Closed-form solution for mode superposition analysis of continuous beams on flexible supports under moving harmonic loads

Colmenares, Daniel; Andersson, Andréas; Karoumi, Raid

doi:10.1016/j.jsv.2021.116587

Cited by 21 publications

(12 citation statements)

References 36 publications

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“…T (2) gives the expression for the first angular frequency term ω (1) , and M (2) gives the same kinematic relationship as in the previous order. Thus:…”

Section: Multi-supported Beam With Soft Rotational Supportmentioning

confidence: 96%

“…By introducing (17) into T (2) , we obtain the macroscopic description at leading order, with ω = εω (1) + o(ε):…”

Section: Multi-supported Beam With Stiff Rotational Supportmentioning

confidence: 99%

“…Since ω (2) = 0, the angular frequency expands to: ω = εω (1) + ε 3 ω (3) + o(ε 3 ) and consequently ε 4 2ω (1) ω (3) = ω 2 − (εω (1) ) 2 + o(ε 4 ). By introducing this expression into T (4) , as well as all those resulting from the solutions to the previous problems, we obtain the following macroscopic description:…”

Section: Multi-supported Beam With Soft Rotational Supportmentioning

confidence: 99%

“…Due to their wide range of applications, many studies have focused on dynamics of beams that rest on continuous foundations or on discrete flexible supports. For good reviews in this field one can refer to [1,2].…”

Section: Introductionmentioning

confidence: 99%

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Modal Analysis of a Multi-Supported Beam: Macroscopic Models and Boundary Conditions

Rallu,

Boutin

2024

Mathematics

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This paper deals with the long-wavelength behaviour of a Euler beam periodically supported by co-located rotation and compression springs. An asymptotic homogenization method is applied to derive the several macroscopic models according to the stiffness contrasts between the elastic supports and the beam. Effective models of differential order two or four are obtained, which can be merged into a single unified model whose dispersion relations at long and medium wavelengths fit those derived by Floquet-Bloch. Moreover, the essential role of rotation supports is clearly evidenced. A mixed “discrete/continuous” approach to the boundary conditions is proposed, which allows the boundary conditions actually applied at the local scale to be expressed in terms of Robin-type boundary conditions on macroscopic variables. This approach can be applied to both dominant-order and higher-order models. The modal analysis performed with these boundary conditions and the homogenised models gives results in good agreement with a full finite element calculation, with great economy of numerical resources.

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“…T (2) gives the expression for the first angular frequency term ω (1) , and M (2) gives the same kinematic relationship as in the previous order. Thus:…”

Section: Multi-supported Beam With Soft Rotational Supportmentioning

confidence: 96%

“…By introducing (17) into T (2) , we obtain the macroscopic description at leading order, with ω = εω (1) + o(ε):…”

Section: Multi-supported Beam With Stiff Rotational Supportmentioning

confidence: 99%

Section: Multi-supported Beam With Soft Rotational Supportmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modal Analysis of a Multi-Supported Beam: Macroscopic Models and Boundary Conditions

Rallu,

Boutin

2024

Mathematics

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“…This procedure enables the calculation of the FRF for each modal order. However, the modal decomposition of bridge vibration data necessitates multi-point measurements on the bridge, and the creation of window functions requires knowledge of the vehicle’s relative position [ 22 , 23 , 24 ].…”

Section: Introductionmentioning

confidence: 99%

Estimating Bridge Natural Frequencies Based on Modal Analysis of Vehicle–Bridge Synchronized Vibration Data

Mudahemuka,

Miyagi,

Shin

et al. 2024

Sensors

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This paper presents a method for accurately estimating the natural frequencies of bridges by simultaneously measuring the acceleration vibration data of vehicles and bridges and applying modal analysis theory. Vibration sensors synchronized with GPS timing were installed on both vehicles and bridges, achieving stable and high-precision time synchronization. This enabled the computation of the bridge’s Frequency Response Functions (FRFs) for each mode, leading to a refined estimation of natural frequencies. The validity of the theory was confirmed through numerical simulations and experimental tests. The simulations confirmed its effectiveness, and similar trends were observed in actual bridge measurements. Consequently, this method significantly enhances the feasibility of bridge health monitoring systems. The proposed method is suitable for road bridges with spans ranging from short- to medium-span length, where the vehicle is capable of exciting the bridge.

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Dynamic response characteristics of axially moving plates subjected to moving load

Song,

Yao,

2024

J Braz. Soc. Mech. Sci. Eng.

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Closed-form solution for mode superposition analysis of continuous beams on flexible supports under moving harmonic loads

Cited by 21 publications

References 36 publications

Modal Analysis of a Multi-Supported Beam: Macroscopic Models and Boundary Conditions

Modal Analysis of a Multi-Supported Beam: Macroscopic Models and Boundary Conditions

Estimating Bridge Natural Frequencies Based on Modal Analysis of Vehicle–Bridge Synchronized Vibration Data

Dynamic response characteristics of axially moving plates subjected to moving load

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