Study Of Dynamic Characteristic Of Thin Plate With Any Number Of Piont Masses Based On Analytical And Numerical Combined Method

Many structures can be simplificated to thin plate with point masses in engineering, therefore, the vibration characteristic of thin plate with point masses need to be studied for the purpose to control it.The dynamic characteristics of thin plate with any number of point masses are studied with a new method namely analytical and numerical combined method (ANCM) in this paper. This method is that the inertia force of the concentrated masses is considered as the external exciting force which acts on thin plate , and the characteristic value equation of thin plate with any concentrated masses is obtained by using mode superposition technique, the natural frequency and modes are obtained by solving this equation. Firstly the frequency and modes formulae of rectangle thin plate of simply supported on four sides, fixedly supported on four sides, simply supported on two sides and fixedly supported on two sides with any concentrated masses are obtained based on ANCM. Then, the dynamic formulas of rectangle thin plate of simply supported on four sides, fixedly supported on four sides, simply supported on two sides and fixedly supported on two sides with any concentrated masses subject to point forces are given.Finally, the numerical simulation is executed based Matlab, and frequency and mode shapes are calculated with finite element method for error analyses. According to theoretical analysis and the result of numerical simulation, the conclusions are as follows:After the natural frequency and modes of uniformity thin plate with certain supported are known, the natural frequency and modes of this plate with any concentrated masses can be calculated based on ANCM.After the natural frequency and modes of thin plate with any concentrated masses are obtained, the dynamic response of thin plate with any concentrated masses subject to point forces can be calculated by ANCM.The frequency of complicated thin plate with any concentrated masses can be computed by ANCM, and the time cost is less than FEM.