OPTIMAL PROPERTIES OF LOCAL DEVICES ON FLEXIBLE STRUCTURES

Abstract eng:
The extraction of energy – and the associated damping – by a local device on a flexible structure depends on appropriate calibration of the device parameters. Too small device damping limits the energy extracted, while too large device damping limits the motion of the device and thereby the extracted energy. A general format is developed for the frequency response of a local device mounted on a flexible structure. Two types of devices are considered: non-resonant devices corresponding to a combination of spring and damper elements, and resonant devices including a mass element generating an internal resonance. A common formulation is set up for devices working via absolute motion or relative motion of two points of the supporting structure. The idea is to express the device motion in terms of a modal expansion of the harmonic structure response. The device force activates the structure and the device, and by equating the structure and device motion a characteristic frequency equation is obtained for the combined system. An additional frequency equation can be obtained for the situation in which the damping element has been locked. In general, the structural motion contains many modes, but when concentrating on a particular resonant mode the terms from the non-resonant modes can be considered approximately equal in the two frequency equations, and can therefore be eliminated by subtraction. The result is a reduced approximate frequency equation in which the properties of the structure are represented in condensed form by the original modal frequency and stiffness of the structure, and the frequency obtained by locking the damping component. For the non-resonant device this results in a cubic equation, while the resonant devices lead to a quartic equation. For both types of devices the resulting equations incorporating the properties of the flexible structure represent a simple equivalent mechanical model: either a model with the damper in series with a spring representing the flexibility of the structure, or in the case of the resonant device a spring-damper coupling of a device mass and an equivalent lumped mass representation of the structure. Both device types lead to explicit solutions for the complex roots and thereby the attainable damping, as well as the optimal device parameters.

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