Mechanics in Engineering ›› 2011, Vol. 33 ›› Issue (6): 45-49.DOI: 10.6052/1000-0879-lxysj2011-137

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NUMERICAL CALCULATION OF NATURAL FREQUENCY OF TRANSVERSE VIBRATION OF NON-UNIFORM BEAMS

Bo Qian,Huaying Yue   

  • Received:2011-04-06 Revised:2011-08-02 Online:2011-12-15 Published:2011-12-23
  • Contact: Bo Qian

Abstract: Based on the boundary conditions of transverse vibration of non-uniform beams, second order inexplicit-recursive differential equations with variable coefficients about deflection and bending moment are obtained from the fourth order differential vibration equation with variable coefficients by the method of order reduction. By the method of finite difference, the numerical calculation method and its precision for the natural frequency of the transverse vibration of the simply supported non-uniform beams are studied. Examples of theoretical analysis and orthogonal calculation show that the numerical calculation algorithm is very simple, and its precision depends on the number of calculation steps and the vertical variation rates of the gradually changed cross-section and is independent of width and length of beams; the precision of the numerical calculation can be estimated according to a given length or the number of calculation steps and the reasonable length or the number of calculation steps can be determined by a given precision requirement.

Key words: precision

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