DYNAMIC BEHAVIOUR UNDER MOVING CONCENTRATED MASSES OF SIMPLY SUPPORTED RECTANGULAR PLATES RESTING ON VARIABLE WINKLER ELASTIC FOUNDATION

Abstract

THE RESPONSE OF SIMPLY SUPPORTED RECTANGULAR PLATES CARRYING MOVING MASSES AND RESTING ON VARIABLE WINKLER ELASTIC FOUNDATIONS IS INVESTIGATED IN THIS WORK. THE GOVERNING EQUATION OF THE PROBLEM IS A FOURTH ORDER PARTIAL DIFFERENTIAL EQUATION. IN ORDER TO SOLVE THIS 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. FOR THE SOLUTIONS OF THESE EQUATIONS, A MODIFICATION OF THE STRUBLE’S TECHNIQUE AND METHOD OF INTEGRAL TRANSFORMATIONS ARE EMPLOYED. NUMERICAL RESULTS IN PLOTTED CURVES ARE THEN PRESENTED. THE RESULTS SHOW THAT RESPONSE AMPLITUDES OF THE PLATE DECREASE AS THE VALUE OF THE ROTATORY INERTIA CORRECTION FACTOR RO INCREASES. FURTHERMORE, FOR FIXED VALUE OF RO, THE DISPLACEMENTS OF THE SIMPLY SUPPORTED RECTANGULAR PLATES RESTING ON VARIABLE ELASTIC FOUNDATIONS DECREASE AS THE FOUNDATION MODULUS FO INCREASES. THE RESULTS FURTHER SHOW THAT, FOR FIXED RO AND FO, 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. ALSO, THE ANALYSES SHOW THAT THE RESPONSE AMPLITUDES OF BOTH MOVING FORCE AND MOVING MASS PROBLEMS DECREASE BOTH WITH INCREASING FOUNDATION MODULUS AND WITH INCREASING ROTATORY INERTIA CORRECTION FACTOR. THE RESULTS AGAIN SHOW THAT THE CRITICAL SPEED FOR THE MOVING MASS PROBLEM IS REACHED PRIOR TO THAT OF THE MOVING FORCE FOR THE SIMPLY SUPPORTED RECTANGULAR PLATES ON VARIABLE WINKLER ELASTIC FOUNDATION.