Nonlinear random vibrations of micro-beams with fractional viscoelastic core

Loghman, Ehsan; Bakhtiari-Nejad, Firooz; E., Ali Kamali; Abbaszadeh, Mostafa

doi:10.1016/j.probengmech.2022.103274

Cited by 10 publications

(3 citation statements)

References 38 publications

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“…In 2022, Loghman et al [43] examined the nonlinear vibration behavior of a microbeam with a fractional viscoelastic core and subjected to random excitation. The formulation of the nonlinear FSPDE is based on Von-Karman's nonlinear strain and the Kelvin-Voigt fractional viscoelastic model, namely,…”

Section: Chronological Progression Of Numerical Methods For Fspdesmentioning

confidence: 99%

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

Moghaddam,

Babaei,

Dabiri

et al. 2024

Symmetry

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This article aims to provide a comprehensive review of the latest advancements in numerical methods and practical implementations in the field of fractional stochastic partial differential equations (FSPDEs). This type of equation integrates fractional calculus, stochastic processes, and differential equations to model complex dynamical systems characterized by memory and randomness. It introduces the foundational concepts and definitions essential for understanding FSPDEs, followed by a comprehensive review of the diverse numerical methods and analytical techniques developed to tackle these equations. Then, this article highlights the significant expansion in numerical methods, such as spectral and finite element methods, aimed at solving FSPDEs, underscoring their potential for innovative applications across various disciplines.

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Section: Chronological Progression Of Numerical Methods For Fspdesmentioning

confidence: 99%

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

Moghaddam,

Babaei,

Dabiri

et al. 2024

Symmetry

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show abstract

“…Malara et al 38 investigate the efficient computation of the nonlinear response of rods containing fractional-order eigenstructure models under stochastic excitation. Loghman et al 39 investigate the vibrational characteristics, stability and response of fractional order viscoelastic microbeams under random excitation. These investigate the vibrational characteristics, stability and response of fractional order viscoelastic microbeams under random excitation.…”

Section: Introductionmentioning

confidence: 99%

Dynamic vibration analysis of cantilever beams on nonlinear fractional viscoelastic foundation under Gaussian white noise

Qu,

Cui,

Cui

et al. 2024

Preprint

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This paper presents the dynamic response of cantilever beam on fractional-order nonlinear viscoelastic foundation subjected to Gaussian white noise. The control equations of the cantilever beam on viscoelastic foundation are established using Hamilton’s principle. The problem is solved using the shifted Chebyshev polynomial algorithm, and the control equations are transformed into a system of nonlinear algebraic equations. Numerical examples analyse the correction error and the second norm error, confirming the effectiveness and accuracy of the algorithm in solving such problems. Furthermore, the algorithm’s robustness was verified by comparing the responses of Gaussian white noise and non-Gaussian white noise cantilever beam on the viscoelastic foundation. The study examined the impact of various loads and parameters on the cantilever beam, as well as the effect of different harmonic loads on its stress. The research results are in line with the existing literature. These studies offer valuable guidance for practical engineering and enhance comprehension of the dynamic response of cantilevers on foundation in complex environments.

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“…Fractionalorder calculus has been used to analyze and solve various phenomena, including Quantum mechanics [15,16], fluid-dynamics, traffic [17][18][19][20][21], colored noise [22], shock waves [18], underwater acoustics [23], statistical mechanics [24], soliton dynamics [25], earthquake science [26], materials properties [16,27], semiconductor [27], super-fluids [16], particle and plasma physics [6], cryptography [28], steganography [28], etc. The field of fractional calculus is being applied in physics, chemistry, mathematics, engineering, and biosciences [29][30][31][32][33][34][35][36][37]. As a result, there has been a growing need to find solutions for these types of equations.…”

Section: Introductionmentioning

confidence: 99%

Employing a Fractional Basis Set to Solve Nonlinear Multidimensional Fractional Differential Equations

Rahman,

Bhatti,

Dimakis

2023

Mathematics

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Fractional-order partial differential equations have gained significant attention due to their wide range of applications in various fields. This paper employed a novel technique for solving nonlinear multidimensional fractional differential equations by means of a modified version of the Bernstein polynomials called the Bhatti-fractional polynomials basis set. The method involved approximating the desired solution and treated the resulting equation as a matrix equation. All fractional derivatives are considered in the Caputo sense. The resulting operational matrix was inverted, and the desired solution was obtained. The effectiveness of the method was demonstrated by solving two specific types of nonlinear multidimensional fractional differential equations. The results showed higher accuracy, with absolute errors ranging from 10−12 to 10−6 when compared with exact solutions. The proposed technique offered computational efficiency that could be implemented in various programming languages. The examples of two partial fractional differential equations were solved using Mathematica symbolic programming language, and the method showed potential for efficient resolution of fractional differential equations.

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Nonlinear random vibrations of micro-beams with fractional viscoelastic core

Cited by 10 publications

References 38 publications

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

Dynamic vibration analysis of cantilever beams on nonlinear fractional viscoelastic foundation under Gaussian white noise

Employing a Fractional Basis Set to Solve Nonlinear Multidimensional Fractional Differential Equations

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