The Adjustable Bandgap of Novel Local Resonance Sandwich-Like Metamaterial Plates with Buckling Beam Oscillators

Abstract

Sandwich structures possess a high stiffness-to-mass ratio, which facilitates flexural wave propagation at lower frequencies and enhances their vibration isolation and sound insulation capabilities, therefore, sandwich-like metamaterial plates with the nonlinear local oscillator is constructed in this paper to obtain adjustable bandgap in low-frequency. The buckling beam oscillator consists of a small mass, linear support spring, and buckling elastic elements for nonlinear stiffness. First, governing equations of flexural vibrations of plates are deduced based on the Hamilton principle. By utilizing the harmonic balance method (HBM), the dispersion relation of a sandwich-like plate can be determined. Theoretical analysis reveals the presence of structural bandgap ranges at lower frequencies, which are subject to the excitation amplitudes. And in order to validate the theoretical findings, the finite element method (FEM) is employed. Moreover, the influence of structural parameters, including oscillator mass, linear spring stiffness, buckling beam angle, and Young’s modulus, are conducted to enhance the vibration control in the low-frequency. Interestingly, it is observed that the effectiveness of low-frequency suppression in the nonlinear metamaterial plate varies significantly across different boundary conditions. Therefore, the sandwich structures with nonlinear local oscillators can provide an effective way to suppress low-frequency vibration and maintain dynamic stability.