Analysis of Nonlinear Vibrations of a Cylindrical Shell in a Supersonic Gas Flow

2015 ◽  
Vol 799-800 ◽  
pp. 660-664
Author(s):  
Lelya Khajiyeva ◽  
Askhat Kudaibergenov
Keyword(s):  
Cylindrical Shell ◽  
Gas Flow ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Drill String ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
The Third ◽  
Runge Kutta Method ◽  
Supersonic Gas Flow

In the paper nonlinear vibrations of a drill string’s section in a supersonic gas flow are studied. The drill string is modelled in the form of a circular cylindrical shell under the effect of a longitudinal compressing load and torque. In contrast to the previous research, pressure of an unperturbed gas is defined nonlinearly in the third approximation. The eighth order partial differential equation describing the motion of the shell reduces to a nonlinear system of ordinary differential equations with application of the Bubnov-Galerkin technique. An implicit Runge-Kutta method is applied to construct modes of vibrations.

STABILITY ANALYSIS OF A CIRCULAR CYLINDRICAL SHELL BY THE EQUILIBRIUM METHOD

2008 ◽  
Vol 08 (03) ◽  
pp. 465-485 ◽  
Author(s):  
YUH-CHYUN TZENG ◽  
CHING-CHURN CHERN
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Critical Stress ◽  
Circular Cylindrical Shell ◽  
Slenderness Ratio ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Finite Element Program

Presented herein is a formulation for the buckling of a cylindrical shell subjected to external loads using an infinitesimal shell element defined in a convenient coordinate system. The governing equation in terms of the radial deflection is derived for the element by adopting an operator. The eighth order partial differential equation derived can be applied for cylindrical shells with various boundary conditions. For illustration, simply supported cylindrical shells subjected to axial compressive forces are studied using either a one-variable or a two-variable shape function. The critical stresses obtained for the buckling of cylindrical shells are compared with those by the finite element program SAP2000. The critical stress of the cylindrical shell is similar to that of the column, in that the critical stress decreases as the thickness ratio (the ratio of R/h) or the slenderness ratio increases. Good agreement has been obtained for most of the comparative cases, while the finite element results appear to be slightly higher for some cases.

scholarly journals To the solution of the problem of bending of a cylindrical shell by the boundary elements method

2018 ◽  
Vol 230 ◽  
pp. 02032 ◽  
Author(s):  
Mykola Surianinov ◽  
Yurii Krutii
Keyword(s):  
Differential Equation ◽  
Cylindrical Shell ◽  
Boundary Elements ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Various Boundary Conditions ◽  
Analytical Construction ◽  
Load Vector ◽  
Plates And Shells ◽  
Boundary Elements Method

The solution of the problem of the long cylindrical shell bending by a numerical and analytical boundary elements method is considered. The method is based on the analytical construction of a fundamental system of solutions and Green’s functions for the differential equation of the problem under consideration. This paper is devoted to the determination of these expressions. The semi-moment theory of the cylindrical shell calculation, proposed by V.Z. Vlasov, which for the problem under consideration leads to one eighth-order partial differential equation is used. The problem of the bending of a cylindrical shell is twodimensional, and in the numerical and analytical boundary elements method, plates and shells are considered as generalized one-dimensional modules, so the variational method of Kantorovich-Vlasov was applied to this equation to obtain an ordinary differential equation of the eighth order. Sixty-four expressions of all the fundamental functions of the problem are constructed, as well as an analytic expression for the Green’s function, which makes it possible to construct a load vector (without any restrictions on the nature of its application), and then proceed to the solution of boundary-value problems for the bending of long cylindrical shells under various boundary conditions.

Internal Resonance and Nonlinear Vibrations of Eccentric Rotating Composite Laminated Circular Cylindrical Shell

2019 ◽  
Author(s):  
Tao Liu ◽  
Wei Zhang ◽  
Yan Zheng ◽  
Yufei Zhang
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Shear Deformation Theory ◽  
Internal Resonances

Abstract This paper is focused on the internal resonances and nonlinear vibrations of an eccentric rotating composite laminated circular cylindrical shell subjected to the lateral excitation and the parametric excitation. Based on Love thin shear deformation theory, the nonlinear partial differential equations of motion for the eccentric rotating composite laminated circular cylindrical shell are established by Hamilton’s principle, which are derived into a set of coupled nonlinear ordinary differential equations by the Galerkin discretization. The excitation conditions of the internal resonance is found through the Campbell diagram, and the effects of eccentricity ratio and geometric papameters on the internal resonance of the eccentric rotating system are studied. Then, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equations in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. Finally, we study the nonlinear vibrations of the eccentric rotating composite laminated circular cylindrical shell systems.

scholarly journals Thermoelastic Response of Closed Cylindrical Shells in a Supersonic Gas Flow

