FLEXURAL MOTIONS UNDER MOVING CONCENTRATED MASSES OF ELASTICALLY SUPPORTED RECTANGULAR PLATES RESTING ON VARIABLE WINKLER ELASTIC FOUNDATION

Abstract

THE FLEXURAL MOTIONS OF ELASTICALLY SUPPORTED RECTANGULAR PLATES CARRYING MOVING MASSES AND RESTING ON VARIABLE WINKLER ELASTIC FOUNDATIONS IS INVESTIGATED IN THIS WORK IN ORDER TO SOLVE THE FOURTH ORDER PARTIAL DIFFERENTIAL EQUATION GOVERNING THE PROBLEM, A TECHNIQUE BASED ON SEPARATION OF VARIABLES IS USED TO REDUCE THE GOVERNING FOURTH ORDER PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE AND SINGULAR COEFFICIENTS TO A SEQUENCE OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS. THESE EQUATIONS ARE THEN SOLVED USING A MODIFICATION OF THE STRUBLE’S TECHNIQUE AND METHOD OF INTEGRAL TRANSFORMATIONS. NUMERICAL RESULTS ARE THEN PRESENTED IN PLOTTED CURVES. THE RESULTS SHOW THAT RESPONSE AMPLITUDES OF THE PLATE DECREASE AS THE VALUE OF THE ROTATORY INERTIA CORRECTION FACTOR R_O INCREASES AND FOR FIXED VALUE OF R_O, THE DISPLACEMENTS OF THE ELASTICALLY SUPPORTED RECTANGULAR PLATES RESTING ON VARIABLE ELASTIC FOUNDATIONS DECREASE AS THE FOUNDATION MODULUS F_O INCREASES. ALSO, FOR FIXED R_O AND F_O, THE TRANSVERSE DEFLECTIONS OF THE RECTANGULAR PLATES UNDER THE ACTIONS OF MOVING MASSES ARE HIGHER THAN THOSE WHEN ONLY THE FORCE EFFECTS OF THE MOVING LOAD ARE CONSIDERED. THEREFORE, THE MOVING FORCE SOLUTION IS NOT A SAFE APPROXIMATION TO THE MOVING MASS PROBLEM. HENCE, SAFETY IS NOT GUARANTEED FOR A DESIGN BASED ON THE MOVING FORCE SOLUTION. FURTHERMORE, THE RESULTS SHOW THAT THE CRITICAL SPEED FOR THE MOVING MASS PROBLEM IS REACHED PRIOR TO THAT OF THE MOVING FORCE FOR THE ELASTICALLY SUPPORTED RECTANGULAR PLATES ON WINKLER ELASTIC FOUNDATION WITH STIFFNESS VARIATION.