The Research About Deflection Problem Of The Deep Beams Under The Forced Vibration

The forced vibration problem of deep beams has always been one of the forefrontengineering research topic. But the problems to be solved are still exist.There are lack oftheoretical writings with engineering examples. In order to adapt to the needs of modernengineering,the forced vibration problem of deep beams has become a imperative task ofscientific research. Due to the shape of deep beams are huge, internal forces in the systemare complex,the establishment of the simple formulas about the forced vibration theory ofdeep beams has profound theoretical significance and practical value。In this paper, the equilibrium differential equations is first set up which is on the basisof considering the section rotation of deep beam, shear deformation of adjacent crosssection and the transverse stress. And then the control equation of the forced vibrationproblem of deep beams was established. At the same time, using the reciprocal theorymethod to solve the basic system and the basic solutions in the form of sine series andpolynomial. The deflection equations of the deep beams under simple harmonic load withthree different boundary conditions such as two edges simply supported, one edge fixed,the other edge simply supported and two edges fixed were solved applying the reciprocaltheory method between the actual system and the basic systems. Using the software ofMatlab to work out the numerical solution of the deflection of deep beams which are highaccuracy solution according to the comparison with the ANSYS finite element simulationvalue. Research suggests that the control equation and the deflection equation of theforced vibration of deep beams are correct. Application of the reciprocal method to solvethe forced vibration problem of the deep beam broke through the shackles of thetraditional method, the deflection equation of the forced vibration can more easily to beget, which rich the engineering solution method of the forced vibration problem of deepbeams.