Dynamic instability of a circular cylindrical shell carrying a top mass under base excitation: Experiments and theory

2019

Shock and Vibration

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This paper presents an investigation on the dynamical properties of single-walled carbon nanotubes (SWCNTs), and nonlinear modal interaction and energy exchange are analysed in detail. Resonance interactions between two conjugate circumferential flexural modes (CFMs) are investigated. The nanotubes are analysed through a continuous shell model, and a thin shell theory is used to model the dynamics of the system; free-free boundary conditions are considered. The Rayleigh–Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. The model is validated in linear field (natural frequencies) by means of comparisons with literature. A convergence analysis is carried out in order to obtain the smallest modal expansion able to simulate the nonlinear regimes. The time evolution of the nonlinear energy distribution over the SWCNT surface is studied. The nonlinear dynamics of the system is analysed by means of phase portraits. The resonance interaction and energy transfer between the conjugate CFMs are investigated. A travelling wave moving along the circumferential direction of the SWCNT is observed.

Section: Introductionmentioning

confidence: 99%

Nonlinear Resonance Interaction between Conjugate Circumferential Flexural Modes in Single‐Walled Carbon Nanotubes

Strozzi

2019

Shock and Vibration

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“…Both theoretical and experimental aspects of nonlinear dynamics and stability of shells are widely explored in literature [46][47][48][49][50]. In these works, the effect of the geometry, boundary conditions, fluid-structure interaction, material distribution, geometric imperfections, external loads on the nonlinear vibrations of circular cylindrical shells is investigated.…”

Section: Introductionmentioning

confidence: 99%

Linear vibrations of triple-walled carbon nanotubes

Strozzi

Mathematics and Mechanics of Solids

2017

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This paper presents an investigation on the dynamical properties of single-walled carbon nanotubes (SWCNTs), nonlinear modal interaction and energy exchange are analysed in detail. Resonance interactions between two conjugate circumferential flexural modes (CFMs) are investigated. The nanotubes are analysed through a continuous shell model, a thin shell theory is used to model the dynamics of the system; free-free boundary conditions are considered. The Rayleigh-Ritz method is applied to approximate linear eigenfunctions of the partial differential equations that govern the shell dynamics. An energy approach, based on Lagrange equations and series expansion of the displacements, is considered to reduce the initial partial differential equations to a set of nonlinear ordinary differential equations of motion. The model is validated in linear field (natural frequencies) by means of comparisons with literature. A convergence analysis is carried out in order to obtain the smallest modal expansion able to simulate the nonlinear regimes. The time evolution of the nonlinear energy distribution over the SWCNT surface is studied. The nonlinear dynamics of the system is analysed by means of phase portraits. The resonance interaction and energy transfer between the conjugate CFMs is investigated. A travelling wave moving along the circumferential direction of the SWCNT is observed.

“…The dynamics of a circular cylindrical shell connected to a rigid disk on top and subjected to seismic base excitation was deeply investigated by Pellicano and Avramov 21 and Pellicano. 22,23 Experimental tests were performed; the results were used to validate several semi-analytical models based on nonlinear Sanders-Koiter theory. Even a model that takes into account the dynamics of an electrodynamic shaker can be found in such references.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The seismic base motion is controlled with an open-loop control strategy. Instead, a real-time closed-loop strategy is used to control the voltage signal sent to the shaker power amplifier: the control voltage is externally generated in MATLAB environment and then is sent to the amplifier through a Testlab module (see references Pellicano; 22 Pellicano et al; 35 Zippo et al 36,37 ). The output provided by the shaker controller is a steppedsine voltage v i (t) function.…”

Section: Test Setupmentioning

confidence: 99%

Resonances and nonlinear vibrations of circular cylindrical shells, effects of thermal gradients

Iarriccio

Zippo

Proceedings of the Institution of Mechanical Engineers, Part C:

et al. 2020

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In this paper, the results of an experimental campaign focused on the vibrations of shells are presented. More specifically, the goal is to investigate the effect of thermal gradients across the shell thickness on the nonlinear dynamics. The shell is made of polymeric material and an aluminum mass is clamped on one end of the shell; the other shell end is clamped to an electrodynamic shaker, which provides a base harmonic excitation. Tests are performed in a controlled environment where a thermal gradient on the shell thickness is generated by means of a climatic chamber and an internal cartridge heater. Different temperature gradients and base excitation levels have been considered. The nonlinear dynamic scenario is analyzed through amplitude–frequency diagrams, bifurcation diagrams, waterfall diagrams, time histories, Fourier spectra, phase portraits, and Poincaré maps. Results show a strong effect of the temperature on the dynamic response of the shell: subharmonic, quasi-periodic, and chaotic vibrations take place as well as large amplitude vibrations, high sound levels are detected.