By Christopher C. Fuller, S. J. Elliott, P. A. Nelson
This publication is a spouse textual content to lively regulate of Sound via P.A. Nelson and S.J. Elliott, additionally released by way of educational Press.
It summarizes the foundations underlying energetic vibration keep an eye on and its sensible functions via combining fabric from vibrations, mechanics, sign processing, acoustics, and keep watch over thought. The emphasis of the publication is at the energetic regulate of waves in constructions, the lively isolation of vibrations, using allotted pressure actuators and sensors, and the energetic keep watch over of structurally radiated sound. The feedforward regulate of deterministic disturbances, the lively regulate of structural waves and the energetic isolation of vibrations are coated intimately, in addition to the extra traditional paintings on modal suggestions. the foundations of the transducers used as actuateors and sensors for such keep an eye on concepts also are given an in-depth description.
The reader will locate relatively attention-grabbing the 2 chapters at the energetic 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 rules and useful software of such thoughts are provided right here for either plates and cylinders. the quantity is written in textbook variety and is aimed toward scholars, training engineers, and researchers.
* Combines fabric from vibrations, sign processing, mechanics, and controls
* Summarizes new study within the box
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Additional resources for Active Control of Vibration
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. The boundary condition is thus specified by w(x) = 0 and bw(x) = 0. 2) bx (c) Free end. For a free end, both the shear force and the internal bending moment must disappear.
3) cL As a relevant example let us consider the response of a semi-infinite beam (existing for x~>0) to a harmonic axial force, f ( t ) = F e j°~t, located at x = 0. 4) where S is the cross-sectional area of the beam. 4) is that a positive force is produced by a compression of the beam material. Since the beam is semi-infinite, only positive-going travelling waves will exist. Applying the appropriate boundary condition of continuity of force at x = 0 , the displacement amplitude of the positive travelling wave is found to be F A= ~ .
7) where the time variation has been suppressed. 8) where ILl is the determinant of matrix L. , 1974). The integration path chosen to ensure causality is shown in Fig. 14 and runs just below ] Rekna / I I I x \ ® \ \\ ) /I ® ) / / k n a plane / \ ) z / / f Im kna Fig. 14 Contour of integration for the cylinder input mobility calculation: ®, poles of the integrand function. 56 ACTIVE CONTROL OF VIBRATION the real axis from mOOto 0 and just above the real axis from 0 to oo. To be compatible with the e j°~' time convention, the contour is closed by a semi-circle of infinite radius in the lower k,,a plane.
Active Control of Vibration by Christopher C. Fuller, S. J. Elliott, P. A. Nelson