Abstract
The concept of local resonance phononic crystals proposed in recent years provides a new chance for theoretical and technical breakthroughs in the structural vibration reduction. In this paper, a novel sandwich-like plate model with local resonator to acquire specific low-frequency bandgaps is proposed. The core layer of the present local resonator is composed by the simply supported overhanging beam, linear spring and mass block, and well connected with the upper and lower surface panels. The simply supported overhanging beam is free at right end, and an additional linear spring is added at the left end. The wave equation is established based on the Hamilton principle, and the bending wave bandgap is further obtained. The theoretical results are verified by the COMSOL finite element software. The bandgaps and vibration characteristics of the local resonance sandwich-like plate are studied in detail. The factors which could have effects on the bandgap characteristics, such as the structural damping, mass of vibrator, position of vibrator, bending stiffness of the beam, and the boundary conditions of the sandwich-like plates, are analyzed. The result shows that the stopband is determined by the natural frequency of the resonator, the mass ratio of the resonator, and the surface panel. It shows that the width of bandgap is greatly affected by the damping ratio of the resonator. Finally, it can also be found that the boundary conditions can affect the isolation efficiency.
Highlights
At the leading edge of the development of acoustics the new concepts such as phononic crystals and acoustic metamaterial have opened a new chapter of the study of wave propagation in artificially controlled elastic media and structures[1,2,3,4]
Based on the existing studies of the structural design of the double-layer plate composing local resonance phononic crystals and bandgap, a novel structure of sandwich-like plate composing local resonators is presented in this paper to acquire specific low-frequency bandgaps
Theoretical results: considering that the system is a sandwich-like plate built by 10 × 5 units of cells, the geometric and material parameters of the sandwich-like plate in this paper are shown in Table 1 and Table 2, respectively
Summary
At the leading edge of the development of acoustics the new concepts such as phononic crystals and acoustic metamaterial have opened a new chapter of the study of wave propagation in artificially controlled elastic media and structures[1,2,3,4]. Liu et al.[27] proposed a new design method of locally resonant sandwich-like plates for the noise insulation in engineering applications. It was found for the first time that laminated metamaterials have wider stopbands than traditional metamaterials. Li et al.[1] presented a design and computation for a sandwich-like plate containing mass-beam resonators to obtain a specific and low-frequency stopband. Based on the existing studies of the structural design of the double-layer plate composing local resonance phononic crystals and bandgap, a novel structure of sandwich-like plate composing local resonators is presented in this paper to acquire specific low-frequency bandgaps. It can adjust the bandgap without changing the functions of main structure by changing its substructure
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