Aerospace ◽  
2020 ◽  
Vol 7 (8) ◽  
pp. 103
Author(s):  
Marine Mikilyan
Keyword(s):  
Cylindrical Shell ◽  
Temperature Field ◽  
Gas Flow ◽  
Nonlinear Oscillations ◽  
Supersonic Velocity ◽  
Inhomogeneous Temperature ◽  
Inhomogeneous Temperature Field ◽  
Supersonic Gas Flow ◽  
The Stability ◽  
The Galerkin Method

The work is devoted to the investigation of flutter oscillations and the stability of the closed cylindrical shell in supersonic gas flow in an inhomogeneous temperature field. It is assumed that supersonic gas flows on the outside of the shell with an unperturbed velocity U, directed parallel to the cylinder generatrix. Under the action of an inhomogeneous temperature field the shell bulges out, this deformed state is accepted as unperturbed, and the stability of this state is studied. The main nonlinear equations and relationships describing the behavior of the examined system are derived. The formulated boundary value problem is solved using the Galerkin method. The joint influence of the flow and the temperature field on the relationship between the amplitude of nonlinear oscillations of a cylindrical shell and the speed of the flowing stream is studied. The critical velocity values are calculated from the corresponding linear system and are given in tables. The numerical results show that: (a) the surrounding flow significantly affects the nature of the investigated relationship; (b) a certain interval of supersonic velocity exists where it is impossible to excite steady-state flutter oscillations (the silence zone); (c) the dependence of amplitude on the supersonic velocity can be either multivalued or single-valued.

Experimental Study on Pre-Stressed Circular Cylindrical Shell

2012 ◽  
Author(s):  
Antonio Zippo ◽  
Marco Barbieri ◽  
Matteo Strozzi ◽  
Vito Errede ◽  
Francesco Pellicano
Keyword(s):  
Experimental Study ◽  
Cylindrical Shell ◽  
Axial Load ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Experimental Studies ◽  
Element Model ◽  
Experimental Setup ◽  
Circular Cylindrical Shells

In this paper an experimental study on circular cylindrical shells subjected to axial compressive and periodic loads is presented. Even though many researchers have extensively studied nonlinear vibrations of cylindrical shells, experimental studies are rather limited in number. The experimental setup is explained and deeply described along with the analysis of preliminary results. The linear and the nonlinear dynamic behavior associated with a combined effect of compressive static and a periodic axial load have been investigated for different combinations of loads; moreover, a non stationary response of the structure has been observed close to one of the resonances. The linear shell behavior is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

Experiments and Simulations in Travelling Wave and Non-Stationary Nonlinear Vibrations of Circular Cylindrical Shells

2016 ◽  
Author(s):  
Marco Amabili ◽  
Prabakaran Balasubramanian ◽  
Giovanni Ferrari
Keyword(s):  
Cylindrical Shell ◽  
Traveling Wave ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Excitation Amplitude ◽  
Added Mass ◽  
Travelling Wave ◽  
Wave Response

The nonlinear vibrations of a water-filled circular cylindrical shell subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated numerically and experimentally by using a seamless aluminum sample. The experimental boundary conditions are close to a simply supported circular cylindrical shell. Modal analysis reveals the presence of predominantly radial driven and companion modes in the low frequency range, implying the existence of a traveling wave phenomenon in the nonlinear field. Experimental studies previously carried out on cylindrical shells did not permit the complete identification of the characteristic traveling wave response and of its non-stationary nature. The added mass of the internal quiescent, incompressible and inviscid fluid results in an increase of the weakly softening behavior of the shell, as expected. The minimization of the added mass due to the excitation system and the negligible entity of the geometric imperfections of the shell allow the appearance of an exact one-to-one internal resonance between driven and companion modes. This internal resonance gives rise to a travelling wave response around the shell circumference and non-stationary, quasi-periodic vibrations, which are experimentally verified by means of stepped-sine testing with feedback control of the excitation amplitude. The same phenomenon is observed in the nonlinear response obtained numerically. The traveling wave is measured by means of state-of-the-art laser Doppler vibrometry applied to multiple points on the structure simultaneously. Previous studies present in literature did not show if this vibration can be chaotic for relatively small vibration amplitudes. Chaos is here observed in the frequency region where the travelling wave response is present for vibrations amplitudes smaller than the thickness of the shell. The relevant nonlinear reduced order model of the shell is based on the Novozhilov nonlinear shell theory retaining in-plane inertia and on an expansion of the displacements in terms of a properly chosen base of linear modes. An energy approach is used to obtain the nonlinear equations of motion, which are numerically studied (i) by using a code based on arc-length continuation and collocation method that allows bifurcation analysis in case of stationary vibrations, (ii) by a continuation code based on direct integration and Poincaré maps, which also evaluates the maximum Lyapunov exponent in case of non-stationary vibrations. The comparison of experimental and numerical results is particularly satisfactory throughout the various excitation amplitude levels considered. The two methods concur in describing the progressive development of the companion mode into a fully developed traveling wave and the subsequent appearance of quasi-periodic and eventually chaotic vibrations.

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