The Reciprocal Method Is Applied To Solve The Forced Vibration Problem Of Rectangular Plates With Different Boundary Conditions

The various types of plate is one of the most widely application in the engineeringconstruction. The problems of bending, stability, forced vibration are often encountered inengineering practice, among them the problem of forced vibration has been one of theacademic research topics in engineering field, but about the forced vibration problem ofrectangular plates theoretical results are still very lacking. A very complicated high orderpartial differential equation need to be built while use the traditional method to solve theforced vibration problem of rectangular plate, the solving process is complex and theresult is not very accurate. Therefore, the calculating formula which can be widely appliedto the practical engineering need to be established.This paper deduced the control equation of forced vibration rectangular plates.Reciprocal method is applied between the actual system and the basic system, respectivelyderived the deflection equation of fixed on one opposite sides and simply supported onone side and one side of freedom, fixed on one opposite sides and the other are free, twoadjacent edges simply supported while the other two adjacent are free and angular pointsupported, two adjacent edges simply supported and the other two adjacent edges are free,two adjacent edges fixed and the other two adjacent edges are free and angular pointsupported rectangular plates under the point harmonic loads. Using MATLAB solvenumerical solution and comparing it with the ANSYS finite element simulation values, theresults show that the deflection numerical solutions obtained in this paper is of highprecision. This theory method is applied to the practical engineering to solve the forcedvibration problem of under uniform load rectangular plate which is simplified as fixed onone opposite sides and simply supported on one side and one side of freedom. It providessecurity for the structure design. The reciprocal method is applied to research forcedvibration problem of rectangular plate can obtain the deflection surface equation easily,thus enriching the forced vibration rectangular plate engineering solution methods.