DYNAMIC RESPONSE UNDER A MOVING LOAD OF AN ELASTICALLY SUPPORTED NON-PRISMATIC BERNOULLI-EULER BEAM ON VARIABLE ELASTIC FOUNDATION

Abstract

:           THE DYNAMIC RESPONSE UNDER A CONCENTRATED MOVING MASS OF AN ELASTICALLY SUPPORTED NON-PRISMATIC BERNOULLI-EULER BEAM RESTING ON AN ELASTIC FOUNDATION WITH STIFFNESS VARIATION IS INVESTIGATED. FOR THE SOLUTION OF THE FOURTH ORDER PARTIAL DIFFERENTIAL EQUATION WITH SINGULAR AND VARIABLE COEFFICIENTS, USE IS MADE OF THE TECHNIQUE BASED ON THE GENERALIZED GALERKIN’S METHOD AND THE STRUBLE’S ASYMPTOTIC TECHNIQUE. THE NUMERICAL RESULTS ARE PRESENTED IN PLOTTED CURVES. THE RESULTS SHOW THAT THE RESPONSE AMPLITUDES OF THE ELASTICALLY SUPPORTED NON-PRISMATIC BERNOULLI-EULER BEAM DECREASE AS THE FOUNDATION MODULLI K INCREASES. ALSO, THE DISPLACEMENTS OF AN ELASTICALLY SUPPORTED NON-PRISMATIC BERNOULLI-EULER BEAM RESTING ON A VARIABLE ELASTIC FOUNDATION, FOR FIXED VALUE OF K, DECREASE AS THE PRE-STRESS N INCREASES. THE RESULTS AGAIN SHOW THAT THE CRITICAL SPEED FOR THE MOVING MASS PROBLEM IS REACHED EARLIER THAN THAT FOR THE MOVING FORCE PROBLEM FOR THE ILLUSTRATIVE EXAMPLES CONSIDERED.