By Christopher C. Fuller, S. J. Elliott, P. A. Nelson
This booklet is a better half textual content to Active keep an eye on of Sound through P.A. Nelson and S.J. Elliott, additionally released by way of educational Press. It summarizes the foundations underlying lively vibration regulate and its useful purposes via combining fabric from vibrations, mechanics, sign processing, acoustics, and keep an eye on thought. The emphasis of the ebook is at the lively keep watch over of waves in constructions, the energetic 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 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 an eye on ideas also are given an in-depth description. The reader will locate rather fascinating the 2 chapters at the lively keep watch over of sound radiation from buildings: lively structural acoustic keep an eye on. the cause of controlling excessive frequency vibration is frequently to avoid sound radiation, and the rules and functional software of such recommendations are offered right here for either plates and cylinders. the quantity is written in textbook variety and is geared toward scholars, practising 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
First, the procedure for obtaining the resonance frequencies is identical to that used for beams, although it is more complicated due to the form of the three individual coupled shell equations. Second, the resonance frequencies could also be obtained, as in the case of the beam, by the intersection points of the eigenvalues specified by sz~/L with the free dispersion curves as shown in Fig. 12. For illustration purposes the location of the second flexural resonance frequency, ~2, and the first longitudinal resonance frequency, f~, are shown graphically.
1b) . 10) and is the same as for plate motion. Setting f l - 0 results in the equations reducing to those describing the motion of a curved membrane. The variable Pa is again an external forcing function or load with the units of pressure. Unlike the wave equations used to describe the motion of beams and plates, the shell equations consist of three coupled equations for each axis of motion which must be solved simultaneously. Important assumptions used in deriving the Donnell-Mushtari equations are similar to those used previously for thin beams and plates with the additional assumption that the variation in transverse shear stress in the circumferential direction is ignored (Junger and Feit, 1986).
If the excitation frequency is away from the resonance frequencies of the beam, the response will be composed of free waves with wavenumbers +kI that travel backwards and forwards, without constructive reinforcement in the beam system. However, when the excitation frequency is such that ki= kn then the free wavenumber (or wavelength) also corresponds to the natural eigenvalue of the free system and the free waves reflect from the beam terminations INTRODUCTION TO WAVES IN STRUCTURES 43 with constructive interference and reinforce the beam motion.