By A. Preumont
This booklet comprises 14 chapters. Chapters 2 and three are dedicated to the dynamics of lively buildings; the open loop move features are derived from the constitutive equations; the dialogue comprises lively trusses with piezoelectric struts, and beams and shells with embedded laminar piezoelectric actuators and sensors. Chapters four and five speak about the virtues of collocated actuator/sensor configurations and the way they are often exploited to enhance energetic damping with assured balance. bankruptcy 6 addresses vibration isolation for one and six d.o.f.. bankruptcy 7 discusses optimum regulate for SISO structures with symmetric root locus. bankruptcy eight discusses the layout tradeoffs for SISO structures within the frequency area, together with the Bode amplitude/phase dating. bankruptcy nine offers a extra basic dialogue of optimum keep an eye on utilizing of optimum keep watch over utilizing the Riccati equation; spillover is tested. Chapters 10 and eleven overview in short the ideas of controllability, observability and balance. bankruptcy 12 discusses the semi-active keep an eye on, together with a few fabrics on magneto-rheological fluids. bankruptcy thirteen describes a number of sensible purposes to lively damping, precision positioning and vibroacoustics, and bankruptcy 14 discusses the energetic damping of cable- buildings.
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Additional info for Vibration Control of Active Structures (Solid Mechanics and Its Applications)
Sample text
The resonance frequency (and therefore the critical frequency ) can be adapted by changing the mass Because the reaction mass is attached to the structure by a spring, the proof-mass actuator has no authority over the rigid body modes (in contrast to reaction wheels). Operation at low frequency requires a large stroke, which is technically difficult. Medium to high frequency actuators (above 40 Hz) can be obtained with loudspeakers (slightly modified with an added mass ) or commercial electrodynamic shakers provided with an appropriate mass at the tip, to lower the natural frequency to the desired value.
For complicated geometries, it may become very large, especially with automated mesh generators. 2) by condensing the degrees of freedom with little or no inertia and which are not excited by external forces. 49), we find the reduced equation which involves only Note that in this case, the reduced equation has been obtained without approximation. 51) applies even if have some inertia (sub-matrix not identically 0) or applied forces. 52). If external loads are applied to , the reduced loads are obtained by equating the virtual work or Finally, the reduced equation of motion reads Usually, it is not necessary to consider the damping matrix in the reduction, because it is rarely known explicitly at this stage.
2), we find that the complex amplitudes of F and X are related by The matrix is the dynamic generalization of the flexibility matrix and is called the dynamic flexibility matrix. 2). 18), we obtain the modal expansion of the dynamic flexibility matrix: where the sum extends to all the modes. 20), we can transform the foregoing result in such a way that the high frequency modes do not appear explicitly in the expansion: The static contribution of the high frequency modes to the flexibility matrix is often called the residual mode; we shall denote it R.