The continuous increase in the level and dynamics of improvement and the creation of new promising designs entails the imposition of higher requirements for knowledge of propagation patterns of vibrations in shells. A special place is occupied by the analysis of the propagation of non-stationary oscillations due to the fact that in such problems the variability of the required solution is substantially inhomogeneous in time and coordinates. The stress-strain behaviour of cylindrical shells under the influence of shock loads simulated by impulse is of theoretical and applied interest. The approach to the study of the propagation of forced transient oscillations in the shell is based on the method of the influence function, which represents normal displacements in response to the action of a single load concentrated along the coordinates. For the mathematical description of the instantaneous concentrated load, the Dirac delta functions are used. To construct the influence function, expansions in exponential Fourier series and integral Laplace and Fourier transforms are applied to the original differential equations. The original integral Laplace transform is found analytically, and for the inverse integral Fourier transform, a numerical method for integrating rapidly oscillating functions is used. The convergence of the result in the Chebyshev norm is estimated. As an example, the spatial distributions of the influence function are constructed.
In this work, a new transient function of normal displacements is obtained in a thin elastic anisotropic cylindrical shell of constant thickness with structural features. Structural features form of two sequences in angular direction of weld spots or rivets. Structural features are mathematically described by point boundary conditions of rigid pinching or point boundary conditions of hinge support, accordingly. A load with time variable amplitude and impact boundaries influences on the outer surface of the shell along the normal. Such movement of the shell is considered in the cylindrical coordinate system as connected with the shell axis. Kirchhoff-Love hypothesis are confirmed as a shell model. The solution of this problem can be formed with the help of Green function method and lift compensation method. The required function of transient normal displacements is represented as the sum of integral operators of Green convolution for an infinite shell with functions of current transient load and compensating loads out of point boundary conditions. Compensating loads satisfying to boundary conditions can be found based on the solution of Volterra integral equations of the first kind with the difference kernel. Green function is such kernel. The system solution can be executed including preliminary discretization of compensating time loads. The convolution integrals can be taken numerically with the help of quadrature formula by the method of rectangles. The verification of the method is represented by comparing the solution of specific case with the known solution for a hinged isotropic cylindrical shell.
Строится нестационарная функция прогиба для тонкой бесконечной цилиндрической оболочки постоянной толщины при воздействии на ее боковую поверхность вынужденной нестационарной движущейся нагрузки, распределенной по прямоугольной области. Материал рассматриваемой цилиндрической оболочки принят упругим и анизотропным, обладающим симметрией относительно ее срединной плоскости. Теория тонких упругих оболочек строится на гипотезах Кирхгофа-Лява. Для математического описания мгновенно приложенной нагрузки используются дельта-функции Дирака. A non-stationary deflection function is determined for a thin infinite cylindrical shell of constant thickness under the influence of non-stationary moving pressure. The pressure is distributed over a rectangular region, which belongs to the side surface of the shell. The shell material is elastic, anisotropic, and has symmetry to the median surface. The theory of thin elastic shells is based on the Kirchhoff-Love’s hypotheses. The Dirac delta-functions are used to describe an instantaneously applied pressure.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.