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Wei Zhang - One of the best experts on this subject based on the ideXlab platform.
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analysis on nonlinear vibrations near internal resonances of a composite laminated piezoelectric rectangular plate
Engineering Structures, 2018Co-Authors: Y F Zhang, Wei ZhangAbstract:Abstract The nonlinear vibrations and chaotic motions of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate subjected to the transverse and in-plane excitations are analyzed in the case of primary parametric resonance and 1:3 internal resonance. It is assumed that different layers of the symmetric cross-ply composite laminated piezoelectric rectangular plate are perfectly bonded to each other and with piezoelectric actuator layers embedded in the plate. Based on the Reddy’s third-order shear deformation plate theory, the nonlinear governing Equation of motion for the composite laminated piezoelectric rectangular plate is derived by using the Hamilton’s principle. The Galerkin’s approach is employed to discretize the partial differential governing Equation to a two-degree-of-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is utilized to obtain the four-dimensional Averaged Equation. Numerical method is used to find the bifurcation diagram, the periodic and chaotic motions of the composite laminated piezoelectric rectangular plate. The numerical results illustrate the existence of the periodic and chaotic motions in the Averaged Equation. It is found that the chaotic responses are especially sensitive to the forcing and the parametric excitations. The influences of the transverse, in-plane and piezoelectric excitations on the bifurcations and chaotic behaviors of the composite laminated piezoelectric rectangular plate are investigated numerically.
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nonlinear dynamics near resonances of a rotor active magnetic bearings system with 16 pole legs and time varying stiffness
Mechanical Systems and Signal Processing, 2018Co-Authors: Wei Zhang, Minghui YaoAbstract:Abstract In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing Equation of motion for rotor-active magnetic bearings is derived by using the Newton’s second law. The resulting dimensionless Equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The Averaged Equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.
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Nonlinear Dynamics of the High-Speed Rotating Plate
Hindawi Limited, 2018Co-Authors: Minghui Yao, Wei ZhangAbstract:High speed rotating blades are crucial components of modern large aircraft engines. The rotating blades under working condition frequently suffer from the aerodynamic, elastic and inertia loads, which may lead to large amplitude nonlinear oscillations. This paper investigates nonlinear dynamic responses of the blade with varying rotating speed in supersonic airflow. The blade is simplified as a pre-twist and presetting cantilever composite plate. Warping effect of the rectangular cross-section of the plate is considered. Based on the first-order shear deformation theory and von-Karman nonlinear geometric relationship, nonlinear partial differential dynamic Equations of motion for the plate are derived by using Hamilton’s principle. Galerkin approach is applied to discretize the partial differential governing Equations of motion to ordinary differential Equations. Asymptotic perturbation method is exploited to derive four-degree-of-freedom Averaged Equation for the case of 1 : 3 internal resonance-1/2 sub-harmonic resonance. Based on the Averaged Equation, numerical simulation is used to analyze the influence of the perturbation rotating speed on nonlinear dynamic responses of the blade. Bifurcation diagram, phase portraits, waveforms and power spectrum prove that periodic motion and chaotic motion exist in nonlinear vibration of the rotating cantilever composite plate
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nonlinear dynamic responses of a truss core sandwich plate
Composite Structures, 2014Co-Authors: Wei Zhang, J Chen, Dongxing Cao, L H ChenAbstract:Abstract Nonlinear dynamic behaviors of a simply supported 3D-Kagome truss core sandwich plate subjected to the transverse and the in-plane excitations are investigated in this paper. The truss core sandwich plate is equivalent to a laminated plate with three laminas according to the equivalent sandwich plate method. The governing Equation of motion for the truss core sandwich plate is derived by using the von Karman type Equation for the geometric nonlinearity and the Reddy’s third-order shear deformation plate theory. The nonlinear governing partial differential Equation is reduced to the ordinary differential Equation by applying the Galerkin’s approach. The four-dimensional Averaged Equation is obtained by using the method of multiple scales. The frequency–response curves are obtained under consideration of strongly coupled of two modes. The results indicate that there are the hardening and softening nonlinearities in the truss core sandwich plate under the specific resonant case. The influences of the amplitudes for the in-plane and transverse excitations on the frequency–response curves are investigated. The results of numerical simulations for the two-degree-of-freedom nonlinear Equation exhibit the existence of the period, multi-period and chaotic responses with the variation of the excitations, which demonstrate that those motions appear alternately.
