FINITE ELEMENT FORMULATION AND ANALYSIS OF A FUNCTIONALLY GRADED TIMOSHENKO BEAM SUBJECTED TO AN ACCELERATING MASS INCLUDING INERTIAL EFFECTS OF THE MASS

Abstract

THIS STUDY DESCRIBES A NEW FINITE ELEMENT METHOD THAT CAN BE USED TO ANALYSE TRANSVERSE AND AXIAL VIBRATIONS OF A FGM BEAM UNDER AN ACCELERATING / DECELERATING MASS. THE COMBINED DIFFERENTIAL EQUATIONS OF THE FGM BEAM ARE OBTAINED USING FIRST ORDER SHEAR DEFORMATION THEORY (FSDT). IN THESE EQUATIONS, THE INTERACTION TERMS OF MASS INERTIA ARE DERIVED FROM SECOND-ORDER EXACT DIFFERENTIAL OF DISPLACEMENT FUNCTIONS WITH RESPECT TO MASS CONTACT POINT. THE FGM BEAM IS MADE OF TWO DIFFERENT MATERIALS, WHICH VARY IN THICKNESS WITH A POWER LAW. BY ADDING THE EFFECTS OF NATURAL AXIS SHIFT AND MASS INERTIA, THE PROPOSED METHOD CAN BE USED WHEN THE DYNAMIC BEHAVIOUR OF FGM TIMOSHENKO BEAMS IS ANALYSED IN TRANSVERSE AND AXIAL DIRECTIONS DEPENDING ON THE INTERACTION WITH THE ACCELERATION OF MOVING LOADS. AFTER CONFIRMING THIS WORK WITH LITERATURE STUDIES, NEW INVESTIGATIONS AND FINDINGS WERE PRESENTED FOR BOTH MOVING LOAD AND MOVING MASS ASSUMPTIONS. IN ADDITION, THE ASSUMPTIONS OF TIMOSHENKO BEAM (TBT) AND EULER BERNOULLI BEAM THEORY (EBT) WERE COMPARED FOR FGM BEAMS AT VARIOUS SPEEDS AND ACCELERATIONS OF MOVING MASS.