Abstract
This paper first employs and develops an exact wave-based vibration analysis approach to investigate a finite Timoshenko beam carrying periodic two-degree-of-freedom (2-DOF) uncoupled force-moment type resonators. In the approach, vibrations are described as structural waves that propagate along uniform structural elements and reflected and transmitted at structural discontinuities. Each uncoupled force-moment type resonator is considered as a cell which injects waves into the distributed beam through the transverse force and the bending moment at the attached point. By assembling wave relations of the cells into the beam, the forced vibration problem of the locally resonant (LR) structure is turned to be the solution to a related set of matrix equations. In addition, the parametric analysis provides an efficient method to obtain wide low-frequency range band-gaps. Accuracy of the proposed wave-based vibration analysis approach is demonstrated by the simulated and measured results of two sets of beam-like resonator samples.
Highlights
In the past decade, the propagation of elastic or acoustic waves in periodic structures, known as phononic crystals (PCs) and phononic metamaterials (PMs), has received growing attention.Such structures are attractive to be used in numerous engineering applications, such as vibration isolators, frequency sensors, sound barriers, acoustic cloaks, vibration energy harvesters, etc. [1,2,3,4], because of the existence of elastic band-gap properties within which no flexural wave can propagate through
Plenty of studies are focused on locally resonant (LR) PCs due to their advantage in achieving low-frequency band-gaps with small lattice constants
This paper first employs and develops the wave-based vibration analysis approach to study a finite Timoshenko LR beam suspended with periodic uncoupled force-moment type resonators
Summary
The propagation of elastic or acoustic waves in periodic structures, known as phononic crystals (PCs) and phononic metamaterials (PMs), has received growing attention. Mei [16] first proposed a finite Euler-Bernoulli beam carrying a single two-degree-of-freedom (2-DOF) spring-mass resonator using a wave-based vibration analysis approach. It is a very useful vibration analysis approach that provides the exact solution for structural waves that propagate along uniform structural elements and are reflected and transmitted at structural discontinuities, such as joints, resonators, loading sites, and boundaries [17,18,19,20,21]. This paper first employs and develops the wave-based vibration analysis approach to study a finite Timoshenko LR beam suspended with periodic uncoupled force-moment type resonators. The accuracy of the approach is validated through comparisons to simulation and experimental results
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