Research On The Propagation Of Transverse Vibrations In Periodic Composite Plates

Periodic composite structures (PCSs) are made of two or more elastic materials periodically with characteristics of stop bands. That is, vibrations in these frequency ranges can not propagate in the PCSs. When the periodicity of PCSs is broken by the introduction of point defects or linear defects, defect modes will appear inside the stop bands and vibrations corresponding to the defect modes will be localized around the point defects or propagate along the linear defects. The existence of stop bands provides a new idea for vibration isolation, damping, noise reduction and vibration control. For example, we may insert the PCSs in the propagation path or design the structures according to the theory of PCSs to isolate or attenuate the vibrations for some certain frequencies. We may also define the propagation path according to the characteristics of the defect states by designing different point defects or linear defects. Therefore it is of both theoretical and practical importance to study the vibration propagation in PCSs.By using the improved plane wave expansion method and finite element method respectively, the propagation of transverse vibrations in binary/ternary periodic composite thin/thick plates has been investigated in this dissertation. The band structures are calculated and the vibration transmission responses are simulated by ABAQUS for the existence of no defect, a point defect or linear defects respectively. The influences of geometric and material parameters on the propagation characteristics are discussed in detail. The results show that:1. There exist stop bands in periodic composite thin/thick plates with no defect. The position and the width of stop bands depend on the material parameters and the geometric size of the components. For the binary case, the width of stop bands first increases and then decreases with the increasing of filling fraction. It is of benefit to obtain wide stop bands in lower frequencies by enlarging the lattice constant and the differences of mass density between the scatter and the matrix. The stop bands frequencies of thick plates are much lower than that of thin plates. For the ternary case, enlarging the differences of mass density between the core and the coat is most likely to obtain wide stop bands in lower frequencies. The stop bands frequencies of ternary plates are lower than that of binary plates. The existence of stop bands in the periodic composite plates makes it possible for vibration isolation, vibration attenuation and noise reduction.2. The phenomenon of vibration localization occurs in the periodic composite thin/thick plates when a point defect introduced. The geometric size of the defect is the most critical factor which influences the vibration localization. For the binary case, decreasing the filling fraction or enhancing the defect of scatter's geometric size or of the scatter's mass density are most likely to obtain lower localization frequencies. For the ternary case, the number of defect bands is less than that in the binary case, the defect of scatter's geometric size and the mass density have great influences on the vibration localization. In all cases considered, vibration localized most takes place in the ternary periodic composite thick plate with a point defect. By modulating the geometric or material parameters, the transverse vibration corresponding to any defect mode could be localized around the point defect. That is, the propagation of transverse vibration in the periodic composite plate with a point defect could be effectively controlled.3. Linear defects in the periodic composite thin/thick plates can guide the propagation of transverse vibration. Transverse vibrations corresponding to the defect modes could propagate along the linear defect path, and the efficiency of transmission in straight linear defect is much better than that in both bending and branching linear defects. For the branching linear defects, transverse vibrations corresponding to different defect modes could propagate along different branch. Therefore it is practical to design linear defects to make the vibrations of specific frequencies propagate along a specified path. That is, the propagation path of transverse vibrations in the periodic composite thin/thick plates could be effectively controlled.In brief, the present investigations are expected not only to provide a theoretical basis on vibration isolation and vibration control of engineering structures, but also to promote the design and applications of periodic composite plates in engineering structures.