Free linear vibrations of a viscoelastic spherical shell with filler

Purpose. Thin multilayered shells are widely used in aviation, shipbuilding, and mechanical engineering. Recently, interest in the dynamic analysis of shell structures under various load effects has increased. This study examines the effect of moving normal internal pressure on a viscoelastic cylindrical shell. Methods. The viscoelastic medium filling the spherical shell has a significantly lower instantaneous modulus of elasticity than the shell itself. The solution is presented for the free vibrations of the viscoelastic system "shell–filler."An analytical frequency equation in the form of a transcendental equation is derived and solved numerically using the M¨uller method. Results. It has been found that, at certain values of viscoelastic and density parameters, low-frequency natural vibrations occur. These vibrations represent an aperiodic motion since the imaginary part of the natural frequency is large. For viscoelastic mechanical systems, the dependence of damping coefficients on physical and mechanical parameters has been identified. Conclusion. A theory and methods for calculating the complex natural frequencies of vibrations of an elastic spherical inhomogeneity in an elastic medium have been developed. A classification of such vibrations into radial, torsional, and spheroidal modes has been carried out. The problem is reduced to finding those frequencies at which the system of motion equations has nonzero solutions in the class of infinitely differentiable functions.  

spherical shell, filler, oscillations, frequency equation, damping coefficient