# Calculating the natural frequency of cantilever tapered beam using classical Rayleigh, modified Rayleigh and finite element methods

## Authors

• Luay S.Alansari University of Kufa â€“ Faculty of Engineering â€“ Mechanical Engineering Department
• Ali M.HAl-Hajjar University of Kufa â€“ Faculty of Engineering â€“ Mechanical Engineering Department
• Husam Jawad A. University of Kufa â€“ Faculty of Engineering â€“ Mechanical Engineering Department

2019-02-15

## Keywords:

Classical Rayleigh Method, Modified Rayleigh Method, Finite Element Method, ANSYS Workbench, Tapered Beam, Frequency.

## Abstract

Beam is a structural element and can be used in different shapes according to its applications and the tapered beam is one of these structural elements. The frequency of tapered beam was investigated in this work using three calculation methods. These methods were Classical Rayleigh Method (CRM), Modified Rayleigh Method (MRM) and Finite Element Method (FEM) using ANSYS Workbench (17.2). The basic idea of Classical Rayleigh Method (CRM) and Modified Rayleigh Method (MRM) was changing the tapered beam into stepped beam with N-steps. The results showed that there was a good agreement between the natural frequency which was calculated by ANSYS and Modified Rayleigh Method (MRM) when the number of steps was (6) and the natural frequency increases when the larger width (or height) increases for different values of smaller width (or height).The frequency ratio is constant when the smaller width (or height) increases. Also, the frequency ratio increases when the width ratio (WL/WS) increases and when the number of divisions (N) increases, the slope of frequency ratio increases too.

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