THE RESPONSE OF INFINITE PERIODIC BEAMS TO POINT HARMONIC FORCES - A FLEXURAL WAVE ANALYSIS

An exact analysis is presented of the vibration response of an infinite beam on periodic supports, subjected to a transverse harmonic point force. The supports must all be the same and can be simply supported or be generally linear with elastic, inertial and dissipative properties. The total response is found as the sum of the flexural wave fields generated by the applied force and the infinite number of support reaction forces and moments. The concept of phased arrays of forces and moments is used to sum the support-generated wave fields. This utilizes the propagation constants of free-wave motion in the periodic beam. Equations for either four, six or eight of the unknown complex reactions (depending on the nature of the supports) are set up and solved numerically. This finite number is sufficient to permit the calculation of the beam displacement at any point and of all the other reactions. Some computed values of the beam direct receptance are presented to demonstrate its variation with forcing frequency, the effect of the location of the excitation force and the effect of changing the elastic properties of the supports. © 1991.