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In this paper, a design strategy to keep a pipe away from resonance by adjusting retaining clips is presented. The pipe natural frequency is within the band of vibration frequencies generated by mechanical operation, which can cause the resonance phenomenon. The resonance of pipes could bring serious disaster to the mechanical operation. Therefore, the band of vibration frequencies generated by the mechanical operation is defined as the preserved frequency band (PFB). The pipe in engineering has been simplified to a multispan pipe conveying fluid. An integral pipe model of a multispan pipe conveying fluid is established by simplifying the retaining clips. The natural frequencies of a pipe with clips are obtained. The resonance range and safety range of pipe length are defined as the natural frequencies inside and outside the PFB, respectively. The absolute safety length and the absolute resonance length with respect to clip number are derived. Moreover, the influence of the clip stiffness and location on the safety range is determined. The results show that the safety range is significantly changed by adjusting the vertical stiffness, torsional stiffness, and location of the clips. Based on the results, a pipe design strategy is proposed to stay away from resonance and make for a smaller number of clips. Subsequently, a design for an aircraft pipe is carried out as an example. As a result of the design, the natural frequencies of the aircraft pipe are kept away from the PFB. In summary, a design strategy is obtained to avoid resonance for pipes by adjusting the clip stiffness and/or location. [ABSTRACT FROM AUTHOR]

The operation of mechanical systems generates vibrations with a certain range of frequencies. Pipes conveying fluid have multiple natural frequencies. It is difficult to avoid one or more natural frequencies of pipes in the operating frequency range of the system, which can lead to resonance and fatigue failure. In this paper, a design strategy to modulate the multi-span pipe's natural frequency by reinforcing pipes with graphene platelets (GPLs) nanofiller is proposed to solve the pipe resonance in engineering. The multi-span functionally graded (FG) pipe is constructed based on an integral pipe model with GPLs uniformly or non-uniformly distributed in the metal matrix. The effective properties of the nanocomposite are determined by using the Halpin-Tsai micromechanics model and rule of mixture. Subsequently, the safety range and resonance range of the multi-span FG pipe are obtained by comparing the first tenth-order natural frequency and preserved frequency band. A comprehensive investigation on the effect of patterns, weight fraction, and geometric parameters of GPL is conducted to identify the most effective way to modulate the pipe's natural frequency. The results indicate that GPL weight fraction is able to modulate the multi-span pipe's natural frequency and safety range over a wide range. In addition, the natural frequency and safety range of the FG pipe reinforced with GPLs increase as the stiffness and number of retaining clip increase. Based on the results, a pipe design strategy with fewer retaining clips is proposed for pipes away from resonance by reinforcing pipes with GPL nanofiller. In the case of an aircraft hydraulic pipe, the natural frequency of the pipe reinforced with GPLs is far away from the preserved frequency band and without resonance in operation. In summary, the design strategy of pipe reinforced with GPLs shed important insights on reducing the vibration level of multimodal structures. • Graphene platelet weight fraction is able to modulate the pipe's natural frequency over a wide range. • A new concept of frequency preserve is proposed for pipe design with low vibration level. • A design strategy for pipes away from resonance by graphene platelets nanofiller is presented. • The proposed design strategy avoids resonance of pipes and makes for a smaller number of clips. [ABSTRACT FROM AUTHOR]

• The integral-model and the two-span model of a pipe with a retaining clip are established respectively. • Critical velocity and natural frequencies of fluid-conveying pipes with a retaining clip are obtained. • Variations in the clip stiffness can cause different types of non-trivial equilibria of the pipe. • Natural frequencies of the pipe can be adjusted in a wide range by changing the clip position. Although retaining clips are widely used to constrain high-velocity fluid-conveying pipes, there are few studies on the influence of retaining clips on the supercritical vibration characteristics of the pipes. In this study, the vibration characteristics of the fluid-conveying pipe with retaining clip are firstly presented in the supercritical regime. According to the generalized Hamiltonian principle, the governing equation of the fluid-conveying pipe with the retaining clip is derived. When the flow velocity exceeds the critical velocity, the equilibrium configuration of the pipe becomes the non-trivial static equilibrium configuration. By coordinate transformation, the governing equation of the supercritical pipe around the non-trivial static equilibrium configuration is obtained. Emphasis is put on the effects of the clip stiffness and position on the critical flow velocity, equilibrium configuration and natural frequencies. It is found that variations in the retaining clip stiffness can cause different types of non-trivial equilibrium configurations. The natural frequencies will not be monotonic with the increasing clip stiffness in the supercritical flow. Furthermore, the two-span model of the pipe with the clip is obtained for verification. In conclusion, this work lays a foundation for the study of the dynamic response of the supercritical fluid-conveying pipe with retaining clip and can provide a reference for the analysis of the vibration characteristics of the clips and pipes system in engineering. [Display omitted] [ABSTRACT FROM AUTHOR]