Intrinsic oscillations of viscoelastic three-layer truncated conical shell

Conical shells are used in rocket engineering, construction, aircraft engineering and shipbuilding. The purpose of the present work is to carry out a technique, algorithm and programs for obtaining resonant frequencies and waveforms for circular viscoelastic three-layer conical shells. On the basis of the Lagrange variation equation integral-differential equations of own vibrations are obtained. Based on the method of finite elements, a method for solving the problem of eigen-wear oscillations of the truncated three-layer shell with handedly and freely resting edges was carried out. The problem comes down to solving algebraic equations a large order. Obtained a frequency equation with complex output parameters. The proper oscillations of truncated conical shells are investigated, some characteristic features are revealed. Solving the frequency equation by the Muller method, complex roots are determined. It is established that as the elastic modulus of the shell increases, the real and imaginary parts of the natural frequencies increase accordingly. Paying attention to the rheological properties allows you to increase the values of frequency up to 15%.