Abstract
The propagation properties of waves in finite Timoshenko locally resonant (LR) beams resting on forced vibrations and periodically attached two-degree-of-freedom force-type resonators are studied by the wave-based analysis approach. By calculating the motion equations of the beam, the transmission and reflection matrices of waves at the resonator attached point are first derived, and the forced vibration response of the finite periodic beam is deduced by the wave-based approach. Several examples are also analyzed by the finite element method to verify the high accuracy of the developed wave-based analysis approach. Numerical results show that wider low-frequency band-gaps exist in this type of LR beams. It was also found that the resonator masses and spring stiffnesses caused different effects on the band-gap properties of the combined LR beam. The desired band-gap widths of the LR beam can be tuned by adjusting the mass blocks and spring stiffness in the resonators based on the results.
Highlights
The propagation of acoustic and elastic waves in periodic structures, known as phononic crystals (PCs) and acoustics/elastic metamaterials (AMs/EMs) [1,2], has attracted growing interest in recent years
locally resonant (LR) beam intointo the propagation characteristics of the periodic into propagation characteristics ofstiffness the LR beam withwith different resonators, andthe how the spring stiffness of finite the resonator influence different resonators, and howmass the and mass and spring ofperiodic the resonator influthe band-gap width, the curves of mass the LR. Beams with these four different sets of of withence different resonators, andthe how spring stiffness of thefour resonator influthe band-gap width, FRFthe curves ofand the LR beams with these different sets ence the band-gap width, the frequency response function (FRF) curves of the LR beams with these four different sets of width associated with resonator 2 in the lower frequency range is increased by 26.8%
The vibration analysis procedure is only a simple assembly of the involved reflection and transmission matrices, which shows the high efficiency of the derived analytical method in vibration analysis of finite LR beams
Summary
The propagation of acoustic and elastic waves in periodic structures, known as phononic crystals (PCs) and acoustics/elastic metamaterials (AMs/EMs) [1,2], has attracted growing interest in recent years. For finite Timoshenko LR beams combined with periodic coupled 2DOF spring-mass systems, a wave-based vibration analysis approach is developed for forced vibration analysis. With the vibration analysis of the LR beam suspended with different resonators using the developed wave-based vibration analysis approach, we analyzed how the mass block value and the spring stiffness of resonator influence the band-gap properties of the finite. The calculation accuracy of the developed wave-based vibration analysis approach is verified by several numerical examples in Section 4 and the effects of mass and spring stiffness of the resonator on the band-gap properties of finite LR beams are studied in detail.
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