TRANSVERSE MOTIONS OF RECTANGULAR PLATES RESTING ON ELASTIC FOUNDATION AND UNDER CONCENTRATED MASSES MOVING AT VARYING VELOCITIES

Abstract

THIS STUDY CONCERNS THE DYNAMIC CHARACTERISTICS OF A PRESTRESSED ISOTROPIC, RECTANGULAR PLATE CONTINUOUSLY SUPPORTED BY AN ELASTIC FOUNDATION AND CARRYING ACCELERATING MASS M.  CLOSED FORM SOLUTIONS OF THE GOVERNING FOURTH ORDER PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE AND SINGULAR COEFFICIENTS ARE PRESENTED.  FOR THE TWO-DIMENSIONAL PLATE PROBLEM, THE SOLUTION TECHNIQUES IS BASED ON THE DOUBLE FOURIER FINITE SINE  INTEGRAL TRANSFORMATION, THE EXPANSION OF THE DIRAC DELTA FUNCTION IN SERIES FORM, A MODIFICATION OF STRUBLE’S ASYMPTOTIC METHOD AND THE USE OF FRESNEL SINE AND FRESNEL COSINE INTEGRALS. NUMERICAL ANALYSES IN PLOTTED CURVES ARE PRESENTED.   THE ANALYSES REVEAL INTERESTING RESULTS ON THE EFFECT OF STRUCTURAL PARAMETERS SUCH AS FOUNDATION MODULI, ROTATORY INERTIA CORRECTION FACTOR AND PRESTRESSING FORCES ON THE DYNAMIC BEHAVIOUR OF ISOTROPIC RECTANGULAR PLATE UNDER THE ACTIONS OF CONCENTRATED MASSES MOVING AT VARIABLE VELOCITY. IN PARTICULAR IT IS FOUND THAT THE CRITICAL VELOCITY OF THE TRAVELLING LOAD WHICH BRINGS ABOUT THE OCCURRENCE OF A RESONANCE STATE INCREASES AS THE VALUES OF THESE STRUCTURAL PARAMETERS INCREASE. ALSO FOR THE SAME NATURAL FREQUENCY OF THE ISOTROPIC PLATE UNDER MOVING LOAD RESONANCE IS REACHED EARLIER IN THE MOVING MASS SYSTEM THAN IN THE MOVING FORCE SYSTEM CONFIRMING RESULTS IN LITERATURE THAT THE MOVING FORCE SOLUTION CANNOT BE RELIED UPON AS A SAFE APPROXIMATION TO THE MOVING MASS PROBLEM.