The Bogolyubov-Mitropolsky method is used to find approximate periodic solutions to the system of nonlinear equations that describes the large-amplitude vibrations of cylindrical shells interacting with a fluid flow. Three quantitatively different cases are studied: (i) the shell is subject to hydrodynamic pressure and external periodical loading, (ii) the shell executes parametric vibrations due to the pulsation of the fluid velocity, and (iii) the shell experiences both forced and parametric vibrations. For each of these cases, the first-order amplitude-frequency characteristic is derived and stability criteria for stationary vibrations are established Keywords: cylindrical shell, perfect incompressible fluid, nonlinear vibrations, single-frequency method, critical velocity, amplitude-frequency characteristic, stability of vibrations Introduction. The problem of dynamic interaction between elastic cylindrical shells and the fluid they contain attracted the attention of many noted scientists in the field of mechanics. The most significant results in this area have been obtained by V. V. Bolotin [2], A. S. Vol'mir [4], J. Gorachek and I. A. Zolotarev [6], M. A. Il'gamov [7], N. A. Kil'chevskii and his disciples [10], and other authors. Most studies were devoted to the buckling of shells under the nonconservative hydrodynamic forces exerted by the fluid flow. As a rule, two qualitatively different types of buckling were examined: static (divergent type) and dynamic (flutter type). The moment of buckling of one type or another was determined from an analysis of the corresponding linearized equations of shell deformation.Much less attention was given to the dynamic deformation of these shells after buckling, i.e., postbuckling deformation. The complexity of the associated problems is in the necessity of accounting for nonlinear factors such as geometrical nonlinearity and nonlinear damping and of using multidimensional design models of shells [2,4]. The nonlinearities limit the increase of vibration amplitudes after buckling, and the multidimensionality is necessary for the adequate description of nonconservative (or, to put it differently, pseudo-gyroscopic [2]) forces, which are the major cause of buckling. M. Amabili, F. Pellicano, and M. P. Paidoussis [11, 12, etc.] set forth several modern approaches to the analysis of multimode (seven modes) free and forced nonlinear vibrations of cylindrical shells containing a flowing fluid. They also briefly reviewed scientific papers devoted to the stability and large-amplitude vibrations of shells with fluid. In most cases, the nonlinear problems mentioned above were solved by the following scheme:(i) geometrically nonlinear equations of the classical theory (such as the Donnell-Mushtari-Vlasov equations) are used as the original equations describing the motion of shells;(ii) hydrodynamic pressure of the fluid is determined by the linearized theory of potential flow along the shell; (iii) the Bubnov-Galerkin method is used to reduce the dynamic (partial differential) equ...
The paper discusses the results of systematic experimental studies of vibrations and dynamic instability of thin shells of revolution made of laminated composite materials (glassfiber-reinforced plastics). The basic patterns in the dynamic deformation of shells during natural, forced, and parametric vibrations are considered. The damping parameters of natural vibrations are analyzed. The wave deformation modes of shells subject to periodic excitation are studied. The effect of long-term vibratory loading (torsion) on the dynamic characteristics of three-layer glassfiber-reinforced plastic shells is examined Keywords: composite, shell of revolution, frequencies and modes of vibration, dynamic instability, amplitude-frequency characteristic, running wave 1. Introduction. The unusual word "composite" came into use in the materials-science literature in the mid-1950s. It refers to then absolutely new, artificial anisotropic materials consisting of several components with different physical properties. The resulting material has properties qualitatively and quantitatively different from those of the components.The most popular structural composites are materials with oriented high-strength reinforcement (reinforced composites [1,3,4,13,25,26,32,34]) of which so-called glassfiber-reinforced plastics lead in practical use. These materials are produced by combining glass fibers or fabrics with polymeric resin as a matrix. Such materials are advantageous due to high mechanical strength at relatively low weight, corrosion resistance, relatively high thermal resistance, radio transparency, electric stability, etc. An exceptional value of fiberglass is that it makes it possible to influence the parameters of structural members being created. Glassfiber-reinforced plastic materials and structures with prescribed stiffness, weight, and other physical constraints are created in a single process cycle. This is very important because a not very complex process allows creating, in a relatively short time, mechanical objects of quite complex geometry, high strength, and low cost.It is therefore no wonder that the scope of application of fiberglass constantly extends. Nowadays glassfiber-reinforced plastic materials and structural elements are used in aircraft and rocket technology, transport space systems, chemical engineering, automotive industry, shipbuilding, pipeline construction, etc. This list could be extended.The basic stages in the development of the mechanics of composites and structures and results obtained to date are well reflected in many publications ([1, 4, 17, 25, 26, 32, etc.]) and in the multivolume collective monographs Mechanics of Composite Materials and Structural Members [in Russian] (1982-1983) and Mechanics of Composite Materials (1993Materials ( -2003 edited by academician A. N. Guz and issued by the S. P. Timoshenko Institute of Mechanics. Modern areas of research on the mechanics of composite materials and structures are indicated in the reviews [38,[40][41][42].In the former USSR, the S. P. Timoshenko...
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.