A semi-analytical method for free vibration of straight orthotropic beams with rectangular cross-sections

Abstract On the basis of the two-dimensional elasticity equations with orthotropy, a semi-analytical method is proposed to analyze free vibration of straight beams with rectangular cross-sections. To this end, the state space method is combined with the differential quadrature method so that state equations with respect to state variables at discrete points are derived. The frequency equation for free vibration of straight orthotropic beams is then formulated. Numerical results are presented and compared with that available in the literature. The present method can be used to analyze either shallow or deep orthotropic beams with arbitrary end conditions.

[1]  M. Levinson,et al.  A new rectangular beam theory , 1981 .

[2]  P.A.A. Laura,et al.  Analysis of Vibrating Timoshenko Beams Using the Method of Differential Quadrature , 1993 .

[3]  C. Shu,et al.  APPLICATION OF GENERALIZED DIFFERENTIAL QUADRATURE TO SOLVE TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS , 1992 .

[4]  N. G. Stephen,et al.  A second order beam theory , 1979 .

[5]  Tarun Kant,et al.  FREE VIBRATION ANALYSIS OF FIBER REINFORCED COMPOSITE BEAMS USING HIGHER ORDER THEORIES AND FINITE ELEMENT MODELLING , 1996 .

[6]  J. N. Reddy,et al.  Analysis of laminated composite plates using a higher‐order shear deformation theory , 1985 .

[7]  C. Bert,et al.  Differential Quadrature Method in Computational Mechanics: A Review , 1996 .

[8]  R. Bellman,et al.  DIFFERENTIAL QUADRATURE AND LONG-TERM INTEGRATION , 1971 .

[9]  Gangan Prathap,et al.  Vibrations of laminated beams using higher-order theory , 1996 .

[10]  Y. C. Das,et al.  Method of Initial Functions in Two-Dimensional Elastodynamic Problems , 1970 .

[11]  K. Chandrashekhara,et al.  Free vibration of composite beams using a refined shear flexible beam element , 1992 .

[12]  Fan Jiarang,et al.  A series solution of the exact equation for thick orthotropic plates , 1990 .

[13]  Hai-chʿang Hu,et al.  Variational Principles of Theory of Elasticity with Applications , 1984 .

[14]  Leon Y. Bahar,et al.  A state space approach to elasticity , 1975 .

[15]  C. Bert,et al.  FREE VIBRATION ANALYSIS OF TAPERED RECTANGULAR PLATES BY DIFFERENTIAL QUADRATURE METHOD: A SEMI-ANALYTICAL APPROACH , 1996 .

[16]  Charles W. Bert,et al.  Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates , 1993 .

[17]  Hiroyuki Matsunaga,et al.  FREE VIBRATION AND STABILITY OF THIN ELASTIC BEAMS SUBJECTED TO AXIAL FORCES , 1996 .