Vibration of non-uniform rod using Differential Transform Method

International Conference on Materials, Alloys and Experimental Mechanics 2017

材料科学;金属学;机械制造

Shali, S.^1 ; Nagaraja, S.R.^2 ; Jafarali, P.^3

Department of Civil Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Amrita University, Bengaluru, India^1

Department of Mechanical Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Amrita University, Bengaluru, India^2

Kuwait Institute for Scientific Research, Kuwait^3

关键词: Algebraic equations;    Differential transform method;    Eigenvalue analysis;    End conditions;    Governing equations;    Ordinary and partial differential equations;    Paper analysis;    Vibration characteristics;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/225/1/012027/pdf
DOI  :  10.1088/1757-899X/225/1/012027

学科分类：材料科学（综合）

来源: IOP

【 摘 要 】

The present paper analyses the vibration characteristics of non-uniform rods using Differential Transform Method. The method is very effective in solving ordinary and partial differential equations. The governing equations are transformed into a set of polynomials and the solution of these algebraic equations gives the desired frequency. Method is implemented for fix-free and fix-fix end conditions of a non-uniform rod. It is seen that the lower modes are sensitive to taper ratio in case of fix-free rod and fix-fix case frequency is same as that of uniform rod for different taper ratios. The method has proved to be accurate, simple and effective for eigenvalue analysis.