Non-axisymmetric problems of unsteady deformation of cylindrical shells with filler

¹ Urgench State University, Dept.of Construction, 220100 Urgench, Uzbekistan
² Bukhara Institute of Natural Resources Management, Dept.of Mathematics & natural sciences, 105009 Bukhara, Uzbekistan
³ Tashkent Chemical Technology Institute, Dept.of Mathematics, 100011 Tashkent, Uzbekistan

Abstract

Circular cylindrical shells, as structural elements, have found wide application in various fields of mechanical engineering. Thin-walled layered shells have also found wide application as components in underwater objects, air and space vehicles and in many other engineering structures. The aim of this work is to study the action of a non-axisymmetric moving wave of normal pressure on a cylindrical shell interacting with an ideal compressible fluid. The problem statement is given, solution methods are developed, and numerical results are obtained for new problems of stationary deformation of infinitely long viscoelastic cylindrical shells on a viscoelastic foundation when a non-axisymmetric normal pressure wave moves along the shell axis with up to resonant velocity. As an example, considered the action of a non-axisymmetric moving wave of normal pressure on a cylindrical shell interacting with an ideal compressible fluid. The solution methods are based on the joint application of the integral Fourier transform along the axial coordinate and the expansion of all given and desired values into Fourier series along the angular coordinate. An efficient algorithm for the joint calculation of integrals and Fourier series has been developed and implemented on a computer. It has been established that paying to attention the viscoelastic properties of the shell material reduces the deflections by 10–15%, and also makes it possible to evaluate the damping capabilities of the system.