Andrew T. Peplow

Surface vibration due to a sequence of high speed moving harmonic rectangular loads

The transmission of vibrations over the surface of the ground, due to high-speed moving, vertical harmonic rectangular loads, is investigated theoretically. The problem is three-dimensional and the interior of the ground is modelled as an elastic half-space or a multilayered ground. The transformed solutions are obtained using the Fourier transform on the space variable. A new damping model in the spatial wavenumber domain, presented in Lefeuve-Mesgouez et al. [J. Sound. Vibr. 231 (2000) 1289] is used. Numerical results for the displacements on the surface are presented for loads moving with speeds up to and beyond the Rayleigh wave speed of the half-space.

Trajectories of a DAE near a pseudo-equilibrium

We consider a class of differential-algebraic equations (DAEs) defined by analytic nonlinearities and study its singular solutions. The main assumption used is that the linearization of the DAE represents a Kronecker index-2 matrix pencil and that the constraint manifold has a quadratic fold along its singularity. From these assumptions we obtain a normal form for the DAE where the presence of the singularity and its effects on the dynamics of the problem are made explicit in the form of a quasi-linear differential equation. Subsequently, two distinct types of singular points are identified through which there pass exactly two analytic solutions: pseudo-nodes and pseudo-saddles. We also demonstrate that a singular point called a pseudo-node supports an uncountable infinity of solutions which are not analytic in general. Moreover, akin to known results in the literature for DAEs with singular equilibria, a degenerate singularity is found through which there passes one analytic solution such that the singular point in question is contained within a quasi-invariant manifold of solutions. We call this type of singularity a pseudo-centre and it provides not only a manifold of solutions which intersects the singularity, but also a local flow on that manifold which solves the DAE.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form

A super-spectral finite element method for sound transmission in waveguides

\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)

NUMERICAL PREDICTIONS OF SOUND PROPAGATION FROM A CUTTING OVER A ROAD-SIDE NOISE BARRIER

(abbreviated

Finite time extinction in nonlinear diffusion equations

\phi = g + K\phi

UNIFORM RADIATION CONDITIONS FOR A SOUND PROPAGATION MODEL

), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated

A Numerical Bifurcation Analysis of the Ornstein-Zernike Equation with Hypernetted Chain Closure

\phi _a = E_a g + K_a \phi _a

Sound propagation over inhomogeneous ground including a sound velocity profile

), obtained by replacing S by

A wave-based finite element analysis for acoustic transmission in fluid-filled elastic waveguides

S_a