Numerical Investigation On Lamb Wave Propagation In Periodic Sandwich Plates

Periodic sandwich plate is a multilayer composite structure with spatially periodicity, with the acoustic or elastic wave band gaps appearing in the band structures. The periodic sandwich plate not only has good applicability, but also has excellent wave propagation characteristics which are not possessed by the traditional composite plate materials. In this thesis, numerical simulations are carried out by the finite element method on two kind of periodic sandwich plate, respectively named the phononic crystal sandwich plate and light-weight grid sandwich plate, for calculating the band structure and response spectrum, analyzing the corresponding eigen-modes and response-modes, studying the influence factors to the band gaps, investigating the defect modes of the systems with defects, and preliminarily exploring the method for detecting defects in the light-weight grid sandwich plates. The main contents and results include:(1) The band structure and response spectrum of the phononic crystal sandwich plates are calculated by the three-dimensional solid element, to study the influence of the geometric parameters and material properties on the band gap, and investigate the defect modes in the systems with a point or line defect. The results show that the optimal values of the thickness of the coating plate and the filling rate exist corresponding to the widest band gaps; in a certain range, the band gap width increases with the core layer thickness increasing; Young’s modulus and density of the material of the coating plate has a obvious effect on the band gap; localized modes exist in the band gaps of the phononic crystal sandwich plates with point defects, and the defect size has a marked impact on the frequencies of the localized modes; waveguide modes appear in the band gaps of the phononic crystal sandwich plates with line defects, and the shape of line defects affects the transmission efficiency of the guided wave.(2) The band structure of the light-weight grid sandwich plates with the square lattice are calculated by using the three-dimensional solid element and the shell element, respectively, to represent the impact of both the coating plate thickness and the grid plate thickness on the results, and conclude the general rules replacing the solid element by the shell element in the band structure calculation. The influence of the core layer thickness on the band gap is studied, as well. The results show that the coating plate thickness and the grid plate thickness are smaller, the results by the two different element match better; when the ratio of the coating plate thickness, as well as the grid plate thickness to the lattice constant and the core layer thickness is less than 0.1, the solid element can be replaced by the shell element in calculating the band structures of the light-weight grid sandwich plate, and the result has high reliability and accuracy in the low frequency region (the first three orders); when the coating plate thickness is consistent with the grid plate thickness, about 1/20 of the lattice constant, and the core layer thickness is approximately 0.85-1.35 times of the lattice constant, the band gap can be obtained and the maximum width appears while the core layer thickness being equal to the lattice constant.(3) The metamaterial layer is defined as the cylinders arranged on the surface of the light-weight grid sandwich plate in the square lattice (each cylinder is consisted of two layers functioned as "oscillator" and "spring", respectively). The characteristics of the metamaterial layer is that the locally resonant band gaps with low central frequency exist in the band structure. The band structures and response spectra of the metamaterial layer covered light-weight grid sandwich plate are calculated to study the influence of the stubs in the metamaterial layer on the locally resonant band gap, and preliminarily explore the method for detecting defects in the light-weight grid sandwich plates by the metamaterial layer with wave guides. The results show that when the total height of the stubs in the metamaterial layer is certain, there is the optimal oscillator/spring stub height ratio corresponding to the maximum band gap; the diameter of the stubs is larger, the band gap width is greater; when the ratio of the Young’s modulus between the spring stubs and the light-weight grid sandwich plate (aluminum) is less than or equal to 102, the locally resonant band gaps with quite a large width appear in the band structures; the localized defect modes produced by the point defects in the light-weight grid sandwich plates can constraint the energy of the guided waves in the metamaterial layer within the vicinity of the point defects, resulting in substantial change of the received signals in the response spectra. It’s a new measure to realize the nondestructive examination to the light-weight grid sandwich plates.