By Christopher C. Fuller, S. J. Elliott, P. A. Nelson
This booklet is a spouse textual content to energetic keep an eye on of Sound by way of P.A. Nelson and S.J. Elliott, additionally released via educational Press.
It summarizes the rules underlying lively vibration regulate and its useful purposes via combining fabric from vibrations, mechanics, sign processing, acoustics, and keep watch over conception. The emphasis of the e-book is at the lively keep watch over of waves in constructions, the energetic isolation of vibrations, using allotted pressure actuators and sensors, and the lively regulate of structurally radiated sound. The feedforward keep an eye on of deterministic disturbances, the energetic regulate of structural waves and the energetic isolation of vibrations are lined intimately, in addition to the extra traditional paintings on modal suggestions. the foundations of the transducers used as actuateors and sensors for such keep watch over ideas also are given an in-depth description.
The reader will locate really attention-grabbing the 2 chapters at the energetic keep watch over of sound radiation from buildings: lively structural acoustic keep an eye on. the cause of controlling excessive frequency vibration is usually to avoid sound radiation, and the rules and sensible software of such suggestions are awarded right here for either plates and cylinders. the amount is written in textbook variety and is aimed toward scholars, working towards engineers, and researchers.
* Combines fabric from vibrations, sign processing, mechanics, and controls
* Summarizes new examine within the box
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Additional resources for Active Control of Vibration
In many cases of interest the plate is excited by input moments. 5), M ( x , y) the disturbance moment distribution has the units of moment per unit length per unit area of plate. 6b) ~2 W M~y = -EI(1 - v) . 7a) " +~. 1). 48 ACTIVE C O N T R O L OF VIBRATION An important forcing function associated with piezoelectric distributed actuators is a line moment around an axis located at Xl. In this case the plate equation is written in moment form as Ox2 +2 ~. OxOy . ph . Ot2 . 8) where t~' (-) is the derivative of the Dirac delta function with respect to its argument and the moment amplitude M has units of moment per unit length.
In order that the resulting motion be determined, it is first necessary to apply the appropriate boundary conditions in order to derive the free response. Commonly encountered simple boundary conditions are as follows. (a) Simply supported end. In this case the end of the beam is free to rotate but is constrained to have zero displacement and moment. The boundary condition is thus specified by w(x) = 0 and ~2w(x) Ox2 = 0. 1) at the constraint location. (b) Clamped end. For a clamped boundary condition, both the displacement and rotation are constrained to zero.
12). Also shown are the mode shapes corresponding to the peaks, or resonance points in the FRF. 15). An interesting characteristic of beam behaviour is that the resonance frequencies become spaced further apart with increasing mode number. This is also apparent from Fig. 5 and is due to the dispersive nature of flexural waves. 8. Boundary conditions other than those for a simply supported beam will result in additional near-field motion located near the discontinuities. e. they will not significantly influence the resonance frequencies and characteristic functions of the system).
Active Control of Vibration by Christopher C. Fuller, S. J. Elliott, P. A. Nelson