Padé approximations for low-frequency motion in a pre-stressed compressible elastic layer

2006 ◽  
Vol 33 (5) ◽  
pp. 699-704 ◽  
Author(s):  
L.A. Prikazchikova ◽  
I.A. Alejnikov ◽  
G.A. Rogerson
1981 ◽  
Vol 103 (3) ◽  
pp. 279-284 ◽  
Author(s):  
Y. Bistritz ◽  
U. Shaked

In many problems of control and simulation of a high order system, it is often advantageous to have an appropriate lower order model for approximate design. Introducing the concept of (mixed) Pade´ approximations to Hurwitz polynomials, a novel method for linear time invariant system simplification is established. The method offers many models of the same order that are stable for a stable system, approximate a desired number of the system eigenvalues near to and far from the origin, and emphasize differently the approximation of the low frequency/steady-state and high frequency/transient responses of the system. The presented method is based entirely on a simple unified Pade´ technique.


Geophysics ◽  
1965 ◽  
Vol 30 (2) ◽  
pp. 204-212 ◽  
Author(s):  
J. H. Rosenbaum

The first significant refraction arrival through a thin high‐velocity elastic layer in an elastic medium has been investigated theoretically by means of an asymptotic theory. This first low‐frequency arrival is closely connected with the longitudinal plate wave in the thin layer. When the medium surrounding the layer is a fluid, the signal does not decay exponentially with horizontal distance; when the surrounding medium is a solid, the signal does decay exponentially. A very simple approximate formula for this exponential decay is presented and compared with numerical results of the more rigorous theory. The decay as well as the shape of the signal is dependent upon the contrast in elastic parameters between the plate and the surrounding medium. Higher‐frequency early arrivals, associated with the second symmetric mode, have also been investigated. They exhibit greater exponential decay with horizontal distance than the low‐frequency first arrivals.


2006 ◽  
Vol 11 (2) ◽  
pp. 139-158 ◽  
Author(s):  
Kathy Driver ◽  
Helmut Prodinger ◽  
Carsten Schneider ◽  
J. A. C. Weideman

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
A. Wagner ◽  
M. E. Johnson ◽  
K. Idrisi ◽  
D. P. Bartylla

The heterogeneous (HG) blanket is a passive treatment used to reduce the low frequency transmission of sound through partitions. HG blankets, glued onto a structure, consist of an elastic medium with embedded mass inhomogeneities that mechanically replicate a mass-spring-damper system to reduce efficient radiating structural modes at low frequencies. The elastic layer typically used has sound absorption properties to create a noise control device with a wide bandwidth of performance. The natural frequency of an embedded dynamic vibration absorber is determined by the mass of the inhomogeneity as well as by its effective stiffness due to the interaction of the mass inclusion with the elastic layer. A novel analytical approach has been developed to describe in detail the interaction of the mass inclusions with the elastic layer and the interaction between the masses by evaluating special elastomechanical concepts. The effective stiffness is predicted by the analytical approach based on the shape of the mass inclusions as well as on the thickness and material properties of the layer. The experimental validation is included and a simplified direct equation to calculate the effective stiffness of a HG blanket is proposed. Furthermore, the stress field inside the elastic material will be evaluated with focus on the stresses at the base to assess the modeling of one or more masses placed on top of the elastic layer as dynamic vibration absorbers. Finally, the interaction between two (or more) masses placed onto the same layer is studied with special focus on the coupling of the masses at low distances between them.


1984 ◽  
Vol 144 ◽  
pp. 13-46 ◽  
Author(s):  
N. J. Cherry ◽  
R. Hillier ◽  
M. E. M. P. Latour

Measurements of fluctuating pressure and velocity, together with instantaneous smoke-flow visualizations, are presented in order to reveal the unsteady structure of a separated and reattaching flow. It is shown that throughout the separation bubble a low-frequency motion can be detected which appears to be similar to that found in other studies of separation. This effect is most significant close to separation, where it leads to a weak flapping of the shear layer. Lateral correlation scales of this low-frequency motion are less than the reattachment length, however; it appears that its timescale is about equal to the characteristic timescale for the shear layer and bubble to change between various shedding phases. These phases were defined by the following observations: shedding of pseudoperiodic trains of vortical structures from the reattachment zone, with a characteristic spacing between structures of typically 60% to 80% of the bubble length; a large-scale but irregular shedding of vorticity; and a relatively quiescent phase with the absence of any large-scale shedding structures and a significant ‘necking’ of the shear layer downstream of reattachment.Spanwise correlations of velocity in the shear layer show on average an almost linear growth of spanwise scale up to reattachment. It appears that the shear layer reaches a fully three-dimensional state soon after separation. The reattachment process does not itself appear to impose an immediate extra three-dimensionalizing effect upon the large-scale structures.


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