By James E. Hubbard
This e-book develops and information rigorous layout methodologies and function measures for the keep an eye on of recent clever constructions. The spatially distributed/continuum or disbursed parameter nature of such buildings makes it tough to use sleek lumped parameter keep an eye on philosophy and methods to such designs. whereas there exist an excessive amount of technical literature at the regulate of dispensed Parameter platforms (DPS), there are nonetheless fairly few purposes or functional implementations of the speculation. The paintings provided during this textbook deal with the difficulty of the layout and implementation of dispensed parameter regulate schemes, for clever buildings, which make the most either spatially dispensed sensing and actuation by utilizing sleek shrewdpermanent fabric know-how. The merging of DPS with allotted parameter transducers results in easy, bodily realizable keep watch over procedure designs. this article offers an important reference for working towards execs, scholars and researchers within the quarter of transducer layout utilizing shrewdpermanent fabrics for top functionality shrewdpermanent constructions.
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Additional info for Spatial Filtering for the Control of Smart Structures: An Introduction
23) to be conveniently rewritten as ∇ 4 w + wtt = ∇ 2 V. 26) This governing equation combined with the appropriate boundary conditions may now be used to investigate the design and corresponding behavior of smart structures with distributed transducers. Note that the input V(x,t) appears in terms of its Laplacian as a result of the structures moment curvature relationship. The resulting analysis will be valid for any coordinate system in which ∇ 4 and ∇ 2 are defined. The concomitant boundary conditions are assumed to be homogeneous with respect to both discrete and distributed system elements and with respect to the control input as well.
31) i=1 y b b a Λxx(x) b 0 x a b a Fig. 15 Laplacian of the linearly shaded transducer distribution 42 2 Spatial Shading of Distributed Transducers where the constant ci represents the amplitudes of the component singularity functions and di defines the length scale of the aperture of interest. It was illustrated earlier that singularity functions can be used to describe both discrete and spatially distributed transducers. The distinction between the two now becomes evident in that a transducer is determined to be “distributed” if its spatial shading function (x) is given as a superposition of at least two singularity functions corresponding to a single, irreducible device.
16. Assuming that the film is an induced strain device, the non-dimensional governing equation for such a system is given by Eq. 26). Assuming a degenerate control distribution which is separable in space and time, a spatially uniform control distribution as illustrated in Fig. 32) where lx and ly are the non-dimensional lengths of the sides parallel to the x and y axes respectively. The control input to the smart structure manifest itself as the Laplacian of the control distribution and is given by Fig.
Spatial Filtering for the Control of Smart Structures: An Introduction by James E. Hubbard