Flow-induced in-plane instabilities of curved pipes

A New Matrix Method for Solving Vibration and Stability of Curved Pipes Conveying Fluid

“…The elastic coe$cients K and K are so large that the boundary condition may be considered as a clamped}clamped case, which has been studied by Chen [4]. Table 1 shows the critical velocities obtained by reference [4] and this paper, where the values of K and K are K "2;10 kgf/cm, K "2;10 kgf cm/rad. It is seen from Table 1 that the authors' results are in good agreement with those by Chen.…”

Nonlinear dynamics of a fluid-conveying curved pipe subjected to motion-limiting constraints and a harmonic excitation

“…(12) can be reduced to that obtained by Chen (1972a). It should be pointed out that, for a cantilevered curved pipe, Chen (1972a) had obtained the static deflections of the curved pipe. These static deflections were shown to be related to the fluid velocity.…”

“…Afterwards, attention was focused on formulating the linear equations of motion of curved pipes. Chen (1972aChen ( , b, 1973 has studied the governing equations of uniformly curved pipes, both for the in-plane and out-of-plane vibrations, and it was found that the curved pipe might be subject to divergent or flutter instabilities. Misra et al (1988a, b) modelled a curved pipe conveying fluid with complex shape by the finite element method, taking into account the steady-state combined tension-pressure forces, neglected by Chen.…”

Vibration of Slender Structures Subjected to Axial Flow or Axially Towed in Quiescent Fluid

“…Work on the vibration and stability of curved pipes conveying fluid appears to have started in the 1960s. Some of the key contributions in this realm were made by, but not limited to, Svetlitskii [33][34][35], Chen [36][37][38], Doll and Mote Jr. [39,40], Hill and Davis [41], Dupuis and Rousselet [42], Misra et al [43][44][45], Ni et al [46], Qiao et al [47,48], and Jung and Chung [49]. The systems studied range from curved pipes shaped as circular arcs, L-or S-shaped configurations, analyzed by finite-element techniques [39][40][41][43][44][45], transfer-matrix technique [42,50] or differential quadrature method (DQM) [46-48, 51, 52].…”

“…There are three main theories available for predicting the stability and vibrations of curved pipes conveying fluid: the so-called "inextensible theories" [36,37,43,[46][47][48], the modified inextensible theory [44], and the complete "extensible" theories [33, 34, 40-42, 44, 45, 49]. The inextensible theories assume that the circular centerline of the pipe is essentially inextensible and all steady-state stress resultants are absent or neglected.…”