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multi pulse chaotic motions of high dimension nonlinear system for a laminated composite piezoelectric rectangular plate
Meccanica, 2014Co-Authors: Wei ZhangAbstract:This paper investigates the multi-pulse global bifurcations and chaotic dynamics of the high-dimension nonlinear system for a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. Using the von Karman type Equations, Reddy’s third-order shear deformation plate theory and Hamilton’s principle, the Equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. Applying the method of multiple scales and Galerkin’s approach to the partial differential governing Equation, the four-dimensional Averaged Equation is obtained for the case of 1:2 internal resonance and primary parametric resonance. From the Averaged Equations obtained, the theory of normal form is used to derive the explicit expressions of normal form with a double zero and a pair of pure imaginary eigenvalues. Based on the explicit expressions of normal form, the extended Melnikov method is used for the first time to investigate the Shilnikov type multi-pulse homoclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multi-pulse chaotic dynamics of the laminated composite piezoelectric rectangular plate are analytically obtained. Numerical simulations also illustrate that the Shilnikov type multi-pulse chaotic motions can also occur in the laminated composite piezoelectric rectangular plate. Overall, both theoretical and numerical studies demonstrate that the chaos in the Smale horseshoe sense exists for the laminated composite piezoelectric rectangular plate.
Minghui Yao - One of the best experts on this subject based on the ideXlab platform.
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nonlinear dynamics near resonances of a rotor active magnetic bearings system with 16 pole legs and time varying stiffness
Mechanical Systems and Signal Processing, 2018Co-Authors: Wei Zhang, Minghui YaoAbstract:Abstract In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing Equation of motion for rotor-active magnetic bearings is derived by using the Newton’s second law. The resulting dimensionless Equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The Averaged Equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.
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Nonlinear Dynamics of the High-Speed Rotating Plate
Hindawi Limited, 2018Co-Authors: Minghui Yao, Wei ZhangAbstract:High speed rotating blades are crucial components of modern large aircraft engines. The rotating blades under working condition frequently suffer from the aerodynamic, elastic and inertia loads, which may lead to large amplitude nonlinear oscillations. This paper investigates nonlinear dynamic responses of the blade with varying rotating speed in supersonic airflow. The blade is simplified as a pre-twist and presetting cantilever composite plate. Warping effect of the rectangular cross-section of the plate is considered. Based on the first-order shear deformation theory and von-Karman nonlinear geometric relationship, nonlinear partial differential dynamic Equations of motion for the plate are derived by using Hamilton’s principle. Galerkin approach is applied to discretize the partial differential governing Equations of motion to ordinary differential Equations. Asymptotic perturbation method is exploited to derive four-degree-of-freedom Averaged Equation for the case of 1 : 3 internal resonance-1/2 sub-harmonic resonance. Based on the Averaged Equation, numerical simulation is used to analyze the influence of the perturbation rotating speed on nonlinear dynamic responses of the blade. Bifurcation diagram, phase portraits, waveforms and power spectrum prove that periodic motion and chaotic motion exist in nonlinear vibration of the rotating cantilever composite plate
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Modeling and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate
Hindawi Limited, 2014Co-Authors: Minghui Yao, Wei Zhang, D. M. WangAbstract:This paper investigates the multipulse heteroclinic bifurcations and chaotic dynamics of a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. According to the von Karman type Equations, Reddy’s third-order shear deformation plate theory, and Hamilton’s principle, the Equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. The method of multiple scales and Galerkin’s approach are applied to the partial differential governing Equation. Then, the four-dimensional Averaged Equation is obtained for the case of 1 : 3 internal resonance and primary parametric resonance. The extended Melnikov method is used to study the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multipulse chaotic dynamics are analytically obtained. From the investigation, the geometric structure of the multipulse orbits is described in the four-dimensional phase space. Numerical simulations show that the Shilnikov type multipulse chaotic motions can occur. To sum up, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists for the laminated composite piezoelectric rectangular plate
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Multipulse Heteroclinic Orbits and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate
