On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution e...On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.展开更多
A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structu...A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional （2D） electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thick- ness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.展开更多
In this paper, the propagation of longitudinal stress waves under a longitu- dinal magnetic field is addressed using a unified nonlocal elasticity model with two scale coefficients. The analysis of wave motion is main...In this paper, the propagation of longitudinal stress waves under a longitu- dinal magnetic field is addressed using a unified nonlocal elasticity model with two scale coefficients. The analysis of wave motion is mainly based on the Love rod model. The effect of shear is also taken into account in the framework of Bishop＇s correction. This analysis shows that the classical theory is not sufficient for this subject. However, this unified nonlocal elasticity model solely used in the present study reflects in a manner fairly realistic for the effect of the longitudinal magnetic field on the longitudinal wave propagation.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10772129)the Youth Science Foundation of Shanxi Province of China (No.2006021005)
文摘On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.
基金supported by the University of Kashan(No.463865/13)the Iranian Nanotechnology Development Committee
文摘A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional （2D） electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thick- ness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.
文摘In this paper, the propagation of longitudinal stress waves under a longitu- dinal magnetic field is addressed using a unified nonlocal elasticity model with two scale coefficients. The analysis of wave motion is mainly based on the Love rod model. The effect of shear is also taken into account in the framework of Bishop＇s correction. This analysis shows that the classical theory is not sufficient for this subject. However, this unified nonlocal elasticity model solely used in the present study reflects in a manner fairly realistic for the effect of the longitudinal magnetic field on the longitudinal wave propagation.
