A NEW FEM PROCEDURE FOR TRANSVERSE AND LONGITUDINAL VIBRATION ANALYSIS OF THIN RECTANGULAR PLATES SUBJECTED TO A VARIABLE VELOCITY MOVING LOAD ALONG AN ARBITRARY TRAJECTORY

Abstract

A COMBINED PLATE ELEMENT IS PRESENTED FOR THE ANALYSIS OF TRANSVERSE AND LONGITUDINAL VIBRATIONS OF A THIN PLATE WHICH HOSTS A LOAD MOVING WITH VARIABLE VELOCITY ALONG AN ARBITRARY TRAJECTORY. DEPENDING ON THE ACCELERATION OF THE POINT LOAD ON ITS TRAJECTORY ON THE PLATE SURFACE, THE COMBINED ELEMENT, WHICH IS A COMBINATION OF THE 24 DOF PLATE ELEMENT AND AN EQUIVALENT MASS ELEMENT, REPRESENTS TRANSVERSE (Z) INERTIA, CORIOLIS AND CENTRIPETAL AND LONGITUDINAL (X, Y) INERTIA EFFECTS OF THE MOVING LOAD. IN ORDER TO OBTAIN THE COMBINED ELEMENT, MASS, DAMPING AND STIFFNESS MATRICES OF THE EQUIVALENT MASS ELEMENT REPRESENTING THE MASS ARE FIRST DERIVED BY USING THE RELATIONS BETWEEN NODAL FORCES, NODAL DEFLECTIONS AND DEFLECTION-SHAPE FUNCTIONS OF THE PLATE ELEMENT AND THE INERTIA AND OTHER FORCES OF THE MOVING MASS ACCORDING TO THE GLOBAL COORDINATES ON THE PLATE AND LOCAL COORDINATES ON THE PLATE ELEMENT. THEN, THE OBTAINED PROPERTY MATRICES OF THE EQUIVALENT MASS ELEMENT AND PROPERTY MATRICES OF THE PLATE ELEMENT WERE ADDED TOGETHER IN ORDER TO OBTAIN THE COMBINED PLATE ELEMENT. IN THE FORMATION OF EFFECTIVE OVERALL MATRICES FOR INSTANTANEOUS EQUATIONS OF MOTION OF THE ENTIRE SYSTEM, THE ALL PLATE ELEMENTS WERE ASSEMBLED EXCEPT FOR THE PLATE ELEMENT ON WHICH THE MASS LOCATED; IT WAS CHANGED BY THE COMBINED PLATE ELEMENT. BY SOLVING THE INSTANTANEOUS EQUATION MOTION OF THE SYSTEM AT A TIME POINT, THE INSTANT DYNAMIC RESPONSE OF THE PLATE IS OBTAINED. FOR VERIFICATION, THE SUGGESTED TECHNIQUE WAS APPLIED ON A SIMPLY SUPPORTED BEAM PLATE UNDER THE IMPACT OF A MOVING LOAD, AND AGREEMENTS WERE OBTAINED WITH EXISTING LITERATURE. IN ADDITION, INTENSIVE ANALYSIS AND SIMULATIONS WERE CONDUCTED AT DIFFERENT DIMENSIONLESS MASS RATES (MASS OF THE LOAD/MASS OF THE PLATE) AND ANGULAR VELOCITIES FOR A CIRCULAR MOTION ON A CCCC PLATE, AND THE RESULTS ARE PROVIDED. FURTHERMORE, ANALYSIS RESULTS ARE PROVIDED FOR MOVING FORCE CONDITION WHICH NEGLECTS THE INERTIA, CORIOLIS AND CENTRIPETAL EFFECTS OF THE LOAD, AND IT WAS SHOWN THAT THE MOVING MASS ASSUMPTION GENERATED VERY DIFFERENT RESULTS WITH MOVING LOAD ASSUMPTION ESPECIALLY AT HIGH MASS RATIO AND VELOCITY VALUES. ANALYSIS RESULTS MADE IT CLEAR THAT THE DYNAMIC BEHAVIOUR OF THE PLATE WAS DIFFERENTLY AFFECTED BY AN ORBITING MASS DEPENDING ON ITS MASS RATIO, ORBITING RADIUS AND ANGULAR VELOCITY