Hindawi Limited, 2013Co-Authors: Minghui Yao, Wei ZhangAbstract:This paper investigates the multipulse global bifurcations and chaotic dynamics for the nonlinear oscillations of the laminated composite piezoelectric rectangular plate by using an energy phase method in the resonant case. Using the von Karman type Equations, Reddy’s third-order shear deformation plate theory, and Hamilton’s principle, the Equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. Applying the method of multiple scales and Galerkin’s approach to the partial differential governing Equation, the four-dimensional Averaged Equation is obtained for the case of 1 : 2 internal resonance and primary parametric resonance. The energy phase method is used for the first time to investigate the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The paper demonstrates how to employ the energy phase method to analyze the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of high-dimensional nonlinear systems in engineering applications. Numerical simulations show that for the nonlinear oscillations of the laminated composite piezoelectric rectangular plate, the Shilnikov type multipulse chaotic motions can occur. Overall, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists
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global bifurcations and chaotic dynamics in nonlinear nonplanar oscillations of a parametrically excited cantilever beam
Nonlinear Dynamics, 2005Co-Authors: Wei Zhang, Fengxia Wang, Minghui YaoAbstract:This paper presents the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. The governing nonlinear Equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing Equation to obtain a two-degree-of-freedom nonlinear system with parametric and forcing excitations. The resonant case considered here is 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance–primary resonance for the out-of-plane mode. The parametrically and externally excited system is transformed to the Averaged Equations by using the method of multiple scales. From the Averaged Equation obtained here, the theory of normal form is applied to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form obtained above, a global perturbation method is utilized to analyze the global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the Averaged Equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the chaotic motions can occur in the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations verify the analytical predictions.
Yuxin Hao - One of the best experts on this subject based on the ideXlab platform.
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complicated nonlinear responses of a simply supported fgm rectangular plate under combined parametric and external excitations
Meccanica, 2012Co-Authors: Wei Zhang, Yuxin Hao, Xingying Guo, Lihua ChenAbstract:In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials (FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties are assumed to be temperature-dependent. Based on the Reddy’s third-order plate theory, the governing Equations of motion for the plate are derived using the Hamilton’s principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance, principal parametric resonance-1/2 subharmonic resonance. Based on the Averaged Equation in polar coordinate form, the stability of steady state solutions is analyzed. The phase portrait, waveform and Poincare map are used to analyze the periodic and chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular plate from periodic motion to the chaotic motion.
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chaotic vibrations of an orthotropic fgm rectangular plate based on third order shear deformation theory
Nonlinear Dynamics, 2010Co-Authors: Wei Zhang, Jie Yang, Yuxin HaoAbstract:In this paper, an analysis on the nonlinear dynamics and chaos of a simply supported orthotropic functionally graded material (FGM) rectangular plate in thermal environment and subjected to parametric and external excitations is presented. Heat conduction and temperature-dependent material properties are both taken into account. The material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on the Reddy’s third-order share deformation plate theory, the governing Equations of motion for the orthotropic FGM rectangular plate are derived by using the Hamilton’s principle. The Galerkin procedure is applied to the partial differential governing Equations of motion to obtain a three-degree-of-freedom nonlinear system. The resonant case considered here is 1:2:4 internal resonance, principal parametric resonance-subharmonic resonance of order 1/2. Based on the Averaged Equation obtained by the method of multiple scales, the phase portrait, waveform and Poincare map are used to analyze the periodic and chaotic motions of the orthotropic FGM rectangular plate. It is found that the motions of the orthotropic FGM plate are chaotic under certain conditions.
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periodic and chaotic motions of a simply supported fgm plate with two degrees of freedom
Advanced Materials Research, 2008Co-Authors: Yuxin Hao, Wei Zhang, Jie Yang, Lihua ChenAbstract:In this paper, we use the asymptotic perturbation method to investigate the nonlinear oscillation and chaotic dynamic behavior of a simply supported rectangular plate made of functionally graded materials (FGMs). We assume that the plate is made from a mixture of ceramics and metals with continuously varying compositional profile such that the top surface of the plate is ceramic rich, whereas the bottom surface is metal rich. The Equations motion of the FGM plate with two-degree-of-freedom under combined parametrical and external excitations are obtained by using Galerkin’s method. Based on the Averaged Equation obtained by the asymptotic perturbation method, the phase portrait and waveform are used to analyze the periodic and chaotic motions. It is found that the FGM plate exhibits chaotic motions under certain circumstances.
M H Zhao - One of the best experts on this subject based on the ideXlab platform.
