Constrained Motion of Nonlinear Systems

概要

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The static and dynamic problems of structural and mechanical systems subjected to certain external excitations are established by a mathematical system consisting of static or dynamic equations and prescribed constraint conditions. The constrained behavior depends on the exact calculation of constraint forces required for satisfying the constraints. The generalized inverse method, which is one of many approaches to describe the constrained static or dynamic responses and takes an explicit equation form, does not require any numerical scheme to determine unknown multipliers but it was derived under the assumption of elastic systems. The static or dynamic responses beyond linearly elastic range also must satisfy the constraints themselves as well as the load-deformation relation. This study presents an analytical method to describe the constrained behavior beyond linearly elastic range, provides the mechanical meanings that the generalized inverse method has, and illustrates the validity of the proposed method through applications. And it is evaluated that the fundamental mode of dynamic system is constrained by the eigenvectors corresponding to the lowest eigenvalue of stiffness matrix at static equilibrium state.
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