ON THE TRANSVERSE MOTIONS OF NON-PRISMATIC DEEP BEAM UNDER THE ACTIONS OF VARIABLE MAGNITUDE MOVING LOADS

Abstract

THIS PAPER INVESTIGATES THE FLEXURAL MOTIONS OF NON-UNIFORM DEEP BEAMS RESTING ON VARIABLE ELASTIC FOUNDATION AND TRAVERSED BY HARMONIC VARIABLE MAGNITUDE MOVING LOADS. THE VERSATILE GALERKIN'S METHOD AND THE INTEGRAL TRANSFORM TECHNIQUES WERE EMPLOYED TO TREAT THE COUPLED SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS GOVERNING THE MOTION OF THE VIBRATING SYSTEM. ANALYTICAL SOLUTION WAS OBTAINED FOR BOTH THE TRANSVERSE DISPLACEMENT RESPONSE AND THE ROTATION OF THE NON-UNIFORM DEEP BEAM. ANALYTICAL AND NUMERICAL RESULTS SHOW THAT, AS THE VALUE OF FOUNDATION STIFFNESS K INCREASES THE DEFLECTION PROFLLE OF THE NON-UNIFORM DEEP BEAM DECREASES. IT IS ALSO FOUND THAT THE CRITICAL VELOCITY OF THE DYNAMICAL SYSTEMS INCREASES WITH AN INCREASE IN THE VALUES OF FOUNDATION STIFFNESS K, THEREBY REDUCING THE RISK OF RESONANCE