On the nonlinear stochastic dynamics of a continuous system with discrete attached elements

Cunha, Americo; Sampaio, Rubens

doi:10.1016/j.apm.2014.07.012

Cited by 6 publications

(9 citation statements)

References 26 publications

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“…For a deeper discussion on the behavior of this physical system, also taking into account the energy spectrum of the system, the reader is encouraged to see the reference [7]. 1 Normalized means a random variable with zero mean and unit standard deviation.…”

Section: Numerical Resultsmentioning

confidence: 99%

Study of the nonlinear longitudinal dynamics of a stochastic system

Cunha

Sampaio

2014

MATEC Web of Conferences

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Abstract. This paper deals with the theoretical study of how discrete elements attached to a continuous stochastic systems can affect their dynamical behavior. For this, it is studied the nonlinear longitudinal dynamics of an elastic bar, attached to springs and a lumped mass, with a random elastic modulus and subjected to a Gaussian white-noise distributed external force. Numerical simulations are conducted and their results are analyzed in function of the ratio between the masses of the discrete and the continuous parts of the system. This analysis reveals that the dynamic behavior of the bar is significantly altered when the lumped mass is varied, being more influenced by the randomness for small values of the lumped mass.

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Section: Numerical Resultsmentioning

confidence: 99%

Study of the nonlinear longitudinal dynamics of a stochastic system

Cunha

Sampaio

2014

MATEC Web of Conferences

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“…In the context of this study, the physical and geometric parameters of the plate are considered as uncertain parameters with a Gaussian random distribution, based on the works by [17,22] that investigated a similar stochastic problem. However, it is important to emphasized that, in the context of the stochastic modeling of a mechanical system, the probability distribution must be constructed based on the available information of it and not arbitrarily chosen, as discussed in the works by [15,16,23]. Also, among the various methods for stochastic modeling available in the literature to represent a Gaussian random field, it has been used here the Karhunen-Loève (KL) expansion [17] to obtain the stochastic matrices of the system.…”

Section: Stochastic Fe Modeling Of the Nonlinear Systemmentioning

confidence: 99%

“…But, none of those considers the presence of parametric uncertainties during the nonlinear modeling to produce stochastic nonlinear computational models to deal with more realistic situations. Only few studies have considered the presence of uncertainties in discrete nonlinear systems [14,15] with the aim of measuring the influence of small variations on the design parameters on the nonlinear responses. Here, the uncertainties have been introduced into the model by using the stochastic finite element method (SFEM), which allows a combination of the classical FE method and statistical tools [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

An efficient iterative model reduction method for stochastic systems having geometric nonlinearities

Belonsi

Lima

Trevilato

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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The dynamic analysis of systems has several applications in the project or monitoring and controlling machines and equipments. In particular, the analysis of nonlinear systems has academic and industrial appeal for owning many particularities such as structural integrity, models updating, stability and real-time predictability. Those particularities complicate the study of these models. However, the development of more representative mathematical models requires normally costly computations. By considering the uncertainties associated with the fabrication process (geometrical dimensions, physical and material properties), as well as those related to the operational conditions (boundary conditions, external forces, etc.), it complicates further the analysis of those nonlinear systems. Thus, this paper proposes a methodology to analyze nonlinear systems subjected to uncertainties using the stochastic finite element method. In view of the high computational cost needed to construct the confidence region predicted with the stochastic nonlinear computational model, it is proposed herein a new model reduction method based on the construction of an adaptive iterative enriched basis to deal with the stochastic nonlinear system addressed herein composed by a thin rectangular plate used as an application. The results demonstrate clearly the efficiency and accuracy of the proposed method as an efficient tool to approximate the nonlinear responses of more complex nonlinear systems subjected to uncertainties. Also, it demonstrates the relevance of taking into account the uncertainties in the modeling of nonlinear systems to consider more realistic situations.

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“…For technical reasons, see Soize (2017) [6] for details, we also supposed that the expected value of ln k and ln c are finite. Using these conditions as known information, such as done in Cunha and Sampaio (2015) [58], the principle of maximum entropy says that the probability density function (PDF) of these random variables is given by…”

Section: Stochastic Version Of the Nonlinear Systemmentioning

confidence: 99%

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

Villani

Silva

Cunha

2019

Mechanical Systems and Signal Processing

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The damage detection problem in mechanical systems, using vibration measurements, is commonly called Structural Health Monitoring (SHM). Many tools are able to detect damages by changes in the vibration pattern, mainly, when damages induce nonlinear behavior. However, a more difficult problem is to detect structural variation associated with damage, when the mechanical system has nonlinear behavior even in the reference condition. In these cases, more sophisticated methods are required to detect if the changes in the response are based on some structural variation or changes in the vibration regime, because both can generate nonlinearities. Among the many ways to solve this problem, the use of the Volterra series has several favorable points, because they are a generalization of the linear convolution, allowing the separation of linear and nonlinear contributions by input filtering through the Volterra kernels. On the other hand, the presence of uncertainties in mechanical systems, due to noise, geometric imperfections, manufacturing irregularities, environmental conditions, and others, can also change the responses, becoming more difficult the damage detection procedure. An approach based on a stochastic version of Volterra series is proposed to be used in the detection of a breathing crack in a beam vibrating in a nonlinear regime of motion, even in reference condition (without crack). The system uncertainties are simulated by the variation imposed in the linear stiffness and damping coefficient. The results show, that the nonlinear analysis done, considering the high order Volterra kernels, allows the approach to detect the crack with a small propagation and probability confidence, even in the presence of uncertainties.

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On the nonlinear stochastic dynamics of a continuous system with discrete attached elements

Cited by 6 publications

References 26 publications

Study of the nonlinear longitudinal dynamics of a stochastic system

Study of the nonlinear longitudinal dynamics of a stochastic system

An efficient iterative model reduction method for stochastic systems having geometric nonlinearities

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

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