Wave propagation under vertically excited surface foundation

Recently developed equipment allows measurement of the shear modulus of soil in situ as a function of level of strain. In these field experiments, the excitation is applied on the ground surface using large scale shakers, and the response of the soil deposit is recorded through embedded receivers. The focus of this paper is on the simulation of signals which would be recorded at the receiver locations in idealized conditions to provide guidelines on the interpretation of field measurements. Discrete and finite element methods are employed to model one dimensional and three dimensional geometries, respectively, under various lateral boundary conditions. When the first times of arrival are detected by receivers under the vertical impulse, they coincide with the arrival of the P wave, related to the constrained modulus of the material, regardless of lateral boundary conditions. If one considers, on the other hand, phase differences between the motions at two receivers the picture is far more complicated and one would obtain propagation velocities, function of frequency and depth, which do not correspond to either the constrained modulus or Young's modulus. It is thus necessary to apply some care when interpreting the data from field tests based on vertical steady state vibrations. The use of inverse analysis can be considered as a way of extracting the shear modulus of soil from the field test measurements. © 2008 ASCE.

Oscillator models and collective motion: Splay state stabilization of self-propelled particles

This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spaced particles on a circle. In designing the control law, the particle headings are treated as a system of coupled phase oscillators. The coupling function which exponentially stabilizes the splay state of particle phases is combined with a decentralized beacon control law that stabilizes circular motion of the particles. © 2005 IEEE.

Wave propagation in a slowly-varying duct with mean vortical swirling flow

The propagation of unsteady disturbances in a slowlyvarying cylindrical duct carrying mean swirling flow is investigated using a multiple-scales technique. This is applicable to turbomachinery flow behind a rotor stage when the swirl and axial velocities are of the same order. The presence of mean vorticity couples acoustic and vorticity equations which produces an eigenvalue problem that is not self-adjoint unlike that for irrotational mean flow. In order to determine the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down where a mode changes from cut on to cut off. In this region the amplitude is governed by a form of Airy's equation, and the effect of swirl is to introduce a small shift in the origin of the Airy function away from the turning-point location. The variation of axial wavenumber and amplitude along the duct is calculated. In hard-walled ducts mean swirl is shown to produce much larger amplitude variation along the duct compared with a nonswirling flow. Mean swirl also has a large effect in ducts with finite-impedance walls which differs depending on whether modes are co-rotating with the swirl or counter rotating. © 2001 by A.J. Cooper, Published by the American Institute of Aeronautics and Astronautics, Inc.