Microstructural topology optimization of viscoelastic materials for maximum modal loss factor of macrostructures

Abstract

The geometric layout and physical properties of a viscoelastic damping material have a significant influence on the damping performance of a passive constrained layer damping (PCLD) structure. This paper presents a two-scale optimization method and aims to find the optimal microstructural configuration of the viscoelastic material (i.e., the optimal effective properties of the material) with maximum modal loss factors of the macrostructures. The modal loss factor is obtained by using the Modal Strain Energy (MSE) method. The material microstructure is assumed to be homogeneous in the macro-scale, i.e., the macrostructure is composed of periodic unit cells (PUC). In the optimization formulation, the relative densities are introduced as the design variables for the material microstructure design, based upon the idea of the Solid Isotropic Material with Penalization (SIMP) method of topology optimization. The modal loss factor of the structure is assigned as the objective function. All the sensitivities of the modal loss factor with respect to the design variables are derived analytically and the optimization problem is solved by Method of Moving Asymptote (MMA) method. Several examples of the design optimization of viscoelastic cellular materials are presented to demonstrate the validity of the method. The effectiveness of the design method is illustrated by comparing a solid and an optimized cellular viscoelastic material as applied to a cantilever beam with the PCLD treatment.

Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization

“…For the nonequilibrium part, since the elastic Finger tensor b e is not known, the nonequilibrium Kirchhoff stress neq and b e have to be calculated by solving the combination of the third equality in Equation (10) and Equation (A8). This set of nonlinear equations is solved using the NR method.…”

“…Within topology optimization, many studies have investigated optimal designs with viscoelastic materials. For instance, Yi et al and Chen and Liu investigated the microstructural designs with a single viscoelastic phase for maximizing the damping effect under steady‐state vibrations. Andreassen and Jensen explored optimal microstructural designs with viscoelastic material for maximizing the attenuation of propagating waves.…”

Performance Evaluation of Five GIS-Based Models for Landslide Susceptibility Prediction and Mapping: A Case Study of Kaiyang County, China

“…The main evaluation methods include the empirical model (fuzzy logic [13][14][15], analytic hierarchy process [16][17][18][19][20][21], etc. ), statistical analysis model (weights of evidence [22][23][24][25], frequency ratio [19,[26][27][28][29], certainty factor (CF) [18,19,30], information value model [31,32], etc. ), and machine-learning models (artificial neural network [33][34][35][36], support vector machine [37][38][39], random forest [40,41], logistic regression [29,[42][43][44], etc.…”

Dynamic response optimization of structures with viscoelastic material using the equivalent static loads method

“…Meanwhile, research on structural optimization was actively performed when the periodic loading condition was applied in the frequency domain. 16–22 This is because a linear static response optimization algorithm can be employed for the periodic loading condition in the frequency domain. Lumsdaine and Scott performed shape optimization of an unconstrained viscoelastic damping layer to achieve effective vibration damping by reducing the displacement at one given frequency near resonance.…”

“…21 Chen and Liu maximized the modal loss factor via topology optimization of a microstructure at particular modes. 22…”