Modeling and Simulation of Optimal Vibrations Control Problems by the Finite Element Method

W. Szyszkowski and M. Baweja (Canada)


Optimal vibration control, finite elements


The governing equations of the problem of optimal control of structural vibrations are transformed to a set of the 4th order ordinary differential equations in the time domain. The equations decouple in the modal space and become suitable for handling by the finite element method technique with the time domain subdivided into 'finite time' elements of class 1 C to secure continuity of the nodal positions and velocities. It is demonstrated that the standard beam element with cubic Hermitian interpolation functions, routinely used in a static analysis of beams, can conveniently be substituted for the required 'finite time' element. The use of such equivalent beam elements to solve the problems of active optimal vibration control of elastic structures is discussed in detail. A simple example illustrates the method.

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