Abstract
An analysis of nonlinear behaviors of pressure thin-wall pipe segment with supported clearance at both ends was presented in this paper. The model of pressure thin-wall pipe segment with supported clearance was established by assuming the restraint condition as the work of springs in the deformation directions. Based on Sanders shell theory, Galerkin method was utilized to discretize the energy equations, external excitation, and nonlinear restraint forces. And the nonlinear governing equations of motion were derived by using Lagrange equation. The displacements in three directions were represented by the characteristic orthogonal polynomial series and trigonometric functions. The effects of supporting stiffness and supported clearance on dynamic behavior of pipe wall were discussed. The results show that the existence of supported clearance may lead to the changing of stiffness of the pipe vibration system and the dynamic behaviors of the pipe system show nonlinearity and become more complex; for example, the amplitude-frequency curve of the foundation frequency showed hard nonlinear phenomenon. The chaos and bifurcation may emerge at some region of the values of stiffness and clearance, which means that the responses of the pressure thin-wall pipe segment would be more complex, including periodic motion, times periodic motion, and quasiperiodic or chaotic motions.
Highlights
An analysis of nonlinear behaviors of pressure thin-wall pipe segment with supported clearance at both ends was presented in this paper
The results show that the existence of supported clearance may lead to the changing of stiffness of the pipe vibration system and the dynamic behaviors of the pipe system show nonlinearity and become more complex; for example, the amplitudefrequency curve of the foundation frequency showed hard nonlinear phenomenon
Harr wavelet method was used by Xie et al [7] for free vibrations of thin cylindrical shells with various boundary conditions based on Goldenveizer-Novozhilov shell theory and the displacements were represented by Haar wavelet series and their integrals in the axial direction and the Fourier series in the circumferential direction
Summary
Pressure pipe is commonly used as structural member or mechanical component in many engineering applications and chemical equipment, such as centrifugal compressor. Lam and Loy [2] studied the effects of boundary conditions on the free vibration characteristic for a multilayered cylindrical shell based on Love’s first approximation theory using Ritz method. Sun and Liu [26, 27] employed the Rayleigh-Ritz method to study the effect of the variations of restraint stiffness on the natural characteristics of rotating cylindrical shells with and without ring-support based on the Sanders’ shell theory and the displacements were considered as the characteristic orthogonal polynomial series. [28] investigated nonlinear free vibration analysis of prestressed circular cylindrical shells placed on Winkler and Pasternak foundation and the effects of prestressed condition and elastic foundation on natural frequencies under various boundary conditions were analyzed. Dimensional spectrum, bifurcation diagram, time domain response graph, frequency spectrum plot, s-v phase diagram, and Poincaresection with different parameters were obtained to analyze the effect of pulsed frequency, supporting stiffness, and supported clearance on dynamic characteristic of pressure pipe
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