Free and forced vibration of double beam with arbitrary end conditions connected with a viscoelastic layer and discrete points

Zhao, Xingzhuang; Chang, Peter

doi:10.1016/j.ijmecsci.2021.106707

Cited by 22 publications

(9 citation statements)

References 63 publications

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“…Deflection of Euler-Bernoulli beam by fractional differential equation described by Villa-Morales et al [11]. Free and forced vibration of a double beam with arbitrary end conditions connected to a viscoelastic layer and discrete points are investigated by Zhao and Chang [12]. Mirzabeigy et al [13] examined the free vibration of two parallel elastically constrained beams connected together through a variable stiffness elastic layer.…”

Section: Introductionmentioning

confidence: 99%

Effects of shear deformation and rotary inertia on elastically constrained beam resting on pasternak foundation

et al. 2023

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This study investigates the free vibrations of elastically constrained shear and Rayleigh beams placed on the Pasternak foundation. Of particular interest, it is aimed to analyze the influence of shear strain, rotational inertia, elastic stiffness, and shear layer on the naturalfrequencies and eigenmodes of beam vibrations. For this purpose, the eigenfrequencies and eigenmodes are determined using analytical and numerical techniques. A finite element scheme is developed employing quadratic and cubic polynomials for slope and transverse displacement, respectively. The efficiency and accuracy of the finite element method are illustrated by comparing it with the analytical results for generalized and special cases. The underlying model analysis justifies that the natural frequencies of the beam vibration depend only on the geometry of the Rayleigh beam, while these frequencies depend on the physical and geometric properties of the shear beam. However, the natural frequencies of the Euler-Bernoulli depend solely on the geometric conditions of the beam.

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Section: Introductionmentioning

confidence: 99%

Effects of shear deformation and rotary inertia on elastically constrained beam resting on pasternak foundation

et al. 2023

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“…Studies have been conducted to predict the dynamics of these systems under various loading and force conditions, such as those found in papers [27]- [35], among others. These studies include the use of analytical and closed-form solutions [31], [36]- [39]; however, analytical methods have limitations in applicability, as they may be useful only for specific types of problems and can become complex for systems with many variables or nonlinear equations. Other approaches, such as the state-space method presented in [33], [40], may also be computationally expensive for systems with a large number of states.…”

Section: Introductionmentioning

confidence: 99%

Predicting traction return current in electric railway systems through physics-informed neural networks

Kapoor

Wang

Núñez

et al. 2022

2022 IEEE Symposium Series on Computational Intelligence (SSCI)

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This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are connected with a Winkler foundation. In particular, forward and inverse problems for the Euler-Bernoulli and Timoshenko partial differential equations (PDEs) are solved using nondimensional equations with the physics-informed loss function. Higher-order complex beam PDEs are efficiently solved for forward problems to compute the transverse displacements and cross-sectional rotations with less than 1e − 3 percent error. Furthermore, inverse problems are robustly solved to determine the unknown dimensionless model parameters and applied force in the entire space-time domain, even in the case of noisy data. The results suggest that PINNs are a promising strategy for solving problems in engineering structures and machines involving beam systems.

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“…In addition, an extra beam and elastic layer can reduce the vibration of the main beam and they also reduce the deflection of the beam. Finally, a double beam can be useful to detect the damage and it can be added as an extra component to the structure when it is required [6].…”

Section: Introductionmentioning

confidence: 99%

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

Hossain¹,

Lellep²

2022

Eng. Res. Express

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In the study, the Maclaurin series technique is presented to analyse the vibration of cracked tapered double nanobeams. The equation of motion is derived from the Euler-Bernoulli beam theory based on the Hamiltonian principle and Eringen's nonlocal theory of elasticity. The double-nanobeam system consists of two parallel nanobeams attached by a Winkler elastic layer. Both beams are identical and their widths vary along the x-axis. A single crack is considered at the upper beam of the system. The mechanical behaviour of cracked cross-sections is simulated by the local stiffness model. According to the model, the cracked double-beam system is divided into two intact segments. A numerical investigation is carried out to scrutinize the effects of nonlocal parameters, crack severity, taper ratio, and spring constant on the vibration of the double nanobeam. The results reveal that the effects of crack depth, crack location, nonlocal parameters, taper ratio, and spring constant influence the natural frequency and dynamic response of the system significantly. This study highlights that a crack at the upper beam influences the mode shape of the upper beam as well as the intact lower beam. Numerical results have been examined with the previously published works and found a good agreement with them.

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Free and forced vibration of double beam with arbitrary end conditions connected with a viscoelastic layer and discrete points

Cited by 22 publications

References 63 publications

Effects of shear deformation and rotary inertia on elastically constrained beam resting on pasternak foundation

Effects of shear deformation and rotary inertia on elastically constrained beam resting on pasternak foundation

Predicting traction return current in electric railway systems through physics-informed neural networks

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

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