Abstract: Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow are calculated when Reynolds number is 1.35×104. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the tube is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-tube interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering the vortex-induced vibration system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of tube are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed by using trajectory, phase portrait, and Poincaré sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum, and the “lock-in” begins simultaneously. In the range of lock-in, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode.
Abstract: In general dynamic analyses, lower mode response is
of interest, however the higher modes of spatially discretized
equations generally do not represent the real behavior and not affects
to global response much. Some implicit algorithms, therefore, are
introduced to filter out the high-frequency modes using intended
numerical error. The objective of this study is to introduce the
P-method and PC α-method to compare that with dissipation method
and Newmark method through the stability analysis and numerical
example. PC α-method gives more accuracy than other methods
because it based on the α-method inherits the superior properties of the
implicit α-method. In finite element analysis, the PC α-method is more
useful than other methods because it is the explicit scheme and it
achieves the second order accuracy and numerical damping
simultaneously.