Fundamental solutions to the transient dynamics of an anisotropic cylindrical Timoshenko shell

Аuthors

Serdyuk D. O.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: d.serduk55@gmail.com

Abstract

In the development of aviation equipment, special attention is devoted to the weight efficiency of the aircraft being designed. Among various factors, advancements in structural materials enable engineers to meet essential design requirements. A prevalent structural material in aviation technology is polymer composite. Developing technologies for creating and utilizing polymer composites, whether through layered or spatial reinforcement techniques, entails addressing numerous challenges, including mathematical ones. A distinct subset of these challenges involves analyzing wave processes in anisotropic thin-walled structures. For instance, in aircraft design, non-stationary impacts on certain fuselage sections are often evaluated. Cylindrical shells serve as fundamental structural components in the fuselages of modern passenger and cargo aircraft. This paper presents novel solutions to elasticity theory, specifically the transient deformation functions for anisotropic, thin, elastic, infinite circular cylindrical shells as described by Timoshenko theory. These foundational solutions are derived using exponential series and integral Laplace and Fourier transforms. The inverse Laplace transform is obtained through residues, while Fourier originals are determined by integrating rapidly oscillating functions. The solutions developed here are applicable to shells made from anisotropic, orthotropic, transversely isotropic, and isotropic materials. These foundational solutions enable the study of wave processes in anisotropic shells within a spatial framework, accounting for the effects of normal pressure with amplitude variation over coordinates and time. The superposition principle allows these fundamental solutions to be applied to scenarios involving multiple load sources, which is demonstrated through a sample calculation. In addition to providing solutions for direct non-stationary problems, these new fundamental solutions are also applicable for other related non-stationary problems, including the propagation of initial disturbances, contact problems, and inverse load identification problems. Moreover, with this solution for an unbounded domain, and by applying the boundary element method or the method of singular boundary conditions, a solution can also be constructed for the side surface of an arbitrary shell.

Keywords:

transient dynamics, anisotropic material, cylindrical shell, integral transformations, generalized functions

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