FUOYE Journal of Engineering and Technology, Volume 3, Issue 2, September 2018 ISSN: 2579-0625 (Online), 2579-0617 (Paper) FUOYEJET © 2018 131 http://dx.doi.org/10.46792/fuoyejet.v3i2.250 engineering.fuoye.edu.ng/journal Natural Frequencies of Pressurized Hot Fluid Conveying Pipes Adekunle O. Adelaja Department of Mechanical Engineering, University of Lagos, Akoka, Yaba, Lagos State, 101017, Nigeria aadelaja@unilag.edu.ng Abstract— 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 —————————— ◆ —————————— 1 INTRODUCTION ipes or tubes conveying hot pressurized fluids are of immense use in many engineering applications, such as medical equipment (e.g., blood pressure monitoring transducers). Other areas of applications include oil and gas exploitation, heat exchangers, nuclear reactors, chemical plants and various process plants. There are other new and emerging applications in drug delivery, microfluidic and nanofluidic devices (Paidoussis 1998; Qirke 2007; Whitby and Wang 2009; Wang 2010). The effect of pressure variation cannot be overemphasized in that most of these systems are designed for specific operational range of pressures outside which danger can occur. Design and analysis of structures, such as pipes should take into account the operating conditions that can affect the vibration and integrity of such structures. Examples of such operating conditions are the operating temperature, operating pressure, and differential pressure that are experienced during the conveyance of fluid in pipes. Several review works have been done by Wickert and Mote (1988) and Chen (2005). Many of the reviewed works are based on elastic models (Thurman and Mote, 1969; Pakdemirli, Ulsoy and Ceranoglu, 1994; Pakdemirli and Ulsoy, 1997; Pakdemirli and Ozkaya, 1998; Pakdemirli, 1999; Vestroni, 2000; Hedrih, 2007; Oz and Olunloyo et al., 2007; Koivurova, 2009; Olunloyo, Osheku and Adelaja, 2010; Ghayesh, 2011; Adelaja, 2013). The nonlinear analysis of a fluid conveying pipe with simply supported ends was first studied by Thurman and Mote (1969) using small perturbation technique. It was discovered that in evaluating the natural frequencies of the system, the importance of nonlinear terms increases with flow velocity so that the range of application of linear theory becomes restricted as the flow velocity increases. On the study of the principal resonance and combination resonances of any two modes for an axially accelerating string, Pakdemirli and Ulsoy (1997) found that there were instabilities when the fluctuating frequency was near twice any natural frequency, but there were no instabilities for frequencies close to zero. Pellicano and Zirilli (1998) applied boundary layer solution for the axially moving beam with small flexural stiffness. * Corresponding Author Oz and Pakdemirli (1999) investigated the stability of an axially accelerating elastic tensioned beam moving with harmonically varying velocity. The method of multiple scales was employed in the analysis of the equation of motion, and the influence of small fluctuations in velocity on the stability of the system was investigated. Oz and Boyaci (2000) applied direct perturbation method for the problem of transverse vibration of tensioned fluid conveying pipes with time-dependent velocity. Operational methods were employed in the study of the dynamic behavior of pipeline laid on the seabed (Olunloyo, et al., 2007; 2010). Adelaja (2013), on the study of the temperature modulation of the dynamic responses of flexible fluid conveying pipes, applied the hybrid Fourier-Laplace transforms method. However, the Coriolis acceleration effect was not properly evaluated because of the mixed term. Ghayesh (2011) investigated the effects of axial speed and ply orientation angle on the natural frequencies, complex mode functions, and critical speeds of axially moving laminated composite beams. The parametric study was also done on the effects of system variables on the vibration characteristics of the system. Hermansen and Thomsen (2018) employed mode shape and damping coefficient methods to develop estimation for the boundary parameter for elastic beam using measured natural frequencies. Both methods can be combined to estimate the effects of boundary tension and boundary damping on the natural frequencies and damping ratios. The methods accurately estimated the natural frequencies, mode shape coefficient close to the measured values. Tan et al. (2018) investigated the equilibrium configurations and natural frequencies of Timoshenko pipe conveying fluid on the supercritical regime. The effects of length and thickness on mid-point deformation of the Euler-Bernoulli and Timoshenko pipes were compared. Timoshenko pipe was said to reach equilibrium bifurcation faster. In this paper, the solution of the nonlinear transverse vibration equation was obtained using the complex mode function. This method has been found to handle the mixed term (i.e., Coriolis force) conveniently compared with the hybrid Fourier-Laplace transformation technique used by Adelaja (2013). The pressurized, hot fluid is mathematically modeled together with the pipe-foundation system and solved P