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

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

Author(s): Voropay A. V.1*, Menshykov O. V.2, Povaliaiev S. I.1, Sharapata A. S.1, Yehorov P. A.1

1 Kharkiv National Automobile and Highway University, 25, Yaroslava Mudrogo St., 61002 Kharkiv, Ukraine;
2 School of Engineering, University of Aberdeen, AB243UE Scotland, United Kingdom

*Corresponding Author’s Address: [email protected]

Issue: Volume 10, Issue 1 (2023)

Submitted: February 27, 2023
Received in revised form: May 10, 2023
Accepted for publication: May 16, 2023
Available online: May 19, 2023

Voropay A. V., Menshykov O. V., Povaliaiev S. I., Sharapata A. S., Yehorov P. A. (2023). Modeling a viscoelastic support considering its mass-inertial characteristics during non-stationary vibrations of the beam. Journal of Engineering Sciences, Vol. 10(1), pp. D8-D14, doi: 10.21272/jes.2023.10(1).d2

DOI: 10.21272/jes.2023.10(1).d2

Research Area:  MECHANICAL ENGINEERING: Dynamics and Strength of Machines

Abstract. 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.

Keywords: Timoshenko multi-span beam, additional viscoelastic support, non-stationary vibration, concentrated mass, Volterra integral equation.


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