Free flexural radial vibrations of a thin circular cylindrical shell bearing added mass

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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FREE VIBRATION of infinite length circular cylindrical shell with initial imperfections AND a SMALL aDDED mass

Scholarly Notes of Komsomolsk-na-Amure State Technical University ◽

10.17084/2014.iv-1(20).5 ◽

2014 ◽

Vol 1 (20) ◽

pp. 36-43 ◽

Cited By ~ 3

Author(s):

Sergei V. Seregin ◽

◽

Grigoriy S. Leizerovich ◽

Keyword(s):

Cylindrical Shell ◽

Free Vibration ◽

Circular Cylindrical Shell ◽

Added Mass ◽

Infinite Length ◽

Initial Imperfections

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Wave Response of Underwater Observation Tower Constructed at the Breaker Zone

Volume 2 ◽

10.1115/esda2004-58339 ◽

2004 ◽

Author(s):

Takahiro Sasaki ◽

Osamu Saijo ◽

Koichi Maruyoshi

Keyword(s):

Cylindrical Shell ◽

Pressure Distribution ◽

Wave Breaking ◽

Circular Cylindrical Shell ◽

Added Mass ◽

Simple Equation ◽

Breaking Force ◽

Underwater Observation ◽

Wave Pressure ◽

Sea Bed

There exist eight underwater observation towers in Japan. Seven of them have been built by vertical circular cylindrical shell structure, which are fixed at the sea bed like cantilever. And the other one is constructed of floating structure. Among the seven fixed-type structures, one stands under the frozen sea. The underwater observation towers are surrounded by sea water, and the inside is perfectly a close-spaced. Sightseers and several interested people visit to observe the undersea scene. Therefore, top priority must be given to structure safety. There is a vast existence of various creatures within the outstanding underwater scene which needed to be maintained to proliferate life. In order to satisfy with convenient access and outstanding scene, most structures have been built at the breaker zone. This paper presents the following contents: 1) Assuming that the underwater observation tower is constructed by vertical circular cylindrical shell, natural frequency analysis will be shown using present simple equation of added mass. We developed this equation uniquely based on fluid-structure interaction problem through water tank experiment and systematic numerical calculation. 2) Sawaragi, et al had presented wave breaking force acting on the vertical cylinder through the experiment. With reference to the force given by total force, we have newly extended its force to the wave pressure distribution so as to correspond to FEM analysis. We will show this developed method with regard to wave pressure distribution on the surface of cylindrical shell. 3) Using this simple equation of added mass and nodal forces obtained from wave breaking force, a procedure of calculation will be shown with demonstration. The evaluation and the validity in terms of added mass, load arrangement and responses will be discussed through the comparison of experimental result.

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