Yih-Hsing Pao

On the determination of phase and group velocities of dispersive waves in solids

A new technique is developed to determine the dispersion relation and the propagational speeds of waves in dispersive solids. The phase spectrum of a broadband pulse is linearly related to the dispersion relation of the dispersive medium. The method is simpler than the continuous‐wave phase comparison technique. Application is made to measure the phase and group velocities of waves in fiber‐reinforced composite materials and in thin wires. This technique is expected to be applicable to measurements of acoustic or electromagnetic wave speeds in other dispersive media.

Scattering of Plane Compressional Waves by a Spherical Obstacle

The scattering of plane compressional waves by a spherical obstacle in an elastic solid, which was investigated by Ying and Truell is examined further. For a rigid inclusion, the boundary conditions are redefined to take into consideration the motion of the inclusion inside the solid. By a proper limiting process, it is shown that the solutions for a rigid insert, a fluid sphere, a cavity, or an obstacle in a fluid are all derivable from the general results of an elastic inclusion. The rates of energy scattering due to a small rigid obstacle (a«λ) are found to be inversely proportional to the fourth power of wavelength.

Interpretation of time records and power spectra of scattered ultrasonic pulses in solids

Experiments were conducted to investigate the scattering of a wide bandwidth pulse by a fluid‐filled cylindrical cavity in an elastic solid. The pulse amplitude‐time record and the corresponding Fourier power spectra of the scattered pulses are analyzed. The sequence of pulses received by a transducer is identified by applying the theory of geometric acoustics and the pulse arrival times are related to the cavity diameter and the wave speed in the fluid. The power spectrum is interpreted in terms of the resonance of the fluid inclusion, the natural frequencies of which also depend on the size and property of the inclusion. Investigations show that both pulse‐time record and power spectrum can be utilized to detect the size and the wave speed of a fluid inclusion in a solid.

Interactions of Point Defects and Elastic Inclusions

Using a continuum model for crystal defects and inclusions, the interaction energies are calculated for one defect with several inclusions and for several defects with a single inclusion. The special cases of the interaction of a center of dilatation and a doublet with a spherical inclusion are discussed. The center of dilatation may be attracted to or repelled from the inclusion depending on the rigidity of the inclusion and of the matrix material.

Spectral analysis of elastic pulses scattered from two cylindrical cavities in a solid

A solution for the scattering of plane harmonic waves from two traction‐free, cylindrical cavities in an elastic solid is obtained in terms of cylindrical wave functions. The scattered waves are expressed as an infinite sum of orders of scattering, the first order being the usual single scattering approximation and each successive order being expressed in terms of single cylinder scattering coefficients. The exact eigenfunction solution is numerically evaluated for incident plane waves of frequency ranging from 0 to 10 MHz and the power spectrum of the backscattered radial stress amplitudes resulting from a delta‐function incident pulse is calculated for various combinations of cavity radii and separations. Approximate high‐frequency, farfield solutions are derived and compared with the exact solution. Experimental backscattering spectra with broadband ultrasonic pulses are obtained in specimens of aluminum containing two side‐drilled, parallel holes. The experimental results are compared with both the ex...