The Boundary Integral Method Of Forced Vibration Of Bending Thick Tectangular Plates Under The Concentrated Load

The thick-plate structural theory has a wide range of applications in the areas ofmodern science technology and production. It is not only the theoretical foundation ofdesign and calculation used by the departments which have a lot of protective engineering,unclear engineering applied thick-plate components, but also involved and applied in themodern engineering of aviation, aerospace shipbuilding, etc. At the same time, the forcedvibration of the thick plates is inevitable and important. However, the classical theory ofthick plates obviously can’t meet the design requirements. Therefore, putting forward newapproach to research the problem of thick plates is very necessary.The Reissner theory is the best in the existing various exact theories to solve theproblems of thick-plate components. The basic formulas of bending problems of thickrectangular plate are commonly using Reissner plate theory. This paper applies theboundary integral method to study the forced vibration of thick rectangular plate that isbased on the Reissner theorem. This paper presents the concept of the quasi basic system,applies the reciprocal method to it between the actual system, derives the control equationand the deflection surface equation of the forced vibration of thick rectangular plates in aconcentrated loads with five kinds of boundary conditions, respectively, four edges simplysupported, two opposite edges is simply supported and other two opposite edges fixed,four edges fixed, two adjacent edges fixed one edges free the other edges simplysupported and three edges fixed one edges is free. And by numerical methods, thedeflection surface equation of the theoretical derivation is calculated on the Matlabplatform. While simulating with the Ansys structural analysis software. From thecomparison of the results it can be seen that the accuracy of applying boundary integralmethod to solve the problems of the forced vibration of thick rectangular plates, and thecorrectness of the control equations and deflection surface equations. It’s a new method tosolve the problem of forced vibration of thick rectangular plates.