A fast accurate artificial boundary condition for the Euler-Bernoulli beam

Abstract

It is difficult to propose boundary conditions for the PDEs with higher order space derivatives like Euler-Bernoulli beam. In this paper we use a absorbing boundary condition method to solve the Cauchy problem for one-dimensional Euler-Bernoulli beam with fast convolution boundary condition which is derived through the Padé approximation for the square root function. We also introduce a constant damping term to control the error between the resulting approximation Euler-Bernoulli system and the original one. Numerical examples verify the theoretical results and demonstrate the performance for the fast numerical method.

An Efficient Local Artificial Boundary Condition for Infinite Long Finite Element Euler–Bernoulli Beam

“…Te Newmark method (see e.g., [27,28]) is employed for time integration. Te MBC5 result from [19] and the fast convolution result from [26] are given for comparison.…”

“…where a j , b j are constant coefcients and thus simplify the computation by using the recursive relation of the discrete convolution of exponential function [26]. Te method is accurate and efcient, but its implementation is tedious.…”

“…In this work, we propose a new ABC for FEM Euler-Bernoulli beam, which is local, efcient, accurate, and easy to implement. It is not a variant of existing ABCs in the literature such as [19,25,26]. Te idea is to attach a carefully designed mass-damper super element to the truncation end, and ensuring it recovers the dynamics response of the removed half infnite segment.…”