Vibration analysis of non-linear beams subjected to a moving load using the finite element method

This paper is concerned with the non-linear vibration of immovably supported variable beams, in which the geometric non-linearity due to the axial force generated by stretching the middle surface is taken into account. When the beam is subjected to a moving load, the dynamic deflections of the beam are computed by using a Galerkin finite element formulation, and the time differential terms are integrated by using the implicit direct integration method. Three types of approximations for solving the non-linear problem are considered, in the first of which both the longitudinal deflections and inertia are considered, with only the longitudinal deflections being considered, and in the second neither the longitudinal deflections nor inertia in the third. The results obtained by using these non-linear models are numerically compared with that obtained by the linear model.

[1]  C. Mei.  comments on “lagrange-type formulation for finite element analysis of non-linear beam vibrations” , 1984 .

[2]  D. Evensen.  Nonlinear vibrations of beams with various boundary conditions. , 1968 .

[3]  G. V. Rao,et al.  Large amplitude free vibrations of tapered beams , 1976 .

[4]  G. Prathap,et al.  Comments on Nonlinear Vibrations of Immovably Supported Beams by Finite-Element Method , 1980 .

[5]  Hidenori Sato.  Non-linear free vibrations of stepped thickness beams , 1980 .

[6]  Toshio Yoshimura,et al.  A finite element method prediction of the vibration of a bridge subjected to a moving vehicle load , 1984 .

[7]  T. K. Varadan,et al.  Lagrange-type formulation for finite element analysis of non-linear beam vibrations , 1983 .

[8]  Klaus-Jürgen Bathe,et al.  Some computational capabilities for nonlinear finite element analysis , 1978 .

[9]  Chuh Mei,et al.  Nonlinear vibration of beams by matrix displacement method. , 1972 .

[10]  G. Venkateswara Rao,et al.  Effect of longitudinal or inplane deformation and inertia on the large amplitude flexural vibrations of slender beams and thin plates , 1976 .

[11]  K. Bathe,et al.  FINITE ELEMENT FORMULATIONS FOR LARGE DEFORMATION DYNAMIC ANALYSIS , 1975 .

[12]  Gangan Prathap,et al.  Galerkin finite element method for non-linear beam vibrations , 1980 .

[13]  B. P. Shastry,et al.  A finite element formulation for the large amplitude vibrations of tapered beams , 1976 .

[14]  R. E. Nickell,et al.  Nonlinear dynamics by mode superposition , 1976 .