Abstract
Traditional methods for analyzing horizontal vibration of the beam, is to solve the high-order differential equations with deflection as variable. In this paper, the band-linear differential equations expressive with state vector was established, which form is simple and solution is easy to solve, this state vector is a mixed variables ,which is represented with the each other relations of the Load Collection Degree, shear, bending moment and deflection in mechanics of materials, it represents the state of deformation and internal forces in the cross-section of the beam. We solve this equations With precise integration of the method, as a result ,there is a beam of horizontal vibration variable equation of state ,which use of analysing free vibration of horizontal beam and indicating the transfer relations of the state at both ends of beam with the transfer matrix. The frequency equation is established whit Boundary conditions, to solve this equation with the second order method for the orders frequency. With the frequency back substituting into frequency equation, the simple equation group with two unknown quantity is obtained,because of this equation is an independent equations, we can only obtain on the relative state vector on border, and then with this vector substitute into the state equation can be obtained the relative status vector of every point on the beam, which is mode vector.This method can be applied to solving the natural frequency and mode voctor of horizontal vibration of beam with ladder,concentrated quality and flexibility on various boundary conditions a horizontal beam, which is universal, and the corresponding Matlab procedures can easily prepared.With this method to analyzing horizontal vibration, to omitted the tedious process of mathematics to solve differential equations,it is convenient, fast accuracy,to calculate.
Key wors: Precise Integration, Transition Matrix, exponential Matrix, Free Vibrations, Equation Of State.
