Hopf-Hopf interactions in a spring-supported pipe conveying fluid

Nonlinear geometrically exact dynamics of fluid-conveying cantilevered hard magnetic soft pipe with uniform and nonuniform magnetizations

“…In order to convert to the partial differential algebraic equations given in Eqs. ( 24), (25), and (43) into a set of ordinary differential algebraic equations based on the Galerkin discretization technique, the elements of the quaternion system and the Lagrangian multiplier function, respectively, are approximated by…”

“…The nonlinear mathematical formulation derived from the third-order 2 approximation is the well-known model to simulate their nonlinear responses in the pre-and postflutter regions. This approximation model has attracted a great number of research interests from both theoretical and experimental studies [18][19][20][21][22][23][24][25][26]. For cantilevered flexible pipes conveying fluid, the third-order approximation model is incapable of estimating their nonlinear behavior when they undergo extremely large deformations.…”

Hopf Bifurcation of a Standing Cantilever Pipe Conveying Fluid with Time Delay

“…Modarres-Sadeghi et al [14] investigated the two-dimensional (2-D) and three-dimensional (3-D) futter of cantilevered pipes conveying fuid. Yamashita et al [15] investigated the dynamics of a pipe with a spring support and an end mass. Tey focus on Hopf-Hopf interactions and conduct nonlinear analyses to clarify the evolutions of the amplitudes of two unstable modes.…”

Nonlinear analysis of L-shaped pipe conveying fluid with the aid of absolute nodal coordinate formulation

“…In addition, the system of the fluid-conveying pipe can display rich dynamical behaviors and has become a new paradigm in the field of dynamics, which has been pointed out by Païdoussis [1]. Thus, due to these facts, the literature concerned with the dynamics of pipes conveying fluid has emerged in the past few decades [2][3][4][5][6][7][8][9].…”