| Gas pipe is a large artery connecting the whole country's transportation resources.It is an essential infrastructure of energy industry and an important support for national economic development.Therefore,it is of great significance to study the dynamic characteristics of buried gas pipes in goaf.In this paper,the effect of temperature on the vibration characteristics of the buried pipe which exposed to natural environment in the underground mining area is studied.The main research includes:(1)Considering the influence of temperature,the vibration differential equation of the bare gas pipe in the goaf is established.(2)The influence of temperature variation and geometric parameters on the vibration characteristics of the pipe are studied respectively under three working conditions.In this paper,firstly,the vibration differential equation of pipe is established by using the D'Alembert's principle and the constitutive relation considering the influence of temperature,then the expression of internal force and internal torque of the pipe is derived.And the partial differential equation of pipe vibration is obtained by displacement.Secondly,according to the actual situation at both ends of the bare pipes,the pipes are divided into three working conditions: Simple supported condition,cantilever condition and solid supported condition.Under each condition,according to its boundary conditions,the corresponding mode function is obtained,and then the mass matrix,stiffness matrix,vibration ordinary differential equations and frequency equation are obtained.Finally,the influences of pipe length,pipe wall thickness,pipe diameter and temperature variationon the vibration characteristics of bare gas pipe are studied by numerical method.In this paper,the influence of the temperature variation and geometrical parameters on the vibration characteristics of the bare gas pipe is studied,the following conclusions are obtained:(1)Under the simply supported condition,the temperature variation has little influence on the first and the second order natural frequencies,and has obvious influence on the third and the fourth order natural frequencies,when the temperature variation exceeds200 C particularly.(2)Under the cantilever condition,the temperature variationhas little influence on the first order natural frequency,and has obvious influence on the second,the third and the fourth order natural frequency.And the influence of the geometrical parameters is obvious under this condition.(3)Under the solid supported condition,the temperaturevariation has an effect on each order natural frequency and it has the greatest influence on the fourth order natural frequency.(4)The each order natural frequency decreases with the increase of the temperature variation.(5)The vibration shape of the pipe can well reflect its vibration form,it can provide reference for the design of gas pipe. |
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