by H. Antes; M. Schanz; S. Alvermann is a Engineering article available to read on EtoBox.

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Since, especially for higher frequencies, Timoshenko's theory gives more reliable results than Euler–Bernoulli's theory, systems of beams, like frames, under arbitrary dynamic excitations should be analyzed on the basis of this refined theory. In this paper, after deriving the basic fundamental solutions of a lateral unit point force and of a unit single moment, the deflection and the rotation of the beam cross-section are given as integral equation forms of the governing second order differential equation system in the Laplace and the frequency domain. Since in frameworks axial displacements also occur, the well-known integral equations for bars under tension or compression are added to complete the modelling of plane frame structures. From these, the unknown boundary values may be exactly determined via point collocation at the beam ends and solution of the resulting algebraic system. With these boundary values, the exact deflection and rotation can also be found at arbitrary interior points. Finally, the convolution quadrature method is applied to the Laplace domain integral equation formulation in order to analyze the time-dependent wave propagation process. Two examples are pr

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Author

H. Antes; M. Schanz; S. Alvermann

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-460X)

Published

2004

Language

EN

Field

Engineering (Physical Sciences)