Research On Propagation Of Vibrations In Two Types Of Periodic Sandwich Panels With Defects

Periodic structures have the properties of band gaps. That is, vibrations in these frequency ranges cannot propagate in the periodic structures. When the periodicity of the periodic structures is broken by the introduction of point defects or linear defects, defect modes will appear inside the band gaps and vibrations corresponding to the defect modes will be localized around the point defects or propagate along the linear defects. Therefore, it is of both theoretical and practical importance to study the properties of band gaps and defect modes in the periodic structures.By using the transfer matrix method and finite element method respectively, the propagation of transverse vibrations in one-dimensional corrugated sandwich plates with defects/without defects has been numerically and theoretically investigated. Equivalent spring modes of the core are built and influences of equivalent spring stiffness on the propagation of vibrations in periodic structure are discussed. By calculating the vibration transmission response and displacement distribution, the propagation of vibrations in the sandwich plates with three types of defects has been studied. Besides, the propagation of vibrations in two-dimensional sandwich panels with cylinder-shaped periodic tubes has been studied by COMSOL for the existence of no defect, point defects, linear defects or combined point-linear defects respectively. Influences of types of defects on the propagation characteristics are discussed, such as location defects, geometry defects and material defects. Sensitivities of the structure for different defect types are discussed by calculating the band structures, vibration transmission response and displacement distribution. The results show that:1. There exist some frequency ranges vibration attenuation both in perfect periodic corrugated sandwich plates and in sandwich panels with cylinder-shaped periodic tubes. The vibration attenuation characteristics in sandwich plates makes it possible for vibration isolation and reduction.2. Vibration localization occurs both in corrugated sandwich plates and in sandwich panels with cylinder-shaped periodic tubes when a point defect is introduced. Different types of point defects lead to different vibration localization. To the corrugated sandwich plates, the vibration is more localized for the case of rod broken or node deboned than that of the thickness change of the rod.. To the sandwich panels with cylinder-shaped periodic tubes, the structure is more sensitive to location defects and strength geometry defects, less sensitive to weaknesses geometry defects and material point defects. The vibration localization of point defects provides some theoretical basis on non-destructive valuation and vibration transmission control of periodic sandwich plates.3. Linear defects in the sandwich panels with cylinder-shaped periodic tubes can guide the propagation of vibration. Sensitivities of the structure to different types of defect are also different. Vacant linear defects is most obvious, translation linear defects is followed and material linear defects is the third. Therefore, it is practical to design linear defects to make the vibrations of specific frequencies propagate along a specified path. That is to say, the propagation path of vibrations in the sandwich panels could be effectively controlled.