Abstract
In order to provide knowledge on the intensity of sound transmission through the whole thickness of an isotropic spherical shell its vibrations are resolved on the radius. The vibrations are caused by harmonic sources located on the inner surface. The relative vibration speed of the outer surface, which emits radial waves into the environment, was found. The analytical solution considers the contact interaction between the outer surface of the shell and the surrounding liquid. The method, which directs the Laplace transformations, enables to obtain a general solution of the wave problem for vibrations on the surface. The solution of the natural vibration equation and the expression of relative amplitude at non-resonance and resonance vibrations of the sphere have been investigated with regard to radial and circumferential elastic modulus as well as the relative parameters of surface thickness.
Highlights
The feature of employing dynamic characteristics is of importance in developing test models for anisotropic materials (Rytov 1956; Lasn et al 2011), along with the averaging and homogenization methods (Barski, Muk 2011) for structurally inhomogeneous materials
The quasistatic model yields a relation between the vibration amplitude and the parameter e for these spheres according to Eq (8)
Based on the analysis performed on the sphere the amplitudes of the forced and resonant vibrations were obtained analytically
Summary
The feature of employing dynamic characteristics is of importance in developing test models for anisotropic materials (Rytov 1956; Lasn et al 2011), along with the averaging and homogenization methods (Barski, Muk 2011) for structurally inhomogeneous materials In this relation, it must be noted that the dynamic solutions in the case of a complicated deformation mechanism of materials that takes into account the interaction between elastic, piezoelectric, and dielectric properties require further modifications of material models (Lagzdin et al 2013). It must be noted that the dynamic solutions in the case of a complicated deformation mechanism of materials that takes into account the interaction between elastic, piezoelectric, and dielectric properties require further modifications of material models (Lagzdin et al 2013) They include calculation models for revealing the relation between the eigenfrequency spectrum of anisotropic plates and the piezoelectric effect in the case of different boundary-value problems (Narita 2003). A non-stationary solution, taking into account the theory of functions of a complex variable (Lavrentyev, Shabat 1973), is considered for the case of resonant coincidence of the disturbance and the first frequencies of waves
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