Waves In The Layered Functionally Graded Nano Copper Structure

Functional gradient nano material is a new special material whose cell size varies from nano scale to macro scale continuously. This structure can effectively avoid mutation in material properties caused by mutation in the structural unit size and improve the overall performance of materials. Because of this, this special material has been widely used in aerospace,electronic equipment, medical science and other fields. In order to provide a theoretical basis for ultrasonic nondestructive testing of the new material, in this paper, we study the different wave motion in layered functionally graded nano copper plate based on the theory of elastic dynamies. The main contents of this paper are as follows:Firstly, in this paper, the concept of "gradient" in functionally graded materials is obtained by assuming that the grain size varies exponentially along the thickness direction.Secondly, the propagation characteristics of SH wave and Lamb wave in a single layer and symmetrical structure functionally graded copper plate are studied by power series method.In addition, considering the continuity between layers, the physical conditions of displacement and stress are transformed into the mathematical conditions of Taylor's zero order and first order of displacement function, and the method of power series and the transfer matrix is combined to solve the wave problems of the multilayer structure functionally graded nano copper plate. The results show that SH wave and Lamb wave in multiple modes can propagate in layered functionally graded copper plate. The rule of phase velocity changing with wave number in each mode is not consistent. Compared with the wave in same order mode, the larger the gradient parameters p is, the smaller the phase velocity is. The phase velocity variation and phase velocity rate are positively correlated with the gradient parameterp.According to different standard, different modes are selected to calibrate the gradient parameters p.Thirdly, we study the propagation characteristics of SH wave and Lamb wave in homogeneous copper plate and different layers of graded nano copper plate, and the phase velocity correlation difference is also studied. The results show that dispersion curves of more layers gradient plates is closer to the dispersion curves of homogenized copper plates. Besides,the group velocity curves of different layers with different gradient parameter p are also studied. Results the gradient parameters and the number of layers corresponding to the larger energy velocity are given.The characteristics of wave propagating in functionally graded nano copper layered structures can be used to guide the design of acoustic devices represented by functionally graded nano copper materials. It is expected to provide theoretical basis for ultrasonic nondestructive testing of functionally graded metal plates.