Abstract
This article investigates the longitudinal vibrations of a semi-infinite circular cylindrical elastic shell filled with a viscous compressible fluid. It is believed that the vibrations are excited by a suddenly switched on longitudinal displacement at the end. To solve the problem, the refined equations of longitudinal vibrations of a circular cylindrical elastic shell interacting with an internal viscous compressible fluid, previously proposed by the authors, were taken as the main resolving equations. In this case, the lateral surfaces of the shell are considered free from external loads; in addition, considering purely longitudinal vibrations, it can be assumed that the radial displacements of the points of the shell are equal to zero.
Highlights
The dynamic theory of shells is one of the sections of the three-dimensional theory of elasticity, in which such problems of calculating shells are considered, under which the boundary conditions on the lateral surfaces are specified in stresses in the form of external loads
One of these areas is the method of using general solutions in transformations of threedimensional problems of the dynamic theory of elasticity, which was developed in the works of IG Filippov et al [8, 9]
This article is devoted to the study of longitudinal vibrations of a cylindrical shell interacting with an internal viscous compressible fluid
Summary
The dynamic theory of shells is one of the sections of the three-dimensional theory of elasticity, in which such problems of calculating shells are considered, under which the boundary conditions on the lateral surfaces are specified in stresses in the form of external loads. One of these areas is the method of using general solutions in transformations of threedimensional problems of the dynamic theory of elasticity, which was developed in the works of IG Filippov et al [8, 9] In this case, in [8], approximate equations of transverse and longitudinal-radial vibrations of a cylindrical shell were constructed, and in [9], the questions of formulating the boundary conditions to them were discussed. The study of non-stationary interaction of structural elements [17] and, in particular, cylindrical shells [18,19,20] with a viscous fluid are becoming increasingly important In these works, various theories of vibrations of plates and shells interacting with a fluid are presented, and an analysis of their applicability in solving various problems of wave dynamics, including transient deformation processes. This article is devoted to the study of longitudinal vibrations of a cylindrical shell interacting with an internal viscous compressible fluid
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