Understanding the contact mechanics of rough tooth surfaces is critical in order to understand phenomena such as tooth surface flash temperature, tooth surface wear, and gear vibration. In this paper, the contact behavior between the meshing tooth surfaces of beveloid gear pairs with elliptical asperities is the focus. The contact area distribution function of the elliptical asperity was proposed for the point contact of curved surfaces by transforming the elastic contact problem between gear meshing surfaces into the contact between elastic curved surfaces with an arbitrary radius of curvature. In addition, a fractal contact mechanics model for the rough surface of a beveloid gear with elliptical asperities was established. The influence of tooth surface topography on the contact load and contact stiffness under different fractal parameters was investigated, and the results demonstrated that the real contact load and the contact stiffness of curved surfaces increase with the increase in the fractal dimension D and the contact coefficient λ. Conversely, the real contact load and normal contact stiffness decrease with the increase in the fractal roughness G and eccentricity e.

In this paper, free vibration and transmission properties of single and composite thin annular plate (TAP) structures are presented by wave approach. The propagation matrix, continuity matrix and reflection matrix are introduced to carry out the analysis. Using the wave approach, natural frequencies of single and composite TAP are calculated theoretically. The results obtained by this method agree well with those calculated by the classical Bessel and Hankel methods. Additionally, transfer matrix is introduced and combined with the boundary conditions to obtain the transmission behaviors of composite multilayer TAP. To thoroughly understand the composite TAP, the influences of thickness, density ratio and radius ratio on natural frequencies are investigated. This study provides very useful information for transverse vibration suppression of TAP structure.

In this paper, free vibration and transmission response for the torsional vibration of circular annular plate are presented. To the author’s knowledge, few studies can be found for the torsional vibration from wave standpoint. For this purpose, in this study, natural frequencies for the torsional vibration of annular plate with clamped–clamped and free–free boundaries are calculated. The natural frequencies obtained by wave approach are compared with those derived by the classical method. Furthermore, transmissibility curves of the periodic annular model and Fibonacci annular model are analyzed. The finite element simulations are carried out to verify the theoretical results. Finally, the influence of inner radius and length ratio on the transmission response is also discussed. The obtained results are useful for the torsional vibration reduction of machinery structures.

Radial vibration of the circular plate is presented using wave propagation approach and classical method containing Bessel solution and Hankel solution for calculating the natural frequency theoretically. In cylindrical coordinate system, in order to obtain natural frequency, propagation and reflection matrices are deduced at the boundaries of free-free, fixed-fixed, and fixed-free using wave propagation approach. Furthermore, radial phononic crystal is constructed by connecting two materials periodically for the analysis of band phenomenon. Also, Finite Element Simulation (FEM) is adopted to verify the theoretical results. Finally, the radial and piezoelectric effects on the band are also discussed.