The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton＇s principle. The viscoelastic ma...The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton＇s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscos- ity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method （DQM） is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.展开更多
This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's ...This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant TPBVPs.Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series.Hence,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are employed.An efficient algorithm is also presented,which has low computational complexity and a fast convergence rate.Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP.The results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.展开更多
Based on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon ...Based on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes(SWCNTs).The material properties of simply supported functionally graded carbon nanotube-reinforced(FGCNTR)plates are assumed to be graded in the thickness direction.The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture.Two types of symmetric carbon nanotubes(CNTs)volume fraction profiles are presented in this paper.The equations of motion and related boundary conditions are derived using the Hamilton’s principle.A semianalytical solution composed of generalized differential quadrature(GDQ)method,as an efficient and accurate numerical method,and series solution is adopted to solve the equations of motions.The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method.The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles,geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates.The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11202136,11372195,11502147,and 11602146)
文摘The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton＇s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscos- ity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method （DQM） is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.
文摘This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant TPBVPs.Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series.Hence,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are employed.An efficient algorithm is also presented,which has low computational complexity and a fast convergence rate.Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP.The results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.
文摘Based on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes(SWCNTs).The material properties of simply supported functionally graded carbon nanotube-reinforced(FGCNTR)plates are assumed to be graded in the thickness direction.The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture.Two types of symmetric carbon nanotubes(CNTs)volume fraction profiles are presented in this paper.The equations of motion and related boundary conditions are derived using the Hamilton’s principle.A semianalytical solution composed of generalized differential quadrature(GDQ)method,as an efficient and accurate numerical method,and series solution is adopted to solve the equations of motions.The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method.The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles,geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates.The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.
