Dynamics of a beam on a bilinear elastic foundation under harmonic moving load

Froio, Diego; Rizzi, Egidio; Simões, Fernando M. F.; Costa, A. Pinto da

doi:10.1007/s00707-018-2213-4

Cited by 33 publications

(18 citation statements)

References 66 publications

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“…Section 5 reports how the previous algorithm could be devoted to the analysis of the considered ML beam problem (and related ones). First of all, the fundamental features of an implemented object-oriented C++ parallel FEM code are briefly sketched, in order to introduce the comparison of performances between a previous sequential MatLab FEM coding, earlier developed by Froio et al [50,51,54,56], and the current C++ parallel version of the program. Moreover, the numerical transient response of a simply supported beam lying on a (visco)elastic foundation and subjected to a ML, with either a constant or a harmonic-varying amplitude in time, is considered.…”

Section: Manuscript Organizationmentioning

confidence: 99%

“…Moreover, the numerical transient response of a simply supported beam lying on a (visco)elastic foundation and subjected to a ML, with either a constant or a harmonic-varying amplitude in time, is considered. In order to validate the devised C++ code, the obtained numerical outcomes in terms of critical velocities are depicted, and compared with recent reference results from the literature (Castro Jorge et al [19], Froio et al [56]). Finally, some benchmark performance results of the achieved parallel computing strategy are reported, to illustrate the achieved speedup, efficiency and scalability of the present object-oriented C++ parallel implementation.…”

Section: Manuscript Organizationmentioning

confidence: 99%

“…During the sequel of the present section, the variety of solution approaches adopted by different authors in dealing with the analysis of the response of finite beams under ML and the investigation of their resonance conditions will be illustrated. Several criteria for classifying the research works in the field of ML problems may be adopted, see for instance the review information already included in Froio et al [55,56]. In the following exposition, a methodological classification is chosen, namely that based on the solution strategy employed toward solving the ML problem.…”

Section: State Of the Art On Moving Load Analysismentioning

confidence: 99%

“…Froio et al [56] concerned with the numerical modelization of the transient dynamic response of a simply supported Euler-Bernoulli beam resting on a bilinear Winkler-type elastic foundation. In that paper, the effect of a transverse concentrated load with a zero-mean harmonicvarying magnitude in time was displayed.…”

Section: Numerical Finite Beam With Foundationmentioning

confidence: 99%

“…5.3, the numerical transient response of a simply supported beam posed on a (visco)elastic foundation and subjected to a ML, with either a constant or a harmonic-varying amplitude is considered. In order to validate the C++ code, the obtained numerical outcomes in terms of critical velocities are successfully compared with corresponding results from the literature [19,51,54,56]. Finally, some benchmark performance results are reported in Sect.…”

Section: Computational Features Of the Implemented Fem Codementioning

confidence: 99%

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On the Numerical Modelization of Moving Load Beam Problems by a Dedicated Parallel Computing FEM Implementation

Froio

Verzeroli

Ferrari

et al. 2020

Arch Computat Methods Eng

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The present work outlines an original numerical modelization approach for Moving Load (ML) beam problems, by a dedicated object-oriented C++ parallel computing FEM implementation, with the purposes of performing efficient numerical analyses resolving the complete dynamic response of beams under the effect of a high-velocity ML. Alongside, main framing state-of-the-art reviews are attempted, on the principal involved issues of: ML context and physical description, numerical FEM modelization, parallel computing implementation. Running ML example cases are explored, for a (long) finite beam on a (visco)elastic foundation and for a continuous beam of a historic railway iron bridge, with per se interesting engineering outcomes. The contribution may serve as a guideline paradigm to readers that may be novel to the treated topics, though motivated in adventuring in the computational challenges involved in the present mechanical research context.

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Section: Manuscript Organizationmentioning

confidence: 99%

Section: Manuscript Organizationmentioning

confidence: 99%

Section: State Of the Art On Moving Load Analysismentioning

confidence: 99%

Section: Numerical Finite Beam With Foundationmentioning

confidence: 99%

Section: Computational Features Of the Implemented Fem Codementioning

confidence: 99%

See 3 more Smart Citations

On the Numerical Modelization of Moving Load Beam Problems by a Dedicated Parallel Computing FEM Implementation

Froio

Verzeroli

Ferrari

et al. 2020

Arch Computat Methods Eng

Self Cite

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Vibration and the cancellation phenomenon of a nanobeam under a moving load via the strain gradient theory

Wang

Zhu

2020

Math Methods in App Sciences

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Forced and free transverse vibrations of a nanobeam under a moving load are investigated in this work. Through the strain gradient theory, high‐order governing partial differential equations of the nanobeam are established by the extended Hamilton's principle, which incorporates its material, geometrical, and nanoscale parameters. The dynamic response of the nanobeam is obtained from spatially discretized equations via the Galerkin's method. Effects of material, geometrical, and nanoscale parameters on the forced transverse vibration of the nanobeam are discussed. Results show that material and nanoscale length parameters play a very important role in determining the amplitude of the forced transverse vibration of the nanobeam. The cancellation velocity of the moving load is determined from the rigorous initial displacement and velocity of the free transverse vibration of the nanobeam, and an approximate expression of the cancellation velocity is presented by means of its first‐mode response. Effects of geometrical and nanoscale parameters on the cancellation velocity are also discussed. It is shown that amplitudes of all modal responses of the nanobeam are not simultaneously equal to zero at the cancellation velocity.

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On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

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This paper presents an investigation of the dynamic behavior of bi-directionally functionally graded (BDFG) micro/nanobeams excited by a moving harmonic load. The formulation is established in the context of the surface elasticity theory and the modified couple stress theory to incorporate the effects of surface energy and microstructure, respectively. Based on the generalized elasticity theory and the parabolic shear deformation beam theory, the nonclassical governing equations of the problem are obtained using Lagrange’s equation accounting for the physical neutral plane concept. The material properties of the beam smoothly change along both the axial and thickness directions according to power-law distribution, accounting for the gradation of the material length scale parameter and the surface parameters, i.e., residual surface stress, two surface elastic constants, and surface mass density. Using trigonometric Ritz method (TRM), the trial functions denoting transverse, axial deflections, and rotation of the cross sections of the beam are expressed in sinusoidal form. Then, with the aid of Lagrange’s equation, the system of equations of motion are derived. Finally, Newmark method is employed to find the dynamic responses of BDFG subjected to a moving harmonic load. To validate the present formulation and solution method, some comparisons of the obtained fundamental frequency and dynamic response with those available in the literature are performed. A parametric study is performed to extensively explore the impact of the key parameters such as the gradient indices in both directions, moving speed, and excitation frequency of the acting load on the dynamic response of BDFG nanobeams. The obtained results can serve as a guideline for assessing the multi-functional and optimal design of micro/nanobeams acted upon by a moving load.

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Dynamics of a beam on a bilinear elastic foundation under harmonic moving load

Cited by 33 publications

References 66 publications

On the Numerical Modelization of Moving Load Beam Problems by a Dedicated Parallel Computing FEM Implementation

On the Numerical Modelization of Moving Load Beam Problems by a Dedicated Parallel Computing FEM Implementation

Vibration and the cancellation phenomenon of a nanobeam under a moving load via the strain gradient theory

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

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