This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuato...This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations.The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations,the 3D divergence equation for magnetic induction,and the 3D divergence equation for the electric displacement.The proposed solution involves the exponential matrix in the thickness direction and primary variables’harmonic forms in the in-plane ones.A closed-form solution is performed considering simply-supported boundary conditions.Interlaminar continuity conditions are imposed for displacements,magnetic potential,electric potential,transverse shear/normal stresses,transverse normal magnetic induction and transverse normal electric displacement.Therefore,a layerwise approach is adopted.The results section is composed of an assessment part,where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part.Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios.Tabular and graphical results are presented for displacements,stresses,magnetic potential,electric potential,transverse normal magnetic induction and transverse normal electric displacement.For each presented benchmark,magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.展开更多
An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise in...An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the展开更多
A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D mo...A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D model allows analyses for layered smart plates in both open-circuit and closed-circuit configurations.The secondorder differential equations written in the mixed curvilinear reference system govern the magneto-electro-elastic free vibration problem for multilayered plates.This set consists of the 3D equations of motion and the 3D divergence equations for the magnetic induction and electric displacement.Navier harmonic forms in the planar directions and the exponential matrix method in the transversal direction of the plate are applied to solve the second-order differential equations in terms of displacements.For these reasons,simply-supported boundary conditions are considered.Imposition of interlaminar continuity conditions on primary variables(displacements,magnetic potential,electric potential),and some secondary variables(transverse normal and transverse shear stresses,transverse normal magnetic induction/electric displacement)allows the implementation of the layer-wise approach.Assessments for both load boundary configurations are proposed in the results section to validate the present 3D approach.3D electro-elastic and 3D magneto-elastic coupling validations are performed separately considering different models from the open literature.A new benchmark involving a full magneto-electro-elastic coupling for multilayered plates is presented considering both load boundary configurations for different thickness ratios.For this benchmark,circular frequency values and related vibration modes through the transverse direction in terms of displacements,magnetic and electric potential,transverse normal magnetic induction/electric displacement are shown to visualize the magneto-electroelastic coupling and material and thickness layer effects.The present formulation has been entirely implemented in an academic Matlab(R2024a)code developed by the authors.In this paper,for the first time,the second-order differential equations governing the magneto-electro-elastic problem for the free vibration analysis of plates has been solved considering the mixed mode of harmonic forms and exponential matrix.The exponential matrix permits computing the secondary variable of the problem(stresses,electric displacement components and magnetic induction components)exactly,directly from constitutive and geometrical equations.In addition,the very simple and elegant formulation permits having a code with very low computational costs.The present manuscript aims to fill the void in open literature regarding reference 3D solutions for the free vibration analysis of magneto-electro-elastic plates.展开更多
文摘This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations.The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations,the 3D divergence equation for magnetic induction,and the 3D divergence equation for the electric displacement.The proposed solution involves the exponential matrix in the thickness direction and primary variables’harmonic forms in the in-plane ones.A closed-form solution is performed considering simply-supported boundary conditions.Interlaminar continuity conditions are imposed for displacements,magnetic potential,electric potential,transverse shear/normal stresses,transverse normal magnetic induction and transverse normal electric displacement.Therefore,a layerwise approach is adopted.The results section is composed of an assessment part,where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part.Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios.Tabular and graphical results are presented for displacements,stresses,magnetic potential,electric potential,transverse normal magnetic induction and transverse normal electric displacement.For each presented benchmark,magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.
基金Project supported by the National Natural Science Foundation of China(Nos.10902020 and 10721062)
文摘An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the
文摘A three-dimensional(3D)analytical formulation is proposed to put together magnetic,electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates.The present 3D model allows analyses for layered smart plates in both open-circuit and closed-circuit configurations.The secondorder differential equations written in the mixed curvilinear reference system govern the magneto-electro-elastic free vibration problem for multilayered plates.This set consists of the 3D equations of motion and the 3D divergence equations for the magnetic induction and electric displacement.Navier harmonic forms in the planar directions and the exponential matrix method in the transversal direction of the plate are applied to solve the second-order differential equations in terms of displacements.For these reasons,simply-supported boundary conditions are considered.Imposition of interlaminar continuity conditions on primary variables(displacements,magnetic potential,electric potential),and some secondary variables(transverse normal and transverse shear stresses,transverse normal magnetic induction/electric displacement)allows the implementation of the layer-wise approach.Assessments for both load boundary configurations are proposed in the results section to validate the present 3D approach.3D electro-elastic and 3D magneto-elastic coupling validations are performed separately considering different models from the open literature.A new benchmark involving a full magneto-electro-elastic coupling for multilayered plates is presented considering both load boundary configurations for different thickness ratios.For this benchmark,circular frequency values and related vibration modes through the transverse direction in terms of displacements,magnetic and electric potential,transverse normal magnetic induction/electric displacement are shown to visualize the magneto-electroelastic coupling and material and thickness layer effects.The present formulation has been entirely implemented in an academic Matlab(R2024a)code developed by the authors.In this paper,for the first time,the second-order differential equations governing the magneto-electro-elastic problem for the free vibration analysis of plates has been solved considering the mixed mode of harmonic forms and exponential matrix.The exponential matrix permits computing the secondary variable of the problem(stresses,electric displacement components and magnetic induction components)exactly,directly from constitutive and geometrical equations.In addition,the very simple and elegant formulation permits having a code with very low computational costs.The present manuscript aims to fill the void in open literature regarding reference 3D solutions for the free vibration analysis of magneto-electro-elastic plates.
