Topology Optimization for Minimizing the Resonant Response of Plates with Constrained Layer Damping Treatment

Abstract

A topology optimization method is proposed to minimize the resonant response of plates with constrained layer damping (CLD) treatment under specified broadband harmonic excitations. The topology optimization problem is formulated and the square of displacement resonant response in frequency domain at the specified point is considered as the objective function. Two sensitivity analysis methods are investigated and discussed. The derivative of modal damp ratio is not considered in the conventional sensitivity analysis method. An improved sensitivity analysis method considering the derivative of modal damp ratio is developed to improve the computational accuracy of the sensitivity. The evolutionary structural optimization (ESO) method is used to search the optimal layout of CLD material on plates. Numerical examples and experimental results show that the optimal layout of CLD treatment on the plate from the proposed topology optimization using the conventional sensitivity analysis or the improved sensitivity analysis can reduce the displacement resonant response. However, the optimization method using the improved sensitivity analysis can produce a higher modal damping ratio than that using the conventional sensitivity analysis and develop a smaller displacement resonant response.

A Comparative Study on Acoustic Optimization and Analysis of CLD/Plate in a Cavity Using ESO and GA

“…The locations number of CLD treatments is initialized in a random integer vector as individuals (design variables) in GA. Due to symmetry of the flexible plate, nine and eighteen variables are defined using locations number of CLD material for 25% and 50% rejection ratios and nine variables are defined using locations number at which the CLD materials are not bonded for 75% rejection ratios. As an example shown in Figure 11, for 25%, 50%, and 75% rejection ratios, the individuals are constructed as [1,2,3,10,17,20,23,32,33], [2,4,9,10,12,13,14,15,16,20,22,23,25,28,29,30,32,34], and [1,3,6,15,21,24,26,31,36], respectively.…”

“…In topology optimization study for CLD structures, the positions of CLD materials are usually considered as design variables while a specific thickness of CLD materials is defined, such as that in [8,9,11,14,17]. To the authors' knowledge, the influences on topology optimization results induced by the thickness of CLD materials are quite less.…”

“…Li et al [8] studied topology optimization problem for vibration reduction of flexible plate treated with CLD, in which evolutionary structural optimization (ESO) method is used to minimize structural modal damping ratios. Fang and Zheng [9] employed moving asymptote (MMA) method to obtain optimal layouts of CLD material on base structure subjected to harmonic excitations or stationary random excitations, in which the solid isotropic material with penalization (SIMP) method was adopted to interpolate the constrained layer damping material.…”

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

“…An experimental verification of these works has also been reported [20]. Fang and Zheng [21] studied the effect of modal sensitivity analysis on optimization of the damping material. Moreover, TO has been further extended to transient response optimization [22] and mode shape optimization [23,24].…”

Random Vibration Suppression of a Truss Core Sandwich Panel Using Independent Modal Resonant Shunt and Modal Criterion

“…The benefit of this character is that morphing of the solid face sheet can be realized by replacing some rods in the back-plane planar truss with in-plane tension-compression actuators. While for panel-like structures, constrained layer damping [17] is usually used for passive damping and a piezoelectric patch [18] is often utilized for active damping, the character of a Kagome structure can be exploited for passive/active controls by replacing a small portion of the rods in the planar Kagome truss with in-plane dampers [19] or actuators [20], which will not destroy the planeness of the face sheet. In this study, the rods in the planar truss are replaced by piezoelectric transducers to convert the mechanical energy to electric energy, which is dissipated by the resistance.…”