Implementation of time-weighted residual method for simulation of flexural waves in multi-span Timoshenko beams subjected to various types of external loads: from stationary loads to accelerating moving masses

Borji, Amin; Movahedian, B.; Boroomand, B.

doi:10.1007/s00419-021-02103-z

Cited by 4 publications

(1 citation statement)

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“…Implementation of the time-weighted residual method for simulation of flexural waves in multi-span Timoshenko beams subjected to various external loads: from stationary loads to accelerating moving masses considered in [9]. Experimental studies of the dynamic response of multi-span beams under the action of moving masses, among which is [10], is also known.…”

Section: Literature Reviewmentioning

confidence: 99%

Modeling a Viscoelastic Support Considering Its Mass-Inertial Characteristics During Non-Stationary Vibrations of the Beam

Voropay

Menshykov

Povaliaiev

et al. 2023

JES

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Non-stationary loading of a mechanical system consisting of a hinged beam and additional support installed in the beam span was studied using a model of the beam deformation based on the Timoshenko hypothesis with considering rotatory inertia and shear. The system of partial differential equations describing the beam deformation was solved by expanding the unknown functions in the Fourier series with subsequent application of the integral Laplace transform. The additional support was assumed to be realistic rather than rigid. Thus it has linearly elastic, viscous, and inertial components. This means that the effect of a part of the support vibrating with the beam was considered such that their displacements coincide. The beam and additional support reaction were replaced by an unknown concentrated external force applied to the beam. This unknown reaction was assumed to be time-dependent. The time law was determined by solving the first kind of Volterra integral equation. The methodology of deriving the integral equation for the unknown reaction was explained. Analytic formulae and results of computations for specific numerical parameters were given. The impact of the mass value on the additional viscoelastic support reaction and the beam deflection at arbitrary points were determined. The research results of this paper can be helpful for engineers in designing multi-span bridges.

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Section: Literature Reviewmentioning

confidence: 99%