Regular and chaotic oscillations of a Timoshenko beam subjected to mechanical and thermal loadings

Warmińska, Anna; Manoach, Emil; Warmiński, Jerzy; Samborski, Sylwester

doi:10.1007/s00161-014-0381-6

Cited by 20 publications

(11 citation statements)

References 40 publications

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“…Threedimensional nonlinear motion characteristics of the perfect and imperfect Timoshenko microbeams under mechanical and thermal forces have been examined numerically by Farokhi and Ghayesh [28]. Large amplitude vibrations and regular and chaotic oscillations of a Timoshenko beam under the influence of temperature were analysed by Warminska et al [29,30], and mechanical and thermal loadings have been discussed. Moreover, nonlinear vibration characteristics of cross-ply composite plates in thermal environments were investigated by Settimi et al [31] and Saetta et al [32].…”

Section: Introductionmentioning

confidence: 99%

Temperature Effects on Nonlinear Vibration Behaviors of Euler‐Bernoulli Beams with Different Boundary Conditions

Zhao

Huang

2018

Shock and Vibration

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This paper is concerned with temperature effects on the modeling and vibration characteristics of Euler-Bernoulli beams with symmetric and nonsymmetric boundary conditions. It is assumed that in the considered model the temperature increases/decreases instantly, and the temperature variation is uniformly distributed along the length and the cross-section. By using the extended Hamilton’s principle, the mathematical model which takes into account thermal and mechanical loadings, represented by partial differential equations (PDEs), is established. The PDEs of the planar motion are discretized to a set of second-order ordinary differential equations by using the Galerkin method. As to three different boundary conditions, eigenvalue analyses are performed to obtain the close-form eigenvalue solutions. First four natural frequencies with thermal effects are investigated. By using the Lindstedt-Poincaré method and multiple scales method, the approximate solutions of the nonlinear free and forced vibrations (primary, super, and subharmonic resonances) are obtained. The influences of temperature variations on response amplitudes, the localisation of the resonance zones, and the stability of the steady-state solutions are investigated, through examining frequency response curves and excitation response curves. Numerical results show that response amplitudes, the number and the stability of nontrivial solutions, and the hardening-spring characteristics are all closely related to temperature changes. As to temperature effects on vibration behaviors of structures, different boundary conditions should be paid more attention.

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Section: Introductionmentioning

confidence: 99%

Temperature Effects on Nonlinear Vibration Behaviors of Euler‐Bernoulli Beams with Different Boundary Conditions

Zhao

Huang

2018

Shock and Vibration

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“…These are determined from the elimination of secular terms at the next level of the approximation. Substituting equations ( 18) into (17)…”

Section: Methodsmentioning

confidence: 99%

Thermal Effects on the Nonlinear Forced Responses of Hinged-Clamped Beam with Multimodal interaction

Ndoukouo

Ngueuteu

2021

IJRCS

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Nonlinear analysis of a forced geometrically nonlinear Hinged-Clamped beam involving three modes interactions with internal resonance and submitted to thermal and mechanical loadings is investigated. Based on the extended Hamilton’s principle, the PDEs governing the thermoelastic vibration of planar motion is derived. Galerkin’s orthogonalization method is used to reduce the governing PDEs of motion into a set of nonlinear non-autonomous ordinary differential equations. The system is solved for the three modes involved by the use of the multiple scales method for amplitudes and phases. For steady states responses, the Newton-Raphson shooting technique is used to solve the three systems of six parametric nonlinear algebraic equations obtained. Results are presented in terms of influences of temperature variations on the response amplitudes of different substructures when each of the modes is excited. It is observed for all substructures and independent of the mode excited a shift within the frequency axis of the temperature influenced amplitude response curves on either side of the temperature free-response curve. Moreover, it is found that thermal loads diversely influence the interacting substructures. Depending on the directly excited mode, higher oscillation amplitudes are found in some substructures under negative temperature difference, while it is observed in others under positive temperature change and in some others for temperature free-response curves.

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“…Primarily, it is on application-based studies rather than emphasizing in accurate measurement of the fatigue. Warminska et al [28] demonstrated that structural response is directed by the level of thermal loading and distribution. A large increase in temperature can shift the vibration centre and it affects the fundamental frequency.…”

Section: Challenge-1: Assessing Fatigue Damage Accurately Under the Vibration-based Loadsmentioning

confidence: 99%

Current challenges in modelling vibrational fatigue and fracture of structures: a review

Kamei

Khan

2021

J Braz. Soc. Mech. Sci. Eng.

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Fatigue damage is a concern in the engineering applications particularly for metal structures. The design phase of a structure considers factors that can prevent or delay the fatigue and fracture failures and increase its working life. This paper compiled some of the past efforts to share the modelling challenges. It provides an overview on the existing research complexities in the area of fatigue and fracture modelling. This paper reviews the previous research work under five prominent challenges: assessing fatigue damage accurately under the vibration-based loads, complications in fatigue and fracture life estimation, intricacy in fatigue crack propagation, quantification of cracks and stochastic response of structure under thermal environment. In the conclusion, the authors have suggested new directions of work that still require comprehensive research efforts to bridge the existing gap in the current academic domain due to the highlighted challenges.

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Regular and chaotic oscillations of a Timoshenko beam subjected to mechanical and thermal loadings

Cited by 20 publications

References 40 publications

Temperature Effects on Nonlinear Vibration Behaviors of Euler‐Bernoulli Beams with Different Boundary Conditions

Temperature Effects on Nonlinear Vibration Behaviors of Euler‐Bernoulli Beams with Different Boundary Conditions

Thermal Effects on the Nonlinear Forced Responses of Hinged-Clamped Beam with Multimodal interaction

Current challenges in modelling vibrational fatigue and fracture of structures: a review

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