Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixe...Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixed supports at both ends is established. The nonlinear differential governing equations and boundary conditions are derived by the Hamilton principle. The generalized differential quadrature method(GDQM) and the Newton Raphson method are used to numerically solve the differential governing equations. The influence of flexoelectric effect on the static and the dynamic pull-in characteristics of laminated nano-beams is analyzed. The results of the numerical calculation are in a good agreement with those in the literature when the model degenerated into a nanobeam model without flexoelectric effect. The stacking sequence,length scale parameter l and piezoelectric layer applied voltage V_(p) of the composite will affect the pull-in voltage,frequency and time-domain response of the structure. Given that the flexoelectric effect will reduce the pull-in voltage and dimensionless natural frequency of the structure,the maximum dimensionless displacement at the midpoint of the beam and the period of time-domain response should be increased.展开更多
The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differ...The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.展开更多
The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and bounda...The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy,and expressed in nominal form with the introduced nominal variables.With the application of generalized differential quadrature method(GDQM),both the differential governing equations and boundary conditions are expressed in discrete form,and a set of linear equations are obtained.The bending deflection can be obtained through solving the linear equations,while buckling loads can be determined through solving general eigenvalue problems.The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.展开更多
文摘Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixed supports at both ends is established. The nonlinear differential governing equations and boundary conditions are derived by the Hamilton principle. The generalized differential quadrature method(GDQM) and the Newton Raphson method are used to numerically solve the differential governing equations. The influence of flexoelectric effect on the static and the dynamic pull-in characteristics of laminated nano-beams is analyzed. The results of the numerical calculation are in a good agreement with those in the literature when the model degenerated into a nanobeam model without flexoelectric effect. The stacking sequence,length scale parameter l and piezoelectric layer applied voltage V_(p) of the composite will affect the pull-in voltage,frequency and time-domain response of the structure. Given that the flexoelectric effect will reduce the pull-in voltage and dimensionless natural frequency of the structure,the maximum dimensionless displacement at the midpoint of the beam and the period of time-domain response should be increased.
文摘The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.
基金supported in part by the National Natural Science Foundation of China(No.12172169)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘The modified couple stress theory(MCST)is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory.The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy,and expressed in nominal form with the introduced nominal variables.With the application of generalized differential quadrature method(GDQM),both the differential governing equations and boundary conditions are expressed in discrete form,and a set of linear equations are obtained.The bending deflection can be obtained through solving the linear equations,while buckling loads can be determined through solving general eigenvalue problems.The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.
