Abstract
In this work, the topology optimization method using the solid isotropic material with penalization (SIMP) approach is employed to find the optimum design of piezoelectric actuators taking into account the excitation of the residual vibration modes. The structure governing equations are written into the state-space representation and the controllability Gramian eigenvalues are used to measure how the residual modes are susceptible to be excited by the control system. The proposed optimization formulation aims to find the distribution of piezoelectric material which maximizes the controllability for a given vibration mode while the undesirable effects of the feedback control on the residual modes are limited by including a spillover constraint term written as a p-norm of the residual controllability Gramian eigenvalues. The optimization of the shape and placement of the embedded piezoelectric actuators are carried out using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented for the control of the first bending vibration mode of a cantilever beam varying the set of residual modes considered in the spillover norm.
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