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Dynamic Stiffness for a Levinson Beam Embedded Within a Pasternak Medium Subjected to Axial Load at Both Ends

Author(s): ORCID


ORCID
Medium: journal article
Language(s): English
Published in: Buildings, , n. 12, v. 14
Page(s): 4008
DOI: 10.3390/buildings14124008
Abstract:

This work presents accurate values for the dynamic stiffness matrix coefficients of Levinson beams under axial loading embedded in a Winkler–Pasternak elastic foundation. Levinson’s theory accounts for greater shear deformation than the Euler–Bernoulli or Timoshenko theories. Using the dynamic stiffness approach, an explicit algebraic expression is derived from the homogeneous solution of the governing equations. The dynamic stiffness matrix links forces and displacements at the beam’s ends. The Wittrick–Williams algorithm solves the eigenvalue problem for the free vibration and buckling of uniform cross-section parts. Numerical results are validated against published data, and reliability is confirmed through consistency tests. Parametric studies explore the effects of aspect ratio, boundary conditions, elastic medium parameters, and axial force on beam vibration properties. The relative deviation for the fundamental frequency is almost 6.89% for a cantilever beam embedded in the Pasternak foundation, 5.16% for a fully clamped beam, and 4.79% for a clamped–hinged beam. Therefore, Levinson beam theory can be used for calculations relevant to loads with short durations that generate transient responses, such as impulsive loads from high-speed railways, using the mode superposition method.

Copyright: © 2024 by the authors; licensee MDPI, Basel, Switzerland.
License:

This creative work has been published under the Creative Commons Attribution 4.0 International (CC-BY 4.0) license which allows copying, and redistribution as well as adaptation of the original work provided appropriate credit is given to the original author and the conditions of the license are met.

  • About this
    data sheet
  • Reference-ID
    10810475
  • Published on:
    17/01/2025
  • Last updated on:
    25/01/2025
 
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