Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory

Awrejcewicz, Jan; Кrysko, V.А.; Павлов, С. П.; Zhigalov, Maxim V.; Kalutsky, L. A.; Krysko, Anton V.

doi:10.1007/s11071-019-04976-w

Cited by 36 publications

(18 citation statements)

References 108 publications

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“…Younis et al [47] proposed the construction of ROMs by multiplying the equation of motion by the electric load denominator. Many systems were analyzed following this strategy, such as arch resonators [28,29,[48][49][50], arches over flexible supports [51], functionally graded viscoelastic microbeams with imperfections [52], cantilever resonators [53][54][55], narrow microbeams subject to fringing fields [56][57][58] and microscale beams described by the modified couple stress theory [30][31][32][59][60][61][62][63].…”

Section: Introductionmentioning

confidence: 99%

Parameter uncertainty and noise effects on the global dynamics of an electrically actuated microarch

Benedetti

Gonçalves

Lenci

et al. 2023

J. Micromech. Microeng.

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This work aims to study the effect of uncertainties and noise on the nonlinear global dynamics of a micro-electro-mechanical arch obtained from an imperfect microbeam under an axial load and electric excitation. An adaptative phase-space discretization strategy based on an operator approach is proposed. The Ulam method, a classical discretization of flows in phase-space, is extended here to nondeterministic cases. A unified description is formulated based on the Perron-Frobenius, Koopman, and Foias linear operators. Also, a procedure to obtain global structures in the mean sense of systems with parametric uncertainties is presented. The stochastic basins of attraction and attractors’ distributions replace the usual basin and attractor concepts. For parameter uncertainty cases, the phase-space is augmented with the corresponding probability space. The microarch is assumed to be shallow and modelled using a nonlinear Bernoulli-Euler beam theory and is discretized by the Galerkin method using as interpolating function the linear vibration modes. Then, from the discretized multi degree of freedom model (mdof) model, an accurate single degree of freedom (sdof) reduced order model, based on theory of nonlinear normal modes, is derived. Several competing attractors are observed, leading to different (acceptable or unacceptable) behaviours. Extensive numerical simulations are performed to investigate the effect of noise and uncertainties on the coexisting basins of attraction, attractors` distributions, and basins boundaries. The appearance and disappearance of attractors and stochastic bifurcation are observed, and the time-dependency of stochastic responses is demonstrated, with long-transients influencing global behaviour. To consider uncertainties and noise in design, a dynamic integrity measure is proposed via curves of constant probability, which give quantitative information about the changes in structural safety. For each attractor, the basin robustness as a function of a stochastic parameter is investigated. The weighted basin area can quantify the integrity of nondeterministic cases, being also the most natural generalization of the global integrity measure. While referring to particular MEMS, the relevance of the dynamical integrity analysis for stochastic systems to quantify tolerances and safety margins is underlined here.

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Section: Introductionmentioning

confidence: 99%

Parameter uncertainty and noise effects on the global dynamics of an electrically actuated microarch

Benedetti

Gonçalves

Lenci

et al. 2023

J. Micromech. Microeng.

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“…The work in paper [17] refers to the pre-twisted blade-shaft system, while paper [18] refers to the pre-twisted double blade-shaft system. In paper [19], the authors studied the influence of von Kármán nonlinearity on the values of frequency, thermoelastic damping and quality factors on Timoshenko beam resonators based on the modified couple stress theory. Another research field is the issue of vibrations of composite shafts.…”

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Analysis of Injection Pump (Stepped) Shaft Vibrations Using Timoshenko Theory

Noga

Rejman

Bałon

et al. 2022

Acta Mechanica Et Automatica

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The free transverse vibrations of shafts with complex geometry are studied using analytical methods and numerical simulations. A methodology is proposed for evaluating the results of a natural transverse vibration analysis as generated by finite element (FE) models of a shaft with compound geometry. The effectiveness of the suggested approach is tested using an arbitrarily chosen model of the injection pump shaft. The required analytical models of the transverse vibrations of stepped shafts are derived based on the Timoshenko thick beam theory. The separation of variables method is used to find the needed solutions to the free vibrations. The eigenvalue problem is formulated and solved by using the FE representation for the shaft and for each shaft-simplified model. The results for these models are discussed and compared. Additionally, the usefulness of the Myklestad–Prohl (MP) method in the field of preliminary analysis of transverse vibration of complex shaft systems is indicated. It is important to note that the solutions proposed in this paper could be useful for engineers dealing with the dynamics of various types of machine shafts with low values of operating speeds.

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“…Awrejcewicz et. al [24] studied the thermoelastic vibrations of a Timoshenko microbeam using modified couple stress theory. Ebrahimi and Mahesh [25] studied the dynamic and forced vibration analysis of the nanobeams.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

Mohammadi¹

2021

Preprint

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In this paper, the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT is studied. Nonlocal elasticity theory is applied to consider the small scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical technique is applied to reduce the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Afterward, the analytical solutions are derived based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature dependent. The impacts of the several variables are investigated on the nonlinear frequency ratio of the nanobeams. The results illustrate that when maximum deflection is smaller/ greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.

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Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory

Cited by 36 publications

References 108 publications

Parameter uncertainty and noise effects on the global dynamics of an electrically actuated microarch

Parameter uncertainty and noise effects on the global dynamics of an electrically actuated microarch

Analytical and Numerical Analysis of Injection Pump (Stepped) Shaft Vibrations Using Timoshenko Theory

Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

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