Dynamic Stability of a Beam Loaded by a Sequence of Moving Mass Particles

Benedetti, G.

doi:10.1115/1.3423435

Cited by 46 publications

(14 citation statements)

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“…The transverse inertial effects have been a topic of interest not only in bridge dynamics and in the design of railway tracks and guide-way systems but also in other engineering applications such as modern high-speed precision machinery processes [1]. The results of researchers highlighted the importance of the moving mass model compared to the moving force model particularly in the cases of large moving mass and high velocity [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 98%

Coupling Ritz Method and Triangular Quadrature Rule for Moving Mass Problem

Eftekhari

Jafari

2012

Journal of Applied Mechanics

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In this paper, a mixed method that combines the Ritz method and the triangular quadrature rule (TQR) is presented for solving time-dependent problems. In this study, the Ritz method is first used to discretize the spatial partial derivatives. The TQR is then employed to analogize the temporal derivatives. The resulting algebraic formulation is a triangular matrix equation, which reduces to the solution of a system of algebraic equations of the size of the problem for each time step. This requires less computational effort compared to the differential quadrature method (DQM) where a larger system of the size of the problem should be solved within each time element. The mixed formulation combines the simplicity of the Ritz method and accuracy and computational efficiency of the TQR. The stability property and computational efficiency of the scheme are discussed in detail. Numerical results show that the proposed mixed methodology can be used as an efficient tool for handling the time-dependent problems.

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Section: Introductionmentioning

confidence: 98%

Coupling Ritz Method and Triangular Quadrature Rule for Moving Mass Problem

Eftekhari

Jafari

2012

Journal of Applied Mechanics

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“…The studies of the dynamic stability of beams under moving loads include the work of Katz et al [13], Benedetti [14], Nelson and Conover [15], Housner [16], Gregory and Paidoussis [17,18]. For example, Housner [16] studied the dynamic stability of uniform pipes supported at both ends and conveying #uids.…”

Section: Introductionmentioning

confidence: 99%

“…Nelson and Conover [15] studied the dynamic stability of a simply supported uniform beam carrying a continuous series of mass particles using Floquet theory and the approximate Galerkin's method. Benedetti [14] extended the work of Nelson and Conover in order to predict the stability maps of a simply supported uniform beam using the Mathieu}Hill method. Katz et al [13] investigated the dynamic stability of a uniform beam with simply supported ends.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Stability of Stepped Beams Under Moving Loads

Aldraihem¹,

Baz²

2002

Journal of Sound and Vibration

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“…For nearly a century, the dynamics of bridges under moving loads has been studied. Initial efforts were devoted to the development of analytical and semi-analytical solutions for simple cases of beams with one or more spans excited by moving forces or masses [1][2][3][4][5][6][7][8]. The dynamic interaction between a rolling slab of a bridge and a moving vehicle is very complex.…”

Section: Introductionmentioning

confidence: 99%

Dynamic amplification of a multi-span, continuous orthotropic bridge deck under vehicular movement

Rezaiguia

Ouelaa

Laefer

et al. 2015

Engineering Structures

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__________________________________________________________________________The response of a multi-span, continuous orthotropic bridge deck during truck loading is investigated to better understand the dynamic interaction between moving vehicles and highway bridge decks. The present study is based on a recently published, semi-analytical approach for free vibration in which the modal superposition method incorporates intermodal coupling. Herein, the bridge deck is modeled as a jointless, multi-span, orthotropic plate, and the vehicle is modeled as a dynamic, multi-body system. The road surface roughness randomness is modeled as a normal, stationary, random process described by its PSD. The coupled equations of the motion vehicle/bridge deck are solved by Newmark's method. An iterative process in each time step is performed to find the equilibrium between the bridge deck and vehicle tires using an uncoupled algorithm previously developed by other authors.Two numerical application examples are presented: an isotropic and an orthotropic, threespan bridge deck both crossed by an AASHTO-based vehicle model. In example one, the intermodal coupling affects the dynamic deflection of bridge deck but only slightly. Example two demonstrates that the loading mode and the vehicle speed have a significant influence on the Dynamic Amplification Factor. However, the most important parameter to affect the 2 dynamic vehicle/bridge deck interaction force is the road's surface roughness, as has been shown for other bridge types under various load conditions. Key-words:

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Dynamic Stability of a Beam Loaded by a Sequence of Moving Mass Particles

Cited by 46 publications

References 0 publications

Coupling Ritz Method and Triangular Quadrature Rule for Moving Mass Problem

Coupling Ritz Method and Triangular Quadrature Rule for Moving Mass Problem

Dynamic Stability of Stepped Beams Under Moving Loads

Dynamic amplification of a multi-span, continuous orthotropic bridge deck under vehicular movement

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