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<p>Low-frequency vibration suppression remains a critical challenge for lightweight double-beam systems in engineering applications. In this paper, we propose a novel inertial amplification metastructure double beam (IAMDB) and develop an energy-based semi-analytical framework to characterize its band structure and vibration transmissibility. To ensure accurate dispersion predictions, Bloch periodic boundary conditions are enforced via an improved Lagrange multiplier method. The proposed model is validated against Finite Element Method (FEM) simulations, demonstrating high accuracy. Wave propagation analysis reveals uncoupled in-plane and out-of-plane waves, alongside distinct in-phase and anti-phase modes. Results indicate that anti-phase bandgaps exhibit significantly stronger and broader attenuation than in-phase bandgaps. Notably, the two modes become indistinguishable when the IA angle is <i>π</i>/4. Parametric studies show that increasing the number of IA levels and additional mass shifts bandgaps to lower frequencies and broadens bandwidths, whereas larger IA angles tend to degrade low-frequency attenuation. To address the challenge of optimizing within an intricate design space characterized by mixed discrete and continuous variables, a surrogate-assisted mixed-integer simulated annealing (SAMI-SA) algorithm is specifically implemented. Optimization results confirm that the optimized IAMDB significantly enhances low-frequency attenuation and expands usable bandgaps, indicating strong potential for practical vibration control applications in double-beam structures.</p>

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Optimization design of inertial amplification metastructure double beams for low-frequency and broadband vibration suppression

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Yonghang Sun,
  • Yong Pang,
  • Jun Li,
  • Lei Zhang,
  • Xueguan Song

摘要

Low-frequency vibration suppression remains a critical challenge for lightweight double-beam systems in engineering applications. In this paper, we propose a novel inertial amplification metastructure double beam (IAMDB) and develop an energy-based semi-analytical framework to characterize its band structure and vibration transmissibility. To ensure accurate dispersion predictions, Bloch periodic boundary conditions are enforced via an improved Lagrange multiplier method. The proposed model is validated against Finite Element Method (FEM) simulations, demonstrating high accuracy. Wave propagation analysis reveals uncoupled in-plane and out-of-plane waves, alongside distinct in-phase and anti-phase modes. Results indicate that anti-phase bandgaps exhibit significantly stronger and broader attenuation than in-phase bandgaps. Notably, the two modes become indistinguishable when the IA angle is π/4. Parametric studies show that increasing the number of IA levels and additional mass shifts bandgaps to lower frequencies and broadens bandwidths, whereas larger IA angles tend to degrade low-frequency attenuation. To address the challenge of optimizing within an intricate design space characterized by mixed discrete and continuous variables, a surrogate-assisted mixed-integer simulated annealing (SAMI-SA) algorithm is specifically implemented. Optimization results confirm that the optimized IAMDB significantly enhances low-frequency attenuation and expands usable bandgaps, indicating strong potential for practical vibration control applications in double-beam structures.