arXiv:2610.31996 · v2

Multi-Material Topology Optimization for Targeted Structural Dynamic Vibration Attenuation

首次提交 2026-10-23 07:34

版本更新 2026-11-12 22:38

雷达观测 2026-11-13 14:15

摘要

Resonance-induced structural vibrations can compromise the performance, reliability, and service life of engineering structures. Multi-material topology optimization (MMTO) offers a promising approach to vibration attenuation by tailoring the spatial distributions of material constituents to optimize structural stiffness, mass, and natural frequencies. However, existing eigenfrequency-based MMTO methods face several challenges, including the need for flexible interpolation of multiple material properties, non-smooth optimization objectives associated with mode switching and repeated eigenvalues, and numerical difficulties in imposing differentiable constraints to exclude natural frequencies from prescribed operating frequency ranges. To address these challenges, we propose a novel MMTO framework for structural vibration attenuation based on several innovations: (1) a novel multivariate weight-based multi-material interpolation scheme to simultaneously represent material stiffness and mass density, (2) a bound-based optimization formulation to improve the smoothness and stability of gradient-based optimization by addressing mode switching, and (3) a smooth frequency-band formulation to smoothly approximate the discontinuous Heaviside function while enabling differentiable frequency-band constraints. Additionally, we systematically investigate and compare three different topology optimization formulations for dynamic vibration attenuation, including maximizing the fundamental eigenfrequency, maximizing the gap between adjacent eigenfrequencies, and excluding natural frequencies from prescribed frequency bands. Furthermore, we present the detailed derivation of analytical design sensitivities for the three formulations.