###
Axisymmetric problem of unsteady interaction of acoustic pressure waves with elastic shell of revolution

Rabinsky LN, Zhavoronok S.I.

#### Abstract:

The task of unsteady interaction of anisotropic elastic membrane with a weak shock wave propagating in the acoustic environment. In addressing the impact of the machine functions, based on the fundamental solutions of non-stationary problem of diffraction of acoustic environment-related problems of acoustics and elasticity is used to smooth convex surfaces. To approximate construction of the fundamental solution is applied the hypothesis of a thin layer. Pressure on the surface of the shell is made up of three components – the pressure of the incident acoustic wave, the wave reflected fixed obstacle and wave emitted by a moving shell. The last two components are determined on the basis of integral equations of convolution type with the fundamental solution speed of the incident wave and the normal speed of the shell surface. The decision related to the initial boundary value problems for partial differential equations that describe the motion of the acoustic environment, and the elastic membrane, thus reduced to the solution of the initial boundary value problem for integro-differential equations of motion of the shell. A model of an anisotropic membrane, which takes into account the normal and shear deformation of the cross. shell model is based on an approximate three-dimensional theory of shell N-th order. An example of the solution of axisymmetric problem of diffraction of an acoustic wave in the isotropic membrane in the shape of a paraboloid of revolution. For the numerical integration of the equations of motion are approximated by discrete analog. Results spatiotemporal dependence for the displacement and velocity of the shell.

5