Active Control of Vibration by Christopher C. Fuller, S. J. Elliott, P. A. Nelson

By Christopher C. Fuller, S. J. Elliott, P. A. Nelson

This e-book is a significant other textual content to lively regulate of Sound by means of P.A. Nelson and S.J. Elliott, additionally released through educational Press.
It summarizes the foundations underlying lively vibration regulate and its functional purposes by means of combining fabric from vibrations, mechanics, sign processing, acoustics, and keep an eye on idea. The emphasis of the booklet is at the lively regulate of waves in buildings, the lively isolation of vibrations, using dispensed pressure actuators and sensors, and the energetic keep an eye on of structurally radiated sound. The feedforward regulate of deterministic disturbances, the lively regulate of structural waves and the lively isolation of vibrations are coated intimately, in addition to the extra traditional paintings on modal suggestions. the rules of the transducers used as actuateors and sensors for such regulate recommendations also are given an in-depth description.
The reader will locate relatively fascinating the 2 chapters at the lively keep an eye on of sound radiation from constructions: energetic structural acoustic regulate. the cause of controlling excessive frequency vibration is usually to avoid sound radiation, and the foundations and functional program of such options are provided right here for either plates and cylinders. the quantity is written in textbook type and is geared toward scholars, training engineers, and researchers.
* Combines fabric from vibrations, sign processing, mechanics, and controls
* Summarizes new examine within the box

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And branch order (s = 1,2, 3 .... ) respectively. The modal order n can be seen to correspond to the number of radial nodal lines, while s indicates the order of particular eigensolutions n=l n=O \ t f"-~ / t Fig. 10 I \ I n=2 / Xln=3 Circumferential mode shapes of an infinite thin cylinder. 50 ACTIVE CONTROL OF VIBRATION for a fixed n. Typical lower order circumferential mode shapes are shown in Fig. 10. A complete solution should use a circumferential distribution with a form e ±j"° which can result in rotating angular distributions or 'spinning modes'.

Is the resonance frequency of the nth mode. ~ f, J 2re I ~- Beam (b) I-- -E I== z //I ! I Frequency, co Fig. 5 Relationship between eigenvalues and free wavenumbers for two differing finite beam systems. 39 I N T R O D U C T I O N TO W A V E S IN S T R U C T U R E S Model lo-2 V Mode 3 Mode 1 A ~. / , " , ,'-2x 10-3 2 •~o 3 " 10 - 4 E ~ rn 0-5 ~o-6 _ I I I 10 I I I I I[ I 100 I t I t I t I I 1000 Frequency (Hz) Fig. 6 Frequency response function and mode shapes of a simply supported beam. 6 shows an example frequency response function (FRF) for a beam of length L = 0 .

5) then becomes W~ = - E I L ( k 4 - k} ) I c 6(x - xi)sin knx dx. 9) which leads to W~= sin knxi ~ . 10) 42 ACTIVE CONTROLOF VIBRATION The total response of the beam including the harmonic time component is then given by w(x,t) = 2F ~ ElL ~= sin k~xi sin k~x ejO~, . 14) manipulated to give k 4 = m'to2JEl and k}= m'to2/El where m' is mass per unit length of the beam. 12) where ton is the natural frequency of the nth mode and M is the total mass of the beam. When kn= kI, or to = ton, the excitation frequency corresponds to the resonance frequency of the nth mode of the beam, and as expected the system response approaches infinity.

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