Phononic Band Gap and Free Vibration Analysis of Fluid-Conveying Pipes with Periodically Varying Cross-Section

Phononic crystals (PCs) are a novel class of artificial periodic structure, and their band gap (BG) attributes provide a new technical approach for vibration reduction in piping systems. In this paper, the vibration suppression performance and natural properties of fluid-conveying pipes with periodically varying cross-section are investigated. The flexural wave equation of substructure pipes is established based on the classical beam model and traveling wave property. The spectral element method (SEM) is developed for semi-analytical solutions, the accuracy of which is confirmed by comparison with the available literature and the widely used transfer matrix method (TMM). The BG distribution and frequency response of the periodic pipe are attained, and the natural frequencies and mode shapes are also obtained. The effects of some critical parameters are discussed. It is revealed that the BG of the present pipe system is fundamentally induced by the geometrical difference of the substructure cross-section, and it is also related to the substructure length and fluid–structure interaction (FSI). The number of cells does not contribute to the BG region, while it has significant effects on the amplitude attenuation, higher order natural frequencies and mode shapes. The impact of FSI is more evident for the pipes with smaller numbers of cells. Moreover, compared with the conventional TMM, the present SEM is demonstrated more effective for comprehensive analysis of BG characteristics and free vibration of PC dynamical structures.

Coupled Bi-Flexural–Torsional Vibration of Fluid-Conveying Pipes Spinning About an Eccentric Axis

This paper presents a dynamical model of a fluid-conveying pipe spinning about an eccentric axis. The coupled bi-flexural–torsional free vibration and stability are analyzed for such a doubly gyroscopic system. The partial differential equations of motions are derived by the extended Hamilton principle, and are then truncated by a 4-term Galerkin technique. The frequency and energy evolutions and representative mode shapes in the two transverse directions and torsional direction are investigated to unveil the essential dynamical attributes of the system. It is indicated that the stability of the present system mainly depends on spinning speed, flow velocity and eccentricity, while the torsional frequencies are almost immune to the flow velocity. The pipe reveals ‘traveling-wave’ modal vibrations in both transverse directions, and a general ‘standing-wave’ modal vibration in the torsional direction.

Natural Frequencies of Pressurized Hot Fluid Conveying Pipes

In this study, the transverse natural frequencies of a pressurized hot fluid conveying pipe is investigated using complex mode function. Employing the dispersive relations and the non-trivial solution of the coefficient matrix obtained from the boundary equations, the eigenvalues and the linear natural frequencies are obtained numerically. The parametric study is conducted to highlight the effects of variation in operating pressure and pressure drop on the first two modes of the natural frequency of the system. The natural frequency was found to increase nonlinearly with the increase in the operating pressure and pressures drop but decreases with flow velocity. Keywords— Fluid-conveying pipe, natural frequency, pressure variation, transverse vibrations