Linear Barycentric Rational Collocation Method for Beam Force Vibration Equation

Jin Li,Yu Sang,Sandro Carbonari

doi:10.1155/2021/5584274

Abstract

The linear barycentric rational collocation method for beam force vibration equation is considered. The discrete beam force vibration equation is changed into the matrix forms. With the help of convergence rate of barycentric rational interpolation, both the convergence rates of space and time can be obtained at the same time. At last, some numerical examples are given to validate our theorem.

Highlights

Beam vibration is the amount and direction of movement that a beam exhibits away from the point of applied force or the area of attachment. ere are lots of application including the material used for the construction, length of the beam, construction of bridges, buildings, towers and the amount of force applied, and so on
In [15,16,17], integro-differential equation, heat conduction equation, and biharnormic equation are solved by linear barycentric rational collocation method and the convergence rate is proved
We focus on the beam force vibration equation by barycentric rational interpolation methods

Summary

Introduction

Beam vibration is the amount and direction of movement that a beam exhibits away from the point of applied force or the area of attachment. ere are lots of application including the material used for the construction, length of the beam, construction of bridges, buildings, towers and the amount of force applied, and so on. Ere are lots of numerical methods [3,4,5] to solve the beam force vibration equation such as the finite difference method, finite element method, differential quadrature method, multiscale method, and spectral methods. In [15,16,17], integro-differential equation, heat conduction equation, and biharnormic equation are solved by linear barycentric rational collocation method and the convergence rate is proved. We focus on the beam force vibration equation by barycentric rational interpolation methods. With the help of barycentric rational polynomial, the collocation scheme for beam force vibration equation and its matrix equation have been presented. E convergence rate of linear barycentric rational collocation methods has been proved. Two examples are presented to illustrate our theorem analysis

Collocation Scheme for Beam Force Vibration Equation

Convergence and Error Analysis

Conclusion