By Christopher C. Fuller, S. J. Elliott, P. A. Nelson
This ebook is a spouse textual content to lively keep an eye on of Sound by way of P.A. Nelson and S.J. Elliott, additionally released through educational Press.
It summarizes the rules underlying energetic vibration keep an eye on and its functional purposes through combining fabric from vibrations, mechanics, sign processing, acoustics, and keep an eye on idea. The emphasis of the booklet is at the energetic regulate of waves in constructions, the lively isolation of vibrations, using dispensed pressure actuators and sensors, and the energetic keep an eye on of structurally radiated sound. The feedforward keep watch over of deterministic disturbances, the energetic regulate of structural waves and the energetic 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 thoughts also are given an in-depth description.
The reader will locate quite fascinating the 2 chapters at the lively regulate of sound radiation from constructions: lively structural acoustic keep an eye on. the cause of controlling excessive frequency vibration is frequently to avoid sound radiation, and the foundations and useful program of such ideas are awarded right here for either plates and cylinders. the quantity is written in textbook sort and is aimed 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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Extra info for Active Control of Vibration
14a,b) and are used when the beam is homogeneous and thus the mass and stiffness does not vary spatially. 3) by ~Pn= sin knx and integrate over the length of the beam L. We then find an expression for the complex amplitudes Wn given by 2 I L F(x) sin k~x dx. 5) demonstrates that in order to solve for the response of the system, we have conveniently expanded the forcing distribution into a series with the system free mode shapes as the basis functions; the magnitude of the modal amplitudes W, are dictated by the shape of the forcing function.
1) where Wm, is modal amplitude and m and n are modal indices. Applying the boundary conditions of zero transverse displacement at the plate edges, shown in Fig. 7, results in expressions for the wavenumber eigenvalues in each coordinate direction that are given by met/a, k,, = net~b, km = m = 1,2,3 .... , n = 1,2, 3 . . . 10) we can solve for the discrete frequencies at which the system resonates in two dimensions. These are given by + ] (1)ran ~-'-~/ L~-~] ~ b I J' where the subscripts m, n denote the (m, n)th mode of vibration.
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'. Substituting the above distributions into the shell equation of motion and setting the disturbance input pressure p~ to zero results in a system of equations which can be conveniently described in matrix form for a particular mode (n, s) as where Ll1 L12 ~ Z31 I Uns 0 /~.
Active Control of Vibration by Christopher C. Fuller, S. J. Elliott, P. A. Nelson