Vibration Analysis And Control Of Rectangular Thin Plate Subjected To Moving Masses

The thin plate structure is widely used in engineering fields such as bridges,ship decks and offshore platforms.Due to its light and thin structural features,the thin plate structure is easy to be generated vibration under the action of external excitation.And it will be caused resonance under certain special conditions,which will be very dangerous.These vibrations are very unfavorable for engineering applications.Because of the vibrations,the function of the instrument on the thin plate may be impaired.And the security of the structure may be damaged,too,which will affect the people's normally use.Therefore,it is of important practical significance to study the vibration characteristics and vibration control research of the rectangular thin plate structure under the action of moving masses.This article has carried out a variety of research on the above issues.The vibration characteristics of rectangular thin plates with the SFSF(S:Simple support,F:Free)boundary under the action of moving masses are studied.Based on the modal superposition method,the basic differential equations of thin plates are discretized into governing equations with finite modal coefficients as generalized coordinates.Then the wilson-? integral method is used to solve the equation,and the response of rectangular thin plates under moving masses is obtained.Based on this,the effects of the masses of the moving masses,the velocity,the spacing between the masses,and the inertial force of the moving masses perpendicular to the plane of the board on the response are studied.It shows,that the larger the moving masses,the larger the amplitude of response;that as the masses spacing ratio changes,a series of formants will appear;that the change in velocity will change the position of the formant;that in addition,the inertial force of the moving mass perpendicular to the plane of the board has little effect on the response when the speed is small,and decreases the response when the speed is large.The vibration characteristics of a rectangular stiffened thin plate with the SSSS boundary condition under moving load are studied.The Hamiltonian principle is used to derive the dynamic equation of the stiffened plate.Then the Galerkin method is used to approximate to the modal solution of the dynamic equation,and the response is obtained by the wilson-?method.By comparing the influence of different response of the center point of the thin plate which has different number of ribs,it is concluded that for the case of adding same number of ribs in single direction,the maximum value of the response is smaller when the ribs transversally;while in the bidirectional ribs plate case,the maximum value of the center point response of the thin plate with fewer transverse ribs and less longitudinal ribs is smaller.The passive control of the vibration of a rectangular stiffened plate with the SSSS boundary under moving load is studied.According to the second equation of Lagrange,the governing equation is derived.And the parameters of the vibration absorber are designed by the optimal design conditions.The response is obtained by the wilson-? method.By comparing the influence of different masses ratio of absorbers to the plate on the response of the thin plate,it is concluded that when the mass ratio of the vibration absorber is too large or too small,the control effect is not good,while the medium one is a better choice;by comparing the effects of the response of the stiffened plates which have been installed multiple absorbers to control the first few modal vibration,it is concluded that the vibration damping effect of multiple absorbers is better than that of a single vibration absorber.The active control of the vibration of the rectangular thin plate with a single moving mass is studied.The equation of state of the system is derived from the dynamic equation of the thin plate.Based on the state feedback control theory of linear system,the MATLAB software is used to carry out numerical simulation analysis of thin plate active control according to the state equation of the system.The responses of the center point of the thin plate are compared when the mass moves at different speeds under controlled and uncontrolled conditions.It shows that when the weighting coefficient k takes the value of 10000,the whole control effect is better.