| With the rapid development of China ’s economy,various building functions and shapes are constantly changing,and thin plates have become one of the common components in construction projects.Thin plate will produce bending,stability and vibration problems in practical engineering.Among them,the forced vibration problem of plate has always been the research direction of scholars.The forced vibration analysis of thin plate can avoid the damage of structure due to vibration and ensure the safety of structure.Therefore,it is necessary to study the forced vibration of thin plates.In this paper,the reciprocal method of work is applied to derive the deflection surface amplitude equation and boundary execution equation of rectangular thin plate under uniform harmonic load under six boundary conditions : the adjacent edge is simply supported and the adjacent edge is free,the opposite edge is simply supported and one side is fixed and one side is free,the opposite edge is simply supported and the opposite side is free,the adjacent edge is simply supported and the adjacent edge is free with one corner support,one side is simply supported and three sides are free with two corner supports,and the opposite side is fixed and the opposite side is simply supported.The unknowns in the equation are solved by Matlab and brought into the amplitude equation of the deflection surface to obtain the numerical solution of this paper.Then the simulation analysis is carried out by Ansys to obtain the simulation solution.The values obtained by the two methods are plotted into charts for comparative analysis.Finally,the method is applied to the forced vibration problem of a dynamic center structure.The calculation process is simple and programmed,and the calculation results are accurate,which provides a guarantee for the safety of practical engineering.The results of this paper enrich the reciprocal theorem of work to solve the forced vibration problem of the plate. |
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