Vibration Analysis of Finite Uniform Structures Using the Harmonic Response Functions of the Infinite Structure

The harmonic response of a uniform infinite structure (e.g. a beam, flat plate, sandwich plate etc) to a point force or moment can usually be found in closed form by solving the corresponding wave equation. The motion of the infinite structure can then be easily understood in terms of the wave motion generated by the source. The harmonic transfer function so obtained can very easily be incorporated in an analysis to study the forced harmonic response of a finite structure to a point force when that structure is on multiple supports having elastic and inertial properties. The method has already been applied by one of the authors to determine the propagation constants of infinite periodic structures This paper shows how the concepts may be applied to finite uniform structures. As an introductory example Euler-Bernoulli beams on multiple irregular supports are studied. Harmonic responses are easily found. Both single-point and multi-point harmonic excitation can be studied wth equal facility The forced response of a single-point-excited infinite periodic beam is also demonstrated, this having application to railway lines on their flexible sleepers. Damping is easily included in the system. An example is also shown of the response of a heavily-damped sandwich piate which is stiffened at regular intervals and is excited by a line force. The superiority of chis method over other methods of analysis described