%0 Journal Article
%T Hermite Finite Element Method for Vibration Problem of Euler-Bernoulli Beam on Viscoelastic Pasternak Foundation
%A Pengfei Ji
%A Zhe Yin
%J Engineering
%P 337-352
%@ 1947-394X
%D 2024
%I Scientific Research Publishing
%R 10.4236/eng.2024.1610025
%X 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 <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>O</mi><mrow><mo>(</mo>
   <mrow>
    <msup>
     <mi>&#x03C4;</mi>
     <mn>2</mn>
    </msup>
    <mo>+</mo><msup>
     <mi>h</mi>
     <mn>4</mn>
    </msup>
    </mrow>
  <mo>)</mo></mrow></mrow>
</math>

, where <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>&#x03C4;</mi>
</math>

 is time step size and <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mi>h</mi>
</math>

 is space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis.
%K Viscoelastic Pasternak Foundation
%K Beam Vibration Equation
%K Hermite Finite Element Method
%K Error Estimation
%K Numerical Simulation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=136860