Abstract
Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough high. In this paper, we will illustrate the high-precision numerical method to solve Euler-Bernoulli beam equation. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision.
Highlights
Under the free vibration, the equation of transverse motion of a uniform Euler-Bernoulli beam is determined by a partial differential equation [1] [2], as shown in EI
Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology
Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision
Summary
The equation of transverse motion of a uniform Euler-Bernoulli beam is determined by a partial differential equation [1] [2], as shown in EI. In [4], define u ( x,t ) as the transverse deflection of the beam, f ( x,t ) as the generic arbitrary dynamic loads that distribute along the beam axis and t is time. We consider the following variable coefficient Euler-Bernoulli beam equation. Where, u ( x,t ) represents an unknown function at position x and time t. If f ( x,t,u) is nonlinear of u, the equation is a nonlinear Partial differential equation. If f (u ) is linear of u, the Equation (3) is linear Partial differential equation
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