The forced vibration probjlem of a finite sphere with an exciting source embedded inside it was treated. The source is assumed to oscillate sinusoidally and the complex dilatational modulus is used to describe the motion inside the sphere. If the outer surface of the sphere is restrained from radial displacement, the ratio of the amplitude of a mid-point to the amplitude of a point on the exciting source could be used as an indication of the dilatational properties of the sphere. From the criterion of maximum amplitude ratio in conjunction with the frequency, the dilatational properties of a testing material can be determined. This method can be applied to visco-elastic fluids as well as solids. (Author).

The technique of forced vibration has been applied to the study of the properties of viscoelastic materials. It is found, through the analysis of a free sphere with a harmonic oscillating internal source, that the vibration amplitude ratio of two measuring points is associated with the complex dilatational constants and the complex ratio of the material, a quantity directly related to the complex Poisson's ratio. Therefore, from the criterion of maximum amplitude ratio (i.e. by adjusting the frequency of the source until the amplitude ratio reaches maximum), these properties can be expressed in terms of the amplitude ratios and their frequencies. For the convenience of laboratory testing, two particular amplitude ratios, in conjunction with their frequencies, have been employed for this purpose. Simple expressions are given, relating the properties of the test material to quantities measurable in the laboratory, namely the maximum amplitude ratios and their corresponding frequencies. (Author).

Following previous investigations on methods of determining dynamic mechanical properties of viscoelastic materials employing forced vibration, this report proposes a similar technique for determining the complex Poisson's ratio and the complex dilatation constants. Through the study of forced vibration of a free viscoelastic sphere with an internal harmonic oscillating source, it is found that these properties of the test material are related to the ratio of the vibration amplitude of two measurable points. Thus, when using the criterion of this ratio approaching its maximum, the maximum amplitude ratio, these properties can be expressed in simple relationship with laboratory-measurable quantities, namely the maximum amplitude ratios and their corresponding vibration frequencies. Investigations have been carried out for three sphere sets. (Author).

Wave propagation generated by vibratory load on a homogeneous, isotropic, linear viscoelastic half-space is studied. The effect of a single concentrated force and a group of forces applied over a circular area has been examined and solutions of the displacement functions are presented. In the case of the group forces, the three types of force distribution used by Reissner and Sung were employed. At a great distance (far field) from the applied load, surface displacements are reduced to closed form expressions. A field method based on these results is recommended for determining the complex modulus and the damping property of a viscoelastic material. For areas near the source (near field), numerical procedures were employed to evaluate the integral solution. To facilitate the application, two simplified versions are provided for calculating the center displacement under the load. They both provide good approximation to the integral solution and, most important of all, they speed up the computation enormously. (Author).