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Wang, T.M. and Stephens, J.E. (1977) Natural Frequencies of Timoshenko Beams on Pasternak Foundations. Journal of Sound and Vibration, 51, 149-155.
https://doi.org/10.1016/s0022-460x(77)80029-1

has been cited by the following article:

• TITLE: Hermite Finite Element Method for Vibration Problem of Euler-Bernoulli Beam on Viscoelastic Pasternak Foundation

  AUTHORS: Pengfei Ji, Zhe Yin

  KEYWORDS: Viscoelastic Pasternak Foundation, Beam Vibration Equation, Hermite Finite Element Method, Error Estimation, Numerical Simulation

  JOURNAL NAME: Engineering, Vol.16 No.10, October 25, 2024

  ABSTRACT: Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Euler-Bernoulli beam on viscoelastic Pasternak foundation can be used to analyze the deformation and response of buildings under complex geological conditions. In this paper, we use Hermite finite element method to get the numerical approximation scheme for the vibration equation of viscoelastic Pasternak foundation beam. Convergence and error estimation are rigourously established. We prove that the fully discrete scheme has convergence order O( τ 2 + h 4 ) , where τ is time step size and h is space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis.