Research in the field of unsteady interaction of shock waves propagating in continuous media with various deformable barriers are of considerable scientific interest, since so far there are only a few scientific works dealing with solving problems of this class only for the simplest special cases. In this work, on the basis of analytical solution, we study the inverse non-stationary boundary-value problem of diffraction of plain pressure wave on convex surface in form of parabolic cylinder immersed in liquid and exposed to plane acoustic pressure wave. The purpose of the work is to construct approximate models for the interaction of an acoustic wave in an ideal fluid with an undeformable obstacle, which may allow obtaining fundamental solutions in a closed form, formulating initial-boundary value problems of the motion of elastic shells taking into account the influence of external environment in form of integral relationships based on the constructed fundamental solutions, and developing methods for their solutions. The inverse boundary problem for determining the pressure jump (amplitude pressure) was also solved. In the inverse problem, the amplitude pressure is determined from the measured pressure in reflected and incident waves on the surface of the body using the least squares method. The experimental technique described in this work can be used to study diffraction by complex obstacles. Such measurements can be beneficial, for example, for monitoring the results of numerical simulations.
Considerable scientific interest is the development of mathematical models that describe the behavior of materials that are sensitive to deformation rate and can improve the accuracy of analytical calculations of their deformation in the region of noticeable changes of loading rates. Nonetheless, in most works, the problems were solved under the assumption of small displacements (geometrically linear statement of the problem). Meanwhile, in practice, this is not always true and bending of cover can be commensurable with its thickness, this article approximately solves the problem of geometrically nonlinear deformation of a thin elastic plate in quasistatic setting under the action of an infinite normal uniformly distributed load moving along its surface at a constant speed. In the article, the methods of mathematical modeling, the analytical method, as well as the methods of spatial characteristics and bicharacteristics are used. The problem is solved in quasistatic formulation and is reduced to a system of two nonlinear differential equations for deflections of the plate and the stress function, which include the speed of the load as a parameter. The results of methodological calculations are presented; on the basis of these solutions of linear and nonlinear problems, they were compared, and the influence of finiteness of displacements on the critical speeds of the forces was determined. Materials of the article can be useful in study of wave dynamics, aircraft, mechanics and engineering.
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