Numerical Analysis of Natural Frequency for U-Shaped Expansion Bellows in Fixed-Fixed and Fixed-Free Conditions

Abstract

In this study, MATLAB code was used to analyze the natural frequency in two types of U-shape metal expansion bellows with various supporting conditions (fixed-fixed and fixed- free). The first bellow has a 10 mm inner diameter., and a length of (100, 200, 300) mm, has (36, 75, and 111) convolutions. While the second bellow, with an inner diameter of 20mm and (100,200,300) mm, has a number of convolutions (25,54 and 82). The result shows that by lowering the bellow length and increasing the bellow diameter, the natural frequency was raised. Were. Where, the maximum frequency was recorded at a maximum value of 20 mm in diameter and a length of 100 mm, about (13549.167 Hz) in the case of fixed-fixed and (13097.528 Hz) in the case of fixed-free. In general, the natural frequency depends directly on the stiffness and total mass of the pipe conveying fluid. The stiffness of the material is determined by the moment of inertia. As a result, increasing the diameter will increase the moment of inertia, which will result in an increase in stiffness, which will result in an increase in natural frequency.