Prediction and control of vibrational power transmission between coupled structural systems

Abstract

Vibration transmission from resiliently mounted machines to flexible seating structures has, in the past, often been studied by over-simplified mass-spring models coupled to rigid foundations. It has been recognised that a more detailed model for the study of machine-induced vibration problems, considering resonance responses of the coupled systems as well as the interactions among governing degrees-of-freedom is necessary. This study examines in detail, using the unifying concept of time-averaged vibrational power, the problem of vibration transmission from a machine source to flexible beam and plate-like seating structures via the translational and rotational motions as well as the coupling between these motions, for the case when the seating structures are subjected to co-located simultaneously acting sinusoidal force and moment excitations. The driving point mobility functions of uniform beams and rectangular plates are obtained analytically based on the classical theories for beams and plates in flexural vibration. For linear structures subjected to simultaneously acting force and moment excitations, the driving point coupling mobility functions always exist, except for the special situation when the excitation point coincides with a point of mode shape symmetry of beams and plates with symmetric boundary conditions. These coupling mobility functions contribute to vibrational power components input to the structures as importantly as the direct force and/or moment mobility functions. Because of the contributions from the coupling terms, cancellation of vibrational power components input to the seating structures is possible, which is the basis of the novel vibration control technique proposed and investigated in this study. Based on the mobility coupling approach, the problem of vibration transmission between a multi-point mounted flexible source-isolator-receiver system is also studied in terms of the vibrational power input, transmission and dissipation in the structures. Vibrational power, being a single quantity which embodies both the force and velocity as well as their phase relationship at the point of concern on the structure, offers a better insight into the problem than the conventional force or motion transmissibility analysis. The novel vibration control technique, as mentioned above, is proposed to reduce the unwanted machine-induced vibration levels on the seating structure, at a specific frequency, by controlling the ratio of the applied moment to the applied force via suitably designed force and moment seatings attached to the mounting points. This control technique is most suitable for the case of a low to medium constant speed machine mounted on a flexible seating structure. These theoretical findings have all been validated by laboratory experimental results.

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