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.

Topology optimization of damping material for reducing resonance response based on complex dynamic compliance

“…Kang et al [18] proposed an optimization methodology based on frequency response analysis. They also extended their work to simultaneous optimization of the damping and host layers [19]. An experimental verification of these works has also been reported [20].…”

“…In addition to the maximizing the imaginary part of the dynamic compliance (abbreviated as IDC hereafter) in Eq. (13), we also minimize the amplitude of the loading point (abbreviated as AMP hereafter), which is a typical objective function in damping material optimization based on frequency response [18,19].…”

“…Of these approaches, we focus on frequency response-based optimization, which is more straightforward than the eigenfrequency-based method when the excitation frequency can be predicted. A typical objective function proposed in previous research is minimization of the amplitude of the loading domain [18,19,21]. However, in actual mechanical design, the damping material is usually used to reduce the response peak at resonance near the excitation frequency rather than the response under the specified single frequency.…”

Topology Optimization of Constrained Layer Damping Structures Subjected to Stationary Random Excitation

“…e optimization objective function is to minimize the structural vibration at specified positions, and the steady-state response of the vibrating structure is obtained by using the complex mode superposition method in the state space to deal with the nonproportional damping. Zhang and Kang [11] proposed an optimization methodology based on the frequency response analysis, and they extended their work to simultaneous optimization of the damping and host layers. Fang and Zheng [12] proposed a topology optimization method to minimize the resonant response of plates with CLD treatment at specified broadband harmonic excitations and studied the effect of the modal sensitivity analysis on optimization of the damping material.…”

Distribution Optimization of Constrained Damping Materials Covering on Typical Panels Under Random Vibration

“…However, the study was only focused on flat panel and shell, not on stiffened panels. Based on this, Zhang et al 20 proposed the integrated topology optimization of host structures and damping layers to reduce vibration levels in the presence of harmonic excitations. During the optimization process, the localized modes in low-density areas were avoided.…”