By S O Reza Moheimani, Dunant Halim, Andrew J Fleming
Vibration is a traditional phenomenon that happens in numerous engineering structures. in lots of situations, vibration vastly impacts the character of engineering layout because it frequently dictates proscribing elements within the functionality of the approach. the traditional remedy is to revamp the approach or to exploit passive damping. the previous can be a high priced workout, whereas the latter is simply potent at better frequencies. energetic keep an eye on suggestions have emerged as workable applied sciences to fill this low-frequency hole. This publication is anxious with the learn of suggestions controllers for vibration regulate of versatile constructions, so that it will minimizing vibration over the total physique of the structure.The e-book introduces a number of versatile constructions reminiscent of beams, strings, and plates with particular boundary stipulations, and explains intimately how a spatially disbursed version of such structures could be got. It addresses the issues of version aid and version correction for spatially allotted structures of excessive orders, and is going directly to expand powerful keep watch over recommendations corresponding to H-infinity and H2 keep watch over layout methodologies to spatially allotted platforms bobbing up in lively vibration regulate difficulties. It additionally addresses different vital subject matters, resembling actuator and sensor placement for versatile platforms, and approach identity for versatile buildings with abnormal boundary stipulations. The textual content includes a number of examples, and experimental effects acquired from laboratory-level equipment, with information of ways related try out beds might be equipped.
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Additional resources for Spatial control of vibration : theory and experiments
Example text
A particular way to solve for such systems is to use the Ritz method (also sometimes called the Rayleigh-Ritz method). In this method, the eigenfunction associated with each mode is approximated by a linear combination of n admissible functions. These functions only need to satisfy the geometric boundary conditions of the system. 94) where cf> G R™ contains the admissible functions and q £ R n is a timedependent vector. We obtain the equation of motion for the system from its kinetic and potential energies.
Traditional performance measures, such as %2 and %oo norms, only deal with point-wise models for such systems. In this chapter, we extend these performance measures to include the spatial characteristics of spatially distributed systems. Another topic that is covered in this chapter is that of model reduction by balanced truncation. The problem of model reduction for dynamical systems has been studied extensively throughout the literature; see, for example, [26, 112, 30]. Here, we address the problem for spatially distributed linear time-invariant systems, following [73].
N. 15. g. a plate with simply-supported boundary conditions. However, exact solutions are usually very difficult to obtain for plates with more general boundary conditions. This is due to the fact that the system eigenfunctions have to simultaneously satisfy the associated eigenvalue problem and boundary conditions. Such eigenfunctions might not exist, hence we have to rely on approximate solutions when dealing with such systems. A particular way to solve for such systems is to use the Ritz method (also sometimes called the Rayleigh-Ritz method).