Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and...Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.展开更多
An analytical solution is obtained for a rotating multiferroic composite hollow cylinder made of radially polarized piezoelectric and piezomagnetic materials. Both the number of layers and the stacking sequence of the...An analytical solution is obtained for a rotating multiferroic composite hollow cylinder made of radially polarized piezoelectric and piezomagnetic materials. Both the number of layers and the stacking sequence of the composite cylinder can be arbitrary. General mechanical, electric and magnetic boundary conditions can be applied at both the inner and outer cylindrical surfaces. The state space method is employed so that only a 2×2 matrix is involved in the whole solving procedure. In the nu-merical experiments, the distributions of elastic, electric as well as magnetic fields in an internally pressurized rotating BaTiO3/CoFe2O4 composite hollow cylinder subjected to different boundary conditions are presented graphically. The results clearly show that the stress fields in a multiferroic composite cylinder are controllable.展开更多
基金Supported by the National Nature Science Foundation of China(10371070)Supported by the Nature Science Foundation of Educational Committee of Liaoning Province(2021401157)
文摘Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.
基金supported by the National Natural Science Foundation of China (Nos. 10872179 and 10725210)the Zhejiang Provincial Natural Science Foundation of China (No. Y7080298)the Zijin Plan of Zhejiang University, China
文摘An analytical solution is obtained for a rotating multiferroic composite hollow cylinder made of radially polarized piezoelectric and piezomagnetic materials. Both the number of layers and the stacking sequence of the composite cylinder can be arbitrary. General mechanical, electric and magnetic boundary conditions can be applied at both the inner and outer cylindrical surfaces. The state space method is employed so that only a 2×2 matrix is involved in the whole solving procedure. In the nu-merical experiments, the distributions of elastic, electric as well as magnetic fields in an internally pressurized rotating BaTiO3/CoFe2O4 composite hollow cylinder subjected to different boundary conditions are presented graphically. The results clearly show that the stress fields in a multiferroic composite cylinder are controllable.
