Vibration suppression using integrated topology optimization of host structures and damping layers

Abstract

It is often desirable to simultaneously optimize the damping and stiffness distribution in the design of shell structures incorporating damping material layers for achieving the best vibration mitigation performance. This paper investigates the integrated topology optimization of host structures and damping layers for reducing the vibration level in the presence of harmonic excitations. Therein, the global damping matrix is a nonproportional one due to distributed damping effects. For an efficient frequency response analysis of the system with nonproportional damping, reduced-order equations are obtained by using lower-order eigenvectors of the undamped system, and then the method of complex mode superposition is employed for solving the dynamic equations in the state space. In the optimization model, the vibration amplitudes at specified positions are taken as the objective function. The relative densities of the elements are considered as design variables, and an artificial damping material model relating the local damping properties to the elemental density variables is employed. The Rational Approximation of Material Properties model is adopted to avoid localized modes in low-density areas during the optimization process. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed framework.