Reduced-order models for the analysis of a vertical rod under parametric excitation

Vernizzi, Guilherme Jorge; Franzini, Guilherme Rosa; Lenci, Stefano

doi:10.1016/j.ijmecsci.2019.105122

Cited by 16 publications

(3 citation statements)

References 22 publications

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“…Since the beam vibrates around its equilibrium, y p (t) = {0} which is the trivial solution of equation (1). Hence, the aim is to study the stability of the trivial 4), considering equation (6), in equation ( 1) following would be derived: where E y p (t) = 0 . The periodic function {p(t)} in equation ( 5) can be expanded by the Fourier series.…”

Section: Hill's Methodsmentioning

confidence: 99%

“…They took into account the super periodic and nonlinear periodic parametric excitations and they obtained the boundaries separating chaotic and non-chaotic responses, using Melnikov's method. Vernizzi et al [6] studied the influence of parametric excitation on a vertically floated rod in a fluid. In this paper, the authors proposed three types of reduced order models and obtain the stability plots.…”

Section: Introductionmentioning

confidence: 99%

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Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

2022

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Background The presence of parametric excitation in dynamic structures, caused by friction, crack, varying compliance, electromagnetic field, etc. may generate unbounded responses. In the literature there exist several numerical analyses of systems affected by parametric excitation, while experimental studies are less frequent. Objective The goal of the paper is to create a demonstrator of a parametrically excited system, whose stability can be modified through a controlled physical parameter. This work also investigates the applicability of the recently developed stability analysis method named Jacobian Based Approach (JBA). Methods This paper studies a simple experimental set-up comprising of a cantilever beam mounted on a spring with time – varying stiffness, achieved through the use of an electromagnet. The test rig allows measuring directly the magnetic force without any preknowledge of the values of electrical parameters. Results obtained from the test rig are compared with numerical results obtained from the Finite Element model. In this study, Hill’s method and JBA are employed to obtain the stability plot highlighting the regions of parametric instabilities. Results Good agreement is found between experimental and numerical data and the presence of unstable behavior is verified through the use of the well – known Hill’s method and the JBA. Furthermore, this study demonstrates that the stability plot, highlighting the unstable regions, computed by JBA is in complete agreement with the one obtained by Hill’s method. Conclusions It is shown how the parametric instability can be triggered through the regulation of a simple physical parameter, i.e. the gap between the electromagnet and the beam. The numerical model analyzed by the ad – hoc technique proposed by the authors i.e. JBA has been proven to have predictive capabilities in studying a system under parametric excitation and could be a potential substitution for state-of-the-art stability analysis techniques such Hill’s method.

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Section: Hill's Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

2022

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“…Considering the interaction of the internal and external fluids on the marine riser, Wang et al [14] studied lateral vibration characteristics of the riser. Reduced-order models were proposed by Vernizzi et al [15] to investigate the parametric excitation of a vertical rod. Mao et al [16] established a dynamic model to investigate the mechanical characteristics of a drilling riser and studied the offset of the platform as a series of determined values.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Procedure to Predict Transverse Vibration Response of Jack-Up Riser under the Random Wave Load

Wang

Xiao

Yao

et al. 2020

Shock and Vibration

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Marine riser is a key equipment in offshore drilling operation, and failure of the riser can lead to drilling moratorium; in severe cases, it may cause oil and gas leaks. In this paper, the time-dependent boundary conditions of the riser and the randomness of wave load are considered to improve the calculation efficiency and accuracy of the dynamic response of the jack-up riser. Based on the Euler–Bernoulli beam theory, an analytical method to determine the response of the jack-up riser subjected to the random wave load was established by the Mindlin–Goodman method in the frequency domain, and an experiment was carried out to verify it. The research shows that transverse dynamic response is the main component of the transverse response of the riser, and the method proposed is feasible to calculate the transverse response of the riser.

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An Introduction to Parametrically Excited Systems and Their Importance on the Dynamics of Slender Structures

Franzini,

Vernizzi

2023

Understanding Complex Systems

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Reduced-order models for the analysis of a vertical rod under parametric excitation

Cited by 16 publications

References 22 publications

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

An Analytical Procedure to Predict Transverse Vibration Response of Jack-Up Riser under the Random Wave Load

An Introduction to Parametrically Excited Systems and Their Importance on the Dynamics of Slender Structures

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