Nonlinear vibrations of cylindrical shells filled with a fluid and subjected to longitudinal and transverse periodic excitation

Abstract

The paper proposes an approach to studying the nonlinear vibrations of thin cylindrical shells filled with a fluid and subjected to a combined transverse-longitudinal load. Methods of nonlinear mechanics are used to find and analyze periodic solutions of the system of equations that describes the dynamic behavior of the shell when the natural frequencies of the shell and the frequencies of both periodic forces are in resonance relations Keywords: elastic cylindrical shell, ideal incompressible fluid, combined load, amplitude-frequency response, stabilityIntroduction. The flexural vibrations of thin cylindrical shells filled with a fluid are studied in a geometrically nonlinear formulation in a great many publications. Such studies are reviewed in, e.g., [6, 9-11, etc.]. Most studies deal with dynamic problems for fluid-filled shells subjected to either radial (transverse) or axial (longitudinal) force. However, in real operation conditions, shell structures conveying a fluid (such as segments of pipelines) are quite often subjected to combined loading, i.e., a combination of longitudinal and transverse periodic forces. Therefore, of practical and scientific interest is to study the dynamic behavior of shells filled with a fluid and subjected to a combined vibratory load. The superposition principle fails here because of the nonlinearity of such a problem formulation: the response of the dynamic shell-fluid system to a combination of longitudinal and transverse periodic loads is not the sum of the responses of this system to the individual loads. Here we may expect qualitatively new nonlinear effects that were not observed in the partial problems of forced [7,[10][11][12][13][14]18] or parametric [2,4,11,16] vibrations of shell-fluid objects.The present paper sets out to develop a method and to apply it to study the nonlinear deformation of elastic cylindrical shells filled with a fluid and subjected to longitudinal-and-transverse periodic excitation. We will primarily analyze the dynamic behavior of filled shells in the worst (with respect to dynamic stress) case where the natural frequencies of the shell-fluid system are in resonance relations with the frequencies of both external periodic forces. The results obtained in the general case will be compared with those obtained in the partial cases where either only longitudinal or only transverse load acts. Nonlinear Equations of Motion of a Fluid-Filled Shell.For the equations of motion of a shell filled with a fluid, we will use the geometrically nonlinear equations of the theory of shallow shells in mixed form [3,4]:

Non-linear vibrations of shells: A literature review from 2003 to 2013

“…Karagiozis et al [110] developed two numer ical models based on Donnell's non linear theory with and with out in plane inertia to study non linear vibrations of clamped fluid filled shells. In a series of papers Koval'chuk and Kruk [111,112], Koval'chuk et al [113] and Kubenko et al [114] discussed the problem of non linear forced vibrations of completely filled simply supported circular cylindrical shells using Donnell's non linear shallow shell theory and the Krylov Bogolyubov Mitro pol'skii averaging technique. Particularly, in Refs.…”

Experimental Study of the Vibrations of a Composite Cylindrical Shell with a Filler Subject to Two-Frequency Excitation

“…are subjected to combined vibratory loading of various types. The dynamic behavior of shells filled with a fluid is more intensive under combined two-frequency vibratory loading [10,11] than under single-frequency loading [8,12].Here we will discuss test data on the nonlinear dynamic deformation of a glassfiber-reinforced plastic shell (empty or filled) subjected to longitudinal kinematic two-frequency vibrational excitation. Our primary task is to establish and analyze the relationship between the two excitation frequencies and the natural frequencies of the shell and the amplitude of the kinematic loading that cause the most intensive deformation of the shell and to analyze the effect of the filler and the way the excitation frequency varies on these processes.…”

“…are subjected to combined vibratory loading of various types. The dynamic behavior of shells filled with a fluid is more intensive under combined two-frequency vibratory loading [10,11] than under single-frequency loading [8,12].…”

Dynamic deformation of a cylindrical composite shell with filler subject to radial two-frequency excitation

“…When in service, however, real shell structures used in aircraft and rocket technology, space transportation systems, chemical engineering etc., are subjected to combined vibratory loading. In this connection, some tests were performed to study the dynamic behavior of shells filled with a fluid and subjected to longitudinal-and-transverse and compound two-frequency vibrational excitation [4,10,17,18].Here we will discuss test data on the nonlinear dynamic deformation of the elastic wall of a glassfiber-reinforced plastic shell (empty or filled) subjected to two-frequency vibrational excitation. Our primary task is to find the combination of the two excitation frequencies and the natural frequencies of the "dry" and filled shells and the amplitude of the vibrational load that cause the most intensive deformation of the shell wall and to analyze the associated processes and the effect of the filler on them.…”

“…When in service, however, real shell structures used in aircraft and rocket technology, space transportation systems, chemical engineering etc., are subjected to combined vibratory loading. In this connection, some tests were performed to study the dynamic behavior of shells filled with a fluid and subjected to longitudinal-and-transverse and compound two-frequency vibrational excitation [4,10,17,18].…”