Superposition Of Partial Waves Research Articles

Partial wave basis adapted to exterior boundary conditions of an elastic plate

An approach to describing normal elastic vibration modes in confined systems is presented. In a standard treatment of the problem, the displacement field is represented by a superposition of partial waves of a general form, e.g., plane waves. The unknown coefficients of superposition are then obtained from the equation of motion and the full set of boundary conditions. In the proposed approach, the functional form of partial waves is chosen in such a way as to satisfy the boundary conditions on exterior surfaces identically, i.e., even if the unknown quantities determined by the remaining constraints are found in an approximation, numerically or analytically. Some examples of solutions for composite elastic plates are discussed to illustrate the efficiency of the approach and its relevance for applications.

Vector beams as the superposition of cylindrical partial waves in bianisotropic media

The exact solutions for arbitrary electromagnetic beams in bianisotropic media are constructed. The solutions are expressed using tensor Fourier transform whose physical meaning is the superposition of partial waves. We use cylindrical partial waves (vector Bessel beams) and derive exact and paraxial solutions for cylindrically symmetric beams in isotropic, bi-isotropic and bianisotropic media. The comparison of the spatial evolution of vector Bessel–Gauss beams in different media is made.

A PC Simulation Of The Propagation Of The Lamb Waves In Pipes

A new method of the simulating of the Lamb waves propagation in pipes was developed. The waves were excited and received by means of the point-form transducers of the longitudinal waves, contacting with the wall of the pipe. Such transducers radiate the antisymmetric Lamb waves of zero order. The wall is like an infinite plate for each direction of the wave propagation, when the diameter of the pipe is much greater than pipe's wall thickness. In this case, the use of beam model for simulating is possible. The wave reaches the receiving point not only directly by the shortest way, but also by rotating around of the circumference of the pipe 1,2,3,. . . times. The resulting wave is a superposition of all partial waves. A transient response corresponding the switching-on of the harmonic exciting voltage may be obtained as a sum of simple trigonometric functions or phasors. On the other hand, this signal and the transient response may be used as the test fbnction/response for calculating of the transient process by not point-form transducers or by modulating of exciting harmonic voltage with more complicated, as step-function, signal. Some interesting phenomena were simulated and tested experimentally. For example, interference was discovered and investigated by one point-form transducer and homogenous propagating media for each ray.

Longitudinal guided wave propagation in a transversely isotropic rod immersed in fluid

The propagation of longitudinal guided waves in fluid-loaded transversely isotropic rods has been investigated based on the superposition of partial waves. The numerical results indicate that fluid loading causes not only significant attenuation via energy leakage into the fluid but also strongly affects the phase velocity of the modes in certain frequency ranges. There is an apparent ‘‘mode switching’’ between the two lowest-order modes when the rod is loaded by a relatively high-density fluid. This phenomenon is analogous to the anomalous topology previously observed in the Lamb wave spectra of low-density water-loaded plates.

Generalized Scattering Theory for One Dimension

If one is interested in computing reflection and transmission coefficients for a plane wave in a medium where the propagation function varies continuously, one may not have at his disposal the usual boundary-condition problem in a sufficiently simple form as to easily yield a solution. In this case, the WKB method is often resorted to. In this paper, another technique is developed that is analogous to the partial-wave method of treating two- and three-dimensional scattering. It is shown that the problem may be cast into an integral-equation form where the first iterated solution corresponds to the weak-scattering Born approximation and which may be used to compute the reflection and transmission coefficients when the properties of the medium vary slightly in an arbitrary way. Further, the reflected and transmitted wave can be viewed as a particular superposition of partial waves that can be obtained by an integral-equation analysis and that yields not only the Born approximation in the case of weak scattering, but also an exact solution in some cases of interest. [This work was supported by the U. S. Office of Naval Research, under contract.]