Wang Yuesheng

Wavelet-based method for computing elastic band gaps of one-dimensional phononic crystals

A wavelet-based method was developed to compute elastic band gaps of one-dimensional phononic crystals. The wave field was expanded in the wavelet basis and an equivalent eigenvalue problem was derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method was then applied to a binary system. For comparison, the elastic band gaps of the same one-dimensional phononic crystals computed with the wavelet method and the well-known plane wave expansion (PWE) method are both presented in this paper. The numerical results of the two methods are in good agreement while the computation costs of the wavelet method are much lower than that of PWE method. In addition, the adaptability of wavelets makes the method possible for efficient band gap computation of more complex phononic structures.

Propagation of slip pulse along frictionless contact interface with local separation between two piezoelectric solids

The Stroh formalism of piezoelectric materials, Fourier analysis and singular integral equation technique were used to investigate the existence of a pulse at the frictionless interface in presence of local separation between two contact piezoelectric solids. The two solids were combined together by uniaxial tractions and laid in the electric field. The problem was cast into a set of Cauchy singular integral equations, from which the closed-form solutions were derived. The numerical discussion on the existence of such a slip pulse was presented. The results show that such a slip pulse, which has square root singularities at both ends of the local separation zone, can propagate in most material combinations. And the existence of such a slip pulse will not be affected by the applied mechanical and electric fields in some special material combinations.

Band structures of elastic waves in two-dimensional eight-fold solid–solid quasi-periodic phononic crystals*

Combined with the supercell method, band structures of the anti-plane and in-plane modes of two-dimensional (2D) eight-fold solid–solid quasi-periodic phononic crystals (QPNCs) are calculated by using the finite element method. The influences of the supercell on the band structure and the wave localization phenomenon are discussed based on the modal distributions. The reason for the appearance of unphysical bands is analyzed. The influence of the incidence angle on the transmission spectrum is also discussed.

Analysis of dynamic instability of interfacial slip waves based on the surface impedance tensor

A new method relying on the Stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves. The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value, and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor. Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle. As an example, the steady frictional sliding of an elastic half-space in contact with a rigid flat surface was considered in details. A quartic complex characteristic equation was derived and its solution behavior in the unit circle was discussed. An explicit expression for the instability condition of the interfacial slip waves was presented.

Progress in some basic problems on contact mechanics of functionally graded materials

Over the past ten years, the contact problems of functionally graded materials (FGMS) have been considered by many investigators owing to the potential applications of these materials for resisting surface contact damage. This paper provides an overview on the progress of some basic contact problems of FGMs, incorporating the results of our recent research in this field. We focus on the following contact problems of FGMs: frictionless and frictional contacts, fretting contact, thermo-elastic contact and instability, electro-magneto-thermo-mechanical contact and adhesive contact. We provide a perspective on the development of contact mechanics of FGMs.