Deflection of Beams Modeled by Fractional Differential Equations

Villa-Morales, José; Esparza, Luz Judith R.; Ramírez-Aranda, Manuel

doi:10.3390/fractalfract6110626

Cited by 7 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mahapatra and Panigrahi [10] applied the Fourier cosine series to investigate the dynamic behavior of the damped beam with elastic constraints. 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].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

View full text Add to dashboard Cite

show abstract

“…Frequency parameters of the beam for non-classical conditions were determined using a Fourier method [13]. In [14], the damped beam study was investigated for a non-classical case employing the Fourier cosine series for the determination of dynamical responses while the fractional approach was implicated on the investigation of a Euler-Bernoulli (EB) beam in [15]. Later came a study about the free double beam with forcing and different conditions associated with the discrete points and a viscoelastic layer [16].…”

Section: Introductionmentioning

confidence: 99%

Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation

2023

View full text Add to dashboard Cite

This article presents a modal analysis of an elastically constrained Rayleigh beam that is placed on an elastic Winkler foundation. The study of beams plays a crucial role in building construction, providing essential support and stability to the structure. The objective of this investigation is to examine how the vibrational frequencies of the Rayleigh beam are affected by the elastic foundation parameter and the rotational inertia. The results obtained from analytical and numerical methods are presented and compared with the configuration of the Euler–Bernoulli beam. The analytic approach employs the technique of separation of variable and root finding, while the numerical approach involves using the Galerkin finite element method to calculate the eigenfrequencies and mode functions. The study explains the dispersive behavior of natural frequencies and mode shapes for the initial modes of frequency. The article provides an accurate and efficient numerical scheme for both Rayleigh and Euler–Bernoulli beams, which demonstrate excellent agreement with analytical results. It is important to note that this scheme has the highest accuracy for eigenfrequencies and eigenmodes compared to other existing tools for these types of problems. The study reveals that Rayleigh beam eigenvalues depend on geometry, rotational inertia minimally affects the fundamental frequency mode, and linear spring stiffness has a more significant impact on vibration frequencies and mode shapes than rotary spring stiffness. Further, the finite element scheme used provides the most accurate results for obtaining mode shapes of beam structures. The numerical scheme developed is suitable for calculating optimal solutions for complex beam structures with multi-parameter foundations.

show abstract

Analysis of fractional Euler-Bernoulli bending beams using Green’s function method

Khabiri,

Asgari,

Taghipour

et al. 2024

Alexandria Engineering Journal

View full text Add to dashboard Cite

Deflection of Beams Modeled by Fractional Differential Equations

Cited by 7 publications

References 21 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

Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation

Analysis of fractional Euler-Bernoulli bending beams using Green’s function method

Contact Info

Product

Resources

About