Forced Vibration Of Plate Under Harmonic Distributed Moment

With the improvement of social infrastructure,structure types of buildings become increasingly diverse and complex.The current challenge is the dynamic analysis,for thin-slab structure with high speed dynamic load,not only will be affected in the stability but also cause fatigue damage which may directly shorten its service life.The research on thin plate forced vibration problem at home mainly focus on centralized or distributed load,while few on plate subject to harmonic torque load,which is very common in actual situations.This thesis aims to study forced vibration of bending square thin plate with complex boundary conditions under harmonic distributed moment by reciprocal theorem.In this paper,the four-edge simply supported thin plate under unit concentrated harmonic load is selected as the basic system to find a basic solution.Assuming the actual boundary bending moment and displacement and the displacement equation of the bending surface will be obtained after applying the reciprocal theorem between the actual plate and basic system.Then taking the boundary conditions into the equation and the final expression of the curved surface equation will be figured out.After fixing four sides,then fixing the other three sides edges simply supported,and three edges free article on the other side,and fixing the two opposite sides with the two opposite simply supported edges and three edges simply supported,and the other side of three edges simply supported another free edges of rectangular thin plate in the distribution of harmonic torque under the action of the curved surface is derived.The following bending surface equations of the square plate subject to harmonic distributed moment can be obtained: fixing four sides,three sides and one simply supported,and fixing three sides and one side free,and two sides and two simply supported,and fixing three sides simply supported and one,and three sides simply supported and one side free.Finding the solution to the equations with Matlab program and making Ansys simulation at the same time.At last,the author will make an analysis of the actual forced vibration of a certain coal workshop with two fixed adjacent sides,and other two simply supported by harmonic distributed moment.