The pressure reflected from a bi-laminated piezoelectric plate hasbeen determined using the Thomson-Haskell matrix method. The plate iscomposed of a piezoelectric layer with grounded vacuum and An elasticlayer in cont...The pressure reflected from a bi-laminated piezoelectric plate hasbeen determined using the Thomson-Haskell matrix method. The plate iscomposed of a piezoelectric layer with grounded vacuum and An elasticlayer in contact with the fluid. An incident plane wave in the fluidmedium strikes the plate at dif- Ferent angles. The required electricpotential across the piezoelectric layer to cancel the reflectionfrom the Fluid/elastic boundary has been determined for thepiezoelectric material PZT-5 at various thickness parame- Ters andincident frequencies.展开更多
The bifurcations and chaotic dynamics of a simply supported symmetric cross-ply composite lami- nated piezoelectric rectangular plate are studied for the first time, which are simultaneously forced by the transverse, ...The bifurcations and chaotic dynamics of a simply supported symmetric cross-ply composite lami- nated piezoelectric rectangular plate are studied for the first time, which are simultaneously forced by the transverse, in-plane excitations and the excitation loaded by piezoelectric layers. Based on the Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the composite laminated piezoelectric rectangular plate are derived by using the Hamilton’s principle. The Galerkin’s approach is used to discretize partial differential governing equations to a two-degree- of-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation. Numerical method is utilized to find the periodic and chaotic responses of the composite laminated piezoelectric rectangular plate. The numerical results indicate the existence of the periodic and chaotic responses in the aver- aged equation. The influence of the transverse, in-plane and piezoelectric excitations on the bifurca- tions and chaotic behaviors of the composite laminated piezoelectric rectangular plate is investigated numerically.展开更多
The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates...The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1：3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the Composite laminated piezoelectric plate are obtained.展开更多
The analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of a composite laminated piezoelectric rectangular plate is given for the first time. The theory of nor...The analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of a composite laminated piezoelectric rectangular plate is given for the first time. The theory of normal form and the energy-phase method are combined to investigate the higher-dimen-sional chaotic dynamics of the composite laminated piezoelectric rectangular plate. Firstly,the theory of normal form is used to reduce the six-dimensional averaged equation to the simpler normal form. Then,the energy-phase method is extended to analyze the global bifurcations and chaotic dynamics of a six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bi-furcation and Shilnikov type multi-pulse chaos for the composite laminated piezoelectric rectangular plate. Finally,numerical simulations are also used to investigate the nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate. The results of numerical simulations also demonstrate that there exist the chaotic motions and the multi-pulse jumping orbits of the composite laminated piezoelectric rectangular plate.展开更多
基金the National Natural Science Foundation of China(No.10172039)
文摘The pressure reflected from a bi-laminated piezoelectric plate hasbeen determined using the Thomson-Haskell matrix method. The plate iscomposed of a piezoelectric layer with grounded vacuum and An elasticlayer in contact with the fluid. An incident plane wave in the fluidmedium strikes the plate at dif- Ferent angles. The required electricpotential across the piezoelectric layer to cancel the reflectionfrom the Fluid/elastic boundary has been determined for thepiezoelectric material PZT-5 at various thickness parame- Ters andincident frequencies.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10732020, 10872010)the National Science Foundation for Distinguished Young Scholars of China (Grant No. 10425209)
文摘The bifurcations and chaotic dynamics of a simply supported symmetric cross-ply composite lami- nated piezoelectric rectangular plate are studied for the first time, which are simultaneously forced by the transverse, in-plane excitations and the excitation loaded by piezoelectric layers. Based on the Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the composite laminated piezoelectric rectangular plate are derived by using the Hamilton’s principle. The Galerkin’s approach is used to discretize partial differential governing equations to a two-degree- of-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation. Numerical method is utilized to find the periodic and chaotic responses of the composite laminated piezoelectric rectangular plate. The numerical results indicate the existence of the periodic and chaotic responses in the aver- aged equation. The influence of the transverse, in-plane and piezoelectric excitations on the bifurca- tions and chaotic behaviors of the composite laminated piezoelectric rectangular plate is investigated numerically.
基金Project supported by the National Natural Science Foundation of China(Nos.11402127,11290152 and 11072008)
文摘The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1：3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the Composite laminated piezoelectric plate are obtained.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10732020 and 10872010)the National Science Foundation for Distinguished Young Scholars of China (Grant No.10425209)the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Munici-pality (PHRIHLB)
文摘The analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of a composite laminated piezoelectric rectangular plate is given for the first time. The theory of normal form and the energy-phase method are combined to investigate the higher-dimen-sional chaotic dynamics of the composite laminated piezoelectric rectangular plate. Firstly,the theory of normal form is used to reduce the six-dimensional averaged equation to the simpler normal form. Then,the energy-phase method is extended to analyze the global bifurcations and chaotic dynamics of a six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bi-furcation and Shilnikov type multi-pulse chaos for the composite laminated piezoelectric rectangular plate. Finally,numerical simulations are also used to investigate the nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate. The results of numerical simulations also demonstrate that there exist the chaotic motions and the multi-pulse jumping orbits of the composite laminated piezoelectric rectangular plate.
