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Geometrically Nonlinear Transverse Vibrations of Discrete Multi-Degrees of Freedom Systems with a Localised Non-Linearity

A. Eddanguir, Z. Beidouri, R. Benamar

Abstract


The purpose of this paper is to extend the method developed, for the solution of the problem of transverse nonlinear vibration of 2-dof systems to N-dof systems, with localized non-linearity. It is to recall that this method is based on the principle of Hamilton and spectral analysis. The method has been successfully used previously to solve the problem of nonlinear vibrations of beams, rectangular and circular plates and shells. The mass tensor, the linear and nonlinear rigidity tensors are expressed in both the displacement basis, denoted in what follows as DB, and the modal basis, denoted as MB. The application of the method to N-dof systems is then developed in the MB. To show the validity and the consistence of this approach, a 5-dof non symmetric system with a localised non-linearity has been treated.

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