The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitut...The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation. ne quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.展开更多
Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatia...Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method （GMLSM） and then, discrete equations of motion based on Lagrange＇s equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between the results of the proposed solution and those obtained by other researchers. The results indicate that, although the load inertia effects in beams with higher span number would be intensified for higher levels of moving mass velocity, the maximum values of design parameters would increase either. Moreover, the possibility of mass separation is shown to be more critical as the span number of the beam increases. This fact also violates the linear relation between the mass weight of the moving load and the associated design parameters, especially for high moving mass velocities. However, as the relaxation rate of the beam material increases, the load inertia effects as well as the possibility of moving mass separation reduces.展开更多
The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. T...The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional derivatives.展开更多
This paper presents the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order.Homotopy Perturbation Method(HPM)is used to obtain...This paper presents the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order.Homotopy Perturbation Method(HPM)is used to obtain the dynamic response with respect to unit impulse load.Obtained results are depicted in term of plots.Comparisons are made with the analytic solutions obtained by Zu-feng and Xiao-yan(2007)to show the effectiveness and validation of the present method.展开更多
文摘The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation. ne quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.
文摘Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method （GMLSM） and then, discrete equations of motion based on Lagrange＇s equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between the results of the proposed solution and those obtained by other researchers. The results indicate that, although the load inertia effects in beams with higher span number would be intensified for higher levels of moving mass velocity, the maximum values of design parameters would increase either. Moreover, the possibility of mass separation is shown to be more critical as the span number of the beam increases. This fact also violates the linear relation between the mass weight of the moving load and the associated design parameters, especially for high moving mass velocities. However, as the relaxation rate of the beam material increases, the load inertia effects as well as the possibility of moving mass separation reduces.
基金Project supported by the National Natural Science Foundation of China(Nos.10547124 and 10475055)
文摘The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional derivatives.
文摘This paper presents the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order.Homotopy Perturbation Method(HPM)is used to obtain the dynamic response with respect to unit impulse load.Obtained results are depicted in term of plots.Comparisons are made with the analytic solutions obtained by Zu-feng and Xiao-yan(2007)to show the effectiveness and validation of the present method.
