ANALYSIS AND CONTROL OF VIBRATIONAL POWER TRANSMISSION TO MACHINERY SUPPORTING STRUCTURES SUBJECTED TO A MULTI-EXCITATION SYSTEM, PART I: DRIVING POINT MOBILITY MATRIX OF BEAMS AND RECTANGULAR PLATES

Abstract

The analysis and control of vibration transmission from a machine source to flexible beam- and plate-like supporting structures via the translational and rotational motions as well as the coupling between these motions are studied in these three companions papers. In these studies, co-located simultaneously acting sinusoidal force and moment excitations are assumed to act on the flexible supporting structures and the transmission of vibrational energy into the structures is expressed in terms of the time-averaged vibrational power. The driving point mobility functions of uniform beams and rectangular plates are derived in the first paper. The existence and contribution of the coupling mobility functions in the case of a multi-excitation system give rise to cancellation of vibrational power components. This observation forms the basis of the proposed vibration control technique, which is studied in the second paper. The experimental arrangements for validation of the cancellation of vibrational power components and the proposed vibration control technique with suitably designed force moment seatings are described in the third paper. The proposed vibration control technique is most suitable for the case of a low to medium constant speed machine mounted on a flexible supporting structure.