Abstract
The vibration of the periodic oscillator coupled damping beam model is reduced through the band gaps designing method, which can be applied in equivalent engineering structures. In this paper, the flexural wave dispersion relations of the infinite long periodic oscillator coupled damping beam were calculated using the reverberation-ray matrix method combined with the Bloch theorem. The flexural wave vibration frequency response function of the finite long periodic oscillator coupled damping beam was carried out using the finite element method. The flexural wave vibration band gaps occur in the infinite long periodic oscillator coupled damping beam model in both the analytical and numerical results. In these band gaps, flexural waves’ propagation is prohibited, and flexural vibration is significantly suppressed. Furthermore, the effects of structure and material parameters on the flexural wave vibration band gaps characteristics are studied. Thus, the structural vibration reduction design can be realized by adjusting the related parameters of the periodic coupled damping beam structures and the equivalent 2D periodic stiffened plate structures.
Highlights
As a common basic structure in engineering, various forms of beam structures are widely used in civil engineering, mechanical power engineering, aerospace, naval architecture, and ocean engineering.The beam structures’ design method has been one of the main research objects in the field of vibration and noise control for many years [1,2,3]
Wang has studied simplified models of two-dimensional and three-dimensional phononic crystals [32], and the results show that the base and local oscillators can be simplified into one-dimensional periodic oscillator coupled beam, which is a periodic spring-mass oscillator coupled homogeneous straight damping beam combined system
The flexural wave vibration band gaps calculation method of the infinite long periodic oscillator coupled damping beam is derived by using the method of the reverberation-ray matrix in combination with the Bloch theorem, and the numerical results expressed by the frequency response function demonstrated the effectiveness of this theoretical calculation method
Summary
As a common basic structure in engineering, various forms of beam structures are widely used in civil engineering, mechanical power engineering, aerospace, naval architecture, and ocean engineering. Studying the band gap characteristics of the periodic oscillator coupled beams and introducing them into the design of the bending vibration beam structures are of great significance to the research on the vibration control of beam structures and periodic stiffened plates in engineering. Numerical and experimental methods are commonly used analysis tools to study the band gaps and transmission characteristics of periodic bi-directionally orthogonal stiffened plates; it is hard to theoretically investigate the effects of parameters on band gaps and guide the vibration reduction design. It is of great theoretical significance and engineering application value to study periodic structure parameters’ influence on band gaps. This research work provides an important reference for the vibration reduction design of beam structures and the equivalent 2D periodic stiffened plate structures, which are widely used in aerospace, naval architecture, and ocean engineering
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