Natural Characteristic of Thin-Wall Pipe under Uniformly Distributed Pressure

Abstract

Natural characteristics of thin-wall pipe of the compressor under uniformly distributed pressure were presented in this paper based on a cylindrical shell model. In the traditional method, the beam model was usually used to analyze the pipe system. In actual fact, the pipe segment of the compressor was always broken in the form of a long crack or a partial hole and the phenomenon was hardly explained by beam model. According to the structure characteristic of compressor pipe segment, whose radius is large and thickness is little, shell model shows the advantage in this kind of pipe problem. Based on Sanders’ shell theory, the vibration differential equation of pipe was established by applying the energy method. The influences of length to radius ratio (L/R), thickness to radius ratio (h/R), circumferential wave number (n) and pressure (q) on the natural frequencies of pipe were analyzed. The study shows: Pressure and structural parameters have a great effect on the natural characteristics of the pipe. Natural frequency increases as the pressure increases, especially for the higher mode. The sensitivity of natural frequency on pressure becomes stronger with h/R ratio increases; when L/R ratio is greater than a certain critical value, the influence of the pressure on natural frequency will no longer be obvious. The value of n corresponding to the minimum natural frequency also depends on the value of pressure. In the end, analysis of the forced vibration of a specific pipeline model was given and the modal shapes were illustrated to understand the break of the pipe. The research here will provide the theory support for the dynamic design of related pressure pipe and further experiment study should be employed.