Research On Dynamic Characteristics Of Rectangular Thin Plate Subjected To Moving Load

Basic theory of thin plate vibration,the vibration problem of rectangular plate with concentrated mass is studied by semi-analytical method,the natural frequency and the mode function of the concentrated mass sheet are determined.The vibration problem of rectangular plates with fixedly supported on four sides is studied,the method of solving the frequency and mode of the four-side fixed plate is analyzed,it can determine the natural frequency and vibration mode of rectangular plate with fixedly supported on four sides.In addition,using the Hamiltonian principle and Duhammer integral,the numerical solution of the dynamic response of the thin plate of concentrated mass with concentrated force and impact force is obtained.The motion equation of the thin plate under the action of moving load is deduced,numerical solution of dynamic response of rectangular thin plate under moving load is solved by using by Newmark step integral method.The natural frequency of thin plate vibration with lumped mass is calculated with MATLAB software when the size of concentrated mass,action position and number of action are different,and the natural frequency of the plate vibration when the plate size changes.The vibration modes of a thin plate with concentrated mass and a thin plate without concentrated mass are analyzed and compared under four edges simply supported and four clamped edges,The dynamic response diagram of rectangular thin plate with concentrated mass with four sides simply supported under the concentrated force and four clamped rectangular plates under impact force is presented.The numerical simulation of the vehicle bridge system is made,The numerical simulation of the vibration response of rectangular thin plate under the action of moving mass and moving force is carried out,the effects of moving mass and moving force size,moving mass and moving force velocity,velocity direction of moving mass and moving force on the vibration of thin plate are studied.The dynamic response of rectangular thin plate with lumped mass and massless quadrilateral simply supported under moving load is compared and analyzed,the dynamic responses of rectangular plates with simply supported edges and clamped edges under moving loads are compared and analyzed.The influence of the position of moving track on bridge deck and the vehicle speed on deck vibration are analyzed.It can be seen from the analysis and numerical simulation results:In the case of the frequency and mode of rectangular plates with known boundary conditions,semi-analytical method can be used to calculate the natural frequency and vibration mode of a rectangular plate with arbitrary concentrated mass.Determination of frequencies and modes based on the frequency and mode shapes of four clamped plates,the dynamic response can be calculated of the plates with fixedly supported on four sides under the effect of concentrated mass,and the four side fixed plates with concentrated mass under the impact force,and the four side fixed plates under the action of moving force.