Nonlinear stability and bifurcations of an axially accelerating beam with an intermediate spring-support

Ghayesh, Mergen H.; Amabili, Marco

doi:10.12989/csm.2013.2.2.159

Cited by 4 publications

(3 citation statements)

References 44 publications

(35 reference statements)

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“…By using the Hamilton principle [44–50], the dynamic equations of the FG honeycomb sandwich plate can be deduced as [12,16]in which q represents the transverse load, two points on the displacements represent the derivation with respect to time t , and the other variables are defined as…”

Section: Theoretical Model Of the Free Vibrationmentioning

confidence: 99%

Free vibration and sound insulation of functionally graded honeycomb sandwich plates

Yuan

Zhang

2021

Jnl of Sandwich Structures & Materials

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Based on the hyperbolic tangent shear deformation theory, free vibration and sound insulation of two different types of functionally graded (FG) honeycomb sandwich plates with negative Poisson’s ratio are studied in this paper. Using Hamilton’s principle, the vibration and vibro-acoustic coupling dynamic equations for FG honeycomb sandwich plates with simply supported edges are established. By applying the Navier’s method and fluid–solid interface conditions, the derived governing dynamic equations are solved. The natural frequencies and the sound insulation of FG honeycomb sandwich plates obtained in this work are compared with the numerical results by the finite element simulation. It is proven that the theoretical models for the free vibration and the sound insulation are accurate and efficient. Moreover, FG sandwich plates with different honeycomb cores are investigated and compared. The corresponding results show that the FG honeycomb core with negative Poisson’s ratio can yield much lower frequencies. Then, the influences of various geometrical and material parameters on the vibration and sound insulation performance are systematically analyzed.

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Section: Theoretical Model Of the Free Vibrationmentioning

confidence: 99%

Free vibration and sound insulation of functionally graded honeycomb sandwich plates

Yuan

Zhang

2021

Jnl of Sandwich Structures & Materials

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“…Also, a similar study on an axially moving string with a time-varying velocity was done by Ponomareva and van Horssen [11] . By considering the effect of intermediate spring-support, the nonlinear stability and bifurcations of an axially accelerating beam were investigated by Ghayesh and Amabili [12] . Based on the Galerkin scheme and direct timeintegration, the three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam was carried out by Farokhi et al [13] .…”

Section: Introductionmentioning

confidence: 99%

Internal resonance of an axially transporting beam with a two-frequency parametric excitation

Zhang

Tang

Liang

et al. 2022

Appl. Math. Mech.-Engl. Ed.

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This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by a speed perturbation. The Kelvin-Voigt model is introduced to describe the viscoelastic characteristics of the axially transporting beam. The governing equation and the associated boundary conditions are obtained by Newton’s second law. The method of multiple scales is utilized to obtain the steady-state responses. The Routh-Hurwitz criterion is used to determine the stabilities and bifurcations of the steady-state responses. The effects of the material viscoelastic coefficient on the dynamics of the transporting beam are studied in detail by a series of numerical demonstrations. Interesting phenomena of the steady-state responses are revealed in the 3:1 internal resonance and two-frequency parametric excitation. The approximate analytical method is validated via a differential quadrature method.

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“…(ii) Papers focusing on nonlinear oscillations of axially moving strings with constant axial velocity and varying transmitted tension [17][18][19][20][21] where parametric excitations and nonlinear stability were analyzed. (iii) Papers analyzing the periodic, quasi-periodic, chaotic, and transient motions of axially moving materials with axial acceleration and constant transmitted tension [22][23][24][25][26][27][28][29][30][31][32]. (iv) Papers presenting parametrically excited nonlinear responses of axially moving strings with time-harmonic varying axial velocity and constant transmitted tension [33][34][35][36] where the effects of parameters such as mean velocity, web stiffness and damping coefficients, and a middle support on frequency response curves and bifurcation points were investigated.…”

Section: Introductionmentioning

confidence: 99%

Influence of roll-to-roll system’s dynamics on axially moving web vibration

Hawwa¹,

Ali²,

Hardt³

2019

J. vibroeng.

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In this paper, a model for transverse web vibration in a roll-to-roll system is presented. Web axial tension and web axial speed, decisive parameters in the equation of motion that describes web vibration, are rigorously obtained by considering the two rolls-web coupled system's dynamics, coupled with the equation of motion. According to the present analysis, the idealized simply-supported boundary conditions, commonly used in studies on vibrations of axially moving structures are not needed. Instead, a mathematical model comprised of the governing equation of web transverse vibration and the roll angular velocity-web axial tension relationship is solved as a coupled system. A finite-difference based algorithm is used for solving the coupled system of differential equations. It is worth noting that the web axial speed and web-transmitted tension are not constants when a certain amount of the web material is transferred from the unwinding roll to the winding roll; they vary nonlinearly after a short transient period. The transverse vibration response at selected points on the web span shows higher (lower) frequency fluctuations corresponding to lower (higher) transport axial speed. This behavior is significantly different from that of a vibrating web under constant axial speed and tension.

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Nonlinear stability and bifurcations of an axially accelerating beam with an intermediate spring-support

Cited by 4 publications

References 44 publications

Free vibration and sound insulation of functionally graded honeycomb sandwich plates

Free vibration and sound insulation of functionally graded honeycomb sandwich plates

Internal resonance of an axially transporting beam with a two-frequency parametric excitation

Influence of roll-to-roll system’s dynamics on axially moving web vibration

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