Band-gap characteristics of elastic metamaterial plate with axial rod core by the finite element and spectral element hybrid method

Abstract

A new kind of elastic metamaterial plate is designed to control the vibration and elastic wave propagation based on the band-gap mechanism. For the proposed elastic metamaterial plate, local resonant rods are periodically distributed between the two cover plates of the metamaterial plate structure. The dynamic stiffness matrix and the frequency response function of the structure under the time-harmonic excitation are obtained by the finite element and spectral element hybrid method (FE-SEHM). The experiment and simulation validations have been carried out. The effects of the material and structural parameters on the band-gap characteristics are analyzed. It is shown that the band-gaps can be computed more accurately and efficiently based on the FE-SEHM to avoid confusion between the pass-bands and band-gaps. Three band-gaps of the elastic metamaterial plate appear near the odd-order natural frequencies of the local resonant rods. Increasing the damping and mass of the local resonant rods results in the enlargement of the band-gap width, this enhances the capacity of the vibration reduction and sound isolation more effectively.

Keywords:

• Elastic metamaterial
• finite element method
• frequency-domain spectral element method
• plate
• vibration band-gaps

Compliance with ethical standards

The authors declare that they have no conflict of interest.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (Nos. 11761131006 and 12072086), the German Research Foundation (DFG, Project-No. ZH 15/30-1), China Postdoctoral Science Foundation (Nos. 2018M630338 and 2019T120253), the Heilongjiang Post–doctoral Scientific Research Funding (LBH–Z18056 and LBH-TZ1007), the Fundamental Research Funds for the Central Universities (3072020CF0204) and the National Key R&D Program of China (No. 2016YFB0201005).