Nonlinear dynamic response of an Euler–Bernoulli beam under a moving mass–spring with large oscillations

Jahangiri, Amir; Attari, Nader K. A.; Nikkhoo, Ali; Waezi, Zakariya

doi:10.1007/s00419-020-01656-9

Cited by 12 publications

(8 citation statements)

References 36 publications

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“…Considering the coupling effect between the axial deformation and lateral vibration of the beam itself, the energy method is widely used to build the system dynamic equation. [ 15 ] Such as Zhang et al [ 16 ] described the dynamic characteristics by energy method and analyzed the steady‐state characteristics by lumped‐state. In short, the nonlinear vibration equation is obtained by the following methods mostly: Hamiltonian approach, [ 17 ] amplitude–frequency formulation, [ 18 ] and other classical methods.…”

Section: Vibration Modeling Of Cantilever Beammentioning

confidence: 99%

Review on the Vibration Suppression of Cantilever Beam through Piezoelectric Materials

Song

Shan

et al. 2022

Adv Eng Mater

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Section: Vibration Modeling Of Cantilever Beammentioning

confidence: 99%

Review on the Vibration Suppression of Cantilever Beam through Piezoelectric Materials

Song

Shan

et al. 2022

Adv Eng Mater

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“…Theoretically, the steel bar has infinite number of natural frequencies, but in most circumstance, only low-mode natural frequencies (less than 6th mode) are concerned [45][46]50]. This is because the lower natural frequency is relatively easier to be excited.…”

Section: I  Corresponding To Natural Frequencymentioning

confidence: 99%

“…In this paper, cement mortar other than concrete material was chosen as the research object for its better homogeneity shown in trial experiments, which is preferable for laboratory research [42][43][44]. A small vibration of the steel bar will be produced when the exposed end of the steel bar is excited, which leads to a limited deformation of the cement mortar in the disturbance range [45][46]. So the effect of the cement mortar material on the steel bar is represented by an elastic element.…”

mentioning

confidence: 99%

New non-destructive method for testing the strength of cement mortar material based on vibration frequency of steel bar: Theory and experiment

Shi

Song

Chen

et al. 2020

Construction and Building Materials

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“…Other works concern the limitations of classical beam theories [55][56][57]. Large deformations are investigated in [58], initial conditions are accounted for in [59], and the non-uniform motion of the inertial object is analyzed in [60]. Related problems include the variation in foundation stiffness [61,62] or analyses concerned with tracks other than classical ballasted tracks [63].…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Approach and Green’s Function Method: A Comparison in the Analysis of the Interaction of a Moving Mass on an Infinite Beam on a Three-Layer Viscoelastic Foundation at the Stability Limit—The Effect of Damping of Foundation Materials

Dimitrovová,

Mazilu

2024

Materials

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In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green’s function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity–moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green’s function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green’s function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described.

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Nonlinear dynamic response of an Euler–Bernoulli beam under a moving mass–spring with large oscillations

Cited by 12 publications

References 36 publications

Review on the Vibration Suppression of Cantilever Beam through Piezoelectric Materials

Review on the Vibration Suppression of Cantilever Beam through Piezoelectric Materials

New non-destructive method for testing the strength of cement mortar material based on vibration frequency of steel bar: Theory and experiment

Semi-Analytical Approach and Green’s Function Method: A Comparison in the Analysis of the Interaction of a Moving Mass on an Infinite Beam on a Three-Layer Viscoelastic Foundation at the Stability Limit—The Effect of Damping of Foundation Materials

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