The present study illustrates a series method for the solutions of one dimensional wave equation together with non-classical dynamic boundary conditions. Matheu-Hill form, a differential equation with polynomial form ...The present study illustrates a series method for the solutions of one dimensional wave equation together with non-classical dynamic boundary conditions. Matheu-Hill form, a differential equation with polynomial form and Laguerre differential equation form dynamic boundary conditions were taken into consideration. Series methods were given in order for the solutions of wave equation together with these dynamic boundary conditions along with semi-infinite axis of the spatial coordinate. Wave profiles were obtained by means of wave solutions of the wave equation given by d’Alembert.展开更多
Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’...Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.展开更多
文摘The present study illustrates a series method for the solutions of one dimensional wave equation together with non-classical dynamic boundary conditions. Matheu-Hill form, a differential equation with polynomial form and Laguerre differential equation form dynamic boundary conditions were taken into consideration. Series methods were given in order for the solutions of wave equation together with these dynamic boundary conditions along with semi-infinite axis of the spatial coordinate. Wave profiles were obtained by means of wave solutions of the wave equation given by d’Alembert.
文摘Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.