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nonlinear dynamics of composite laminated cantilever rectangular plate subject to third order piston aerodynamics
Acta Mechanica, 2014Co-Authors: M H Zhao, Wei ZhangAbstract:This paper presents the analysis of the nonlinear dynamics for a composite laminated cantilever rectangular plate subjected to the supersonic gas flows and the in-plane excitations. The aerodynamic pressure is modeled by using the third-order piston theory. Based on Reddy’s third-order plate theory and the von Karman-type Equation for the geometric nonlinearity, the nonlinear partial differential Equations of motion for the composite laminated cantilever rectangular plate under combined aerodynamic pressure and in-plane excitation are derived by using Hamilton’s principle. The Galerkin’s approach is used to transform the nonlinear partial differential Equations of motion for the composite laminated cantilever rectangular plate to a two-degree-of-freedom nonlinear system under combined external and parametric excitations. The method of multiple scales is employed to obtain the four-dimensional Averaged Equation of the non-automatic nonlinear system. The case of 1:2 internal resonance and primary parametric resonance is taken into account. A numerical method is utilized to study the bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The frequency–response curves, bifurcation diagram, phase portrait and frequency spectra are obtained to analyze the nonlinear dynamic behavior of the composite laminated cantilever rectangular plate, which includes the periodic and chaotic motions.
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nonlinear vibrations of a composite laminated cantilever rectangular plate with one to one internal resonance
Nonlinear Dynamics, 2012Co-Authors: Wei Zhang, M H ZhaoAbstract:The nonlinear vibrations of a composite laminated cantilever rectangular plate subjected to the in-plane and transversal excitations are investigated in this paper. Based on the Reddy’s third-order plate theory and the von Karman type Equations for the geometric nonlinearity, the nonlinear partial differential governing Equations of motion for the composite laminated cantilever rectangular plate are established by using the Hamilton’s principle. The Galerkin approach is used to transform the nonlinear partial differential governing Equations of motion into a two degree-of-freedom nonlinear system under combined parametric and forcing excitations. The case of foundational parametric resonance and 1:1 internal resonance is taken into account. The method of multiple scales is utilized to obtain the four-dimensional Averaged Equation. The numerical method is used to find the periodic and chaotic motions of the composite laminated cantilever rectangular plate. It is found that the chaotic responses are sensitive to the changing of the forcing excitations and the damping coefficient. The influence of the forcing excitation and the damping coefficient on the bifurcations and chaotic behaviors of the composite laminated cantilever rectangular plate is investigated numerically. The frequency-response curves of the first-order and the second-order modes show that there exists the soft-spring type characteristic for the first-order and the second-order modes.
Lihua Chen - One of the best experts on this subject based on the ideXlab platform.
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complicated nonlinear responses of a simply supported fgm rectangular plate under combined parametric and external excitations
Meccanica, 2012Co-Authors: Wei Zhang, Yuxin Hao, Xingying Guo, Lihua ChenAbstract:In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials (FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties are assumed to be temperature-dependent. Based on the Reddy’s third-order plate theory, the governing Equations of motion for the plate are derived using the Hamilton’s principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance, principal parametric resonance-1/2 subharmonic resonance. Based on the Averaged Equation in polar coordinate form, the stability of steady state solutions is analyzed. The phase portrait, waveform and Poincare map are used to analyze the periodic and chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular plate from periodic motion to the chaotic motion.
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periodic and chaotic motions of a simply supported fgm plate with two degrees of freedom
Advanced Materials Research, 2008Co-Authors: Yuxin Hao, Wei Zhang, Jie Yang, Lihua ChenAbstract:In this paper, we use the asymptotic perturbation method to investigate the nonlinear oscillation and chaotic dynamic behavior of a simply supported rectangular plate made of functionally graded materials (FGMs). We assume that the plate is made from a mixture of ceramics and metals with continuously varying compositional profile such that the top surface of the plate is ceramic rich, whereas the bottom surface is metal rich. The Equations motion of the FGM plate with two-degree-of-freedom under combined parametrical and external excitations are obtained by using Galerkin’s method. Based on the Averaged Equation obtained by the asymptotic perturbation method, the phase portrait and waveform are used to analyze the periodic and chaotic motions. It is found that the FGM plate exhibits chaotic motions under certain circumstances.
