Nonlinear dynamics of viscoelastic flexible structural systems by finite element method

Abdelrahman, Alaa A.; Nabawy, Ayman E.; Abdelhaleem, Ayman M. M.; Ali-Eldin, Soliman S.; Eltaher, Mohamed A.

doi:10.1007/s00366-020-01141-5

Cited by 11 publications

(8 citation statements)

References 78 publications

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“…Generally, the reentry process of a vehicle is treated as a stationary random process in the finite element analysis of random vibration [33]. e basic inputs for random vibration are the auto-PSDs and cross-PSDs of fluctuating pressures.…”

Section: Description Of Fluctuating Pressuresmentioning

confidence: 99%

Parallel Calculation of Random Vibration for Reentry Vehicles in Fluctuating Pressure Environment

Fan

Liang

Wang

et al. 2021

Shock and Vibration

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The reentry vehicle is in an unconstrained free-flight state during the reentry process. The pressure of air fluctuations acts on the external surface of the vehicle and induces a random vibration environment with a wide-frequency range, which makes great influences on the structural dynamic properties of vehicles. This paper aims at the parallel calculation of the wide-frequency random vibration problems for the free body under multipoint fluctuating pressure loads. The calculation method is based on the self-developed JAUMIN framework and PANDA platform. The novel algorithm based on the modal superposition method reduces the computational complexity, realizes the parallel calculation, and achieves the maximum numerical simulation calculation capacity of 1.045 billion degrees of freedom (DOFs) while improving the calculation efficiency and the accuracy of the results. Finally, this article also uses typical examples to verify the correctness and parallel scalability of algorithms and programs.

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Section: Description Of Fluctuating Pressuresmentioning

confidence: 99%

Parallel Calculation of Random Vibration for Reentry Vehicles in Fluctuating Pressure Environment

Fan

Liang

Wang

et al. 2021

Shock and Vibration

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“…Many researchers [20][21][22][23][24][25] applied the finite element analysis to achieve different analyses about the viscoelastic behavior in different topics such as the dynamic response of orthotropic viscoelastic composite laminates plate, impact response of viscoelastic-frictionless bodies, Dynamic response of viscoelastic functionally graded porous thick beam and the analysis of viscoelastic bonding layer on the behavior of piezoelectric actuator.…”

Section: Introductionmentioning

confidence: 99%

Performance Evaluation of Nonlinear Viscoelastic Materials using Finite Element Method

Sabri,

Al-Tamimi,

Alshamma

et al. 2024

International Journal of Applied Mechanics and Engineering

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This research paper applies the finite element method as a methodology to evaluate the structural performance of nonlinear viscoelastic solids. A finite element algorithm was built and developed to simulate the mathematical nonlinear viscoelastic material behavior based on incremental constitutive equations. The derived Equation of the incremental constitutive included the complete strain and stress histories. The Schapery’s nonlinear viscoelastic material model was integrated within the displacement-based finite element environment to perform the analysis. A modified Newton-Raphson technique was used to solve the nonlinear part in the resultant equations. In this work, the deviatoric and volumetric strain–stress relations were decoupled, and the hereditary strains were updated at the end of each time increment. It is worth mentioning that the developed algorithm can be effectively employed for all the permissible values of Poisson’s ratio by using a selective integration procedure. The algorithm was tested for a number of applications, and the results were compared with some previously published experimental results. A small percentage error of (1%) was observed comparing the published experimental results. The developed algorithm can be considered a promising numerical tool that overcomes convergence issues, enhancing equilibrium with high-accuracy results.

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“…Łasecka-Plura and Lewandowski [14] investigated dynamic characteristics and frequency response function for frames with dampers using FEM with uncertain design parameters. Abdelrahman et al studied the nonlinear dynamics of viscoelastic flexible structural systems using the finite element method [15]. Ratas et al investigated the solution of the nonlinear boundary value problems by applying the higher-order Haar wavelet functions [16], where the authors carried out a comprehensive analysis of the error and convergence of the obtained solution.…”

Section: Introductionmentioning

confidence: 99%

Eigenvibrations of Kirchhoff Rectangular Random Plates on Time-Fractional Viscoelastic Supports via the Stochastic Finite Element Method

Kamiński,

Guminiak,

Lenartowicz

et al. 2023

Materials

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The present work’s main objective is to investigate the natural vibrations of the thin (Kirchhoff–Love) plate resting on time-fractional viscoelastic supports in terms of the Stochastic Finite Element Method (SFEM). The behavior of the supports is described by the fractional order derivatives of the Riemann–Liouville type. The subspace iteration method, in conjunction with the continuation method, is used as a tool to solve the non-linear eigenproblem. A deterministic core for solving structural eigenvibrations is the Finite Element Method. The probabilistic analysis includes the Monte-Carlo simulation and the semi-analytical approach, as well as the iterative generalized stochastic perturbation method. Probabilistic structural response in the form of up to the second-order characteristics is investigated numerically in addition to the input uncertainty level. Finally, the probabilistic relative entropy and the safety measure are estimated. The presented investigations can be applied to the dynamics of foundation plates resting on viscoelastic soil.

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Nonlinear dynamics of viscoelastic flexible structural systems by finite element method

Cited by 11 publications

References 78 publications

Parallel Calculation of Random Vibration for Reentry Vehicles in Fluctuating Pressure Environment

Parallel Calculation of Random Vibration for Reentry Vehicles in Fluctuating Pressure Environment

Performance Evaluation of Nonlinear Viscoelastic Materials using Finite Element Method

Eigenvibrations of Kirchhoff Rectangular Random Plates on Time-Fractional Viscoelastic Supports via the Stochastic Finite Element Method

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