Multi material design reduces vibration by shifting structure frequencies
Multi-Material Topology Optimization for Targeted Structural Dynamic Vibration Attenuation
Computational Engineering, Finance, and Science
Summary
Too much shaking can harm machines and buildings, especially when vibrations match their natural frequencies. The authors show how to design structures using different materials arranged carefully to move these natural frequencies away from troublesome vibration speeds. They use smart math techniques to find the best material layout that reduces shaking without sudden optimization problems. Their approach compares different ways to shift or separate these vibration frequencies, helping make designs that last longer and work better.
What this means in practice
- •For structural engineers: Design structures that avoid harmful vibration levels by optimizing material layout and selection to shift natural frequencies away from excitation frequencies.
- •For mechanical design teams: Improve machine reliability by tailoring multi-material components to reduce resonance-related vibrations through optimized dynamic properties.
Authors
Bir Bahadur Chaudhary, Bidhan Pandey, Bin Ouyang, Shiguang Deng
Abstract
Resonance-induced excessive vibrations can degrade performance, reduce reliability, and shorten the service life of engineering structures. To reduce the risk of resonance, structural natural frequencies are generally engineered to be shifted away from excitation frequencies. To achieve these frequency shifts, topology optimization provides a systematic approach to tailor structural stiffness and mass as an effective inverse design approach. Multi-material topology optimization exploits the high-dimensional design space of spatially varying material constituents by simultaneously optimizing material selection and spatial distribution over the design domain, offering great flexibility in controlling natural frequencies. This study proposes a multi-material topology optimization that attenuates excessive structural dynamic vibrations in free-vibration scenarios via a novel multivariate weight-based interpolation method. Additionally, to address non-smoothness due to mode switching amid optimization, we employ a bound formulation with an auxiliary scalar design variable to replace the max-min eigenvalue objective with constraints on individual eigenvalues. Furthermore, we study and compare three optimization formulations for multi-material design to attenuate vibrations, including maximizing fundamental eigenfrequency, maximizing the gap between adjacent eigenfrequencies, and excluding frequencies from targeted frequency bands, which are smoothly approximated by a proposed rational polynomial formulation. Numerical examples are presented to demonstrate the effectiveness and applicability of our proposed method.