A further study on the non-linear dynamics of simply supported pipes conveying pulsating fluid

In this paper, the non-linear dynamics of simply supported pipes conveying pulsating fluid is further investigated, by considering the effect of motion constraints modeled as cubic springs. The partial differential equation, after transformed into a set of ordinary differential equations (ODEs) using the Galerkin method with N=2, is solved by a fourth order Runge-Kutta scheme. Attention is concentrated on the possible motions of the system with a higher mean flow velocity. Phase portraits, bifurcation diagrams and power spectrum diagrams are presented, showing some interesting and sometimes unexpected results. The analytical model is found to exhibit rich and variegated dynamical behaviors that include quasi-periodic and chaotic motions. The route to chaos is shown to be via period-doubling bifurcations. Finally, the cumulative effect of two non-linearities on the dynamics of the system is discussed.     

Stability analysis of viscoelastic curved pipes conveying fluid

Based on the Hamilton' s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.     

Nonlinear dynamics of extensible viscoelastic cantilevered pipes conveying pulsatile flow with an end nozzle

Nonlinear dynamics of an extensible cantilevered pipe conveying pulsating flow is considered in this paper. The fluid flow fluctuates harmonically and exhausts via a nozzle attached to the end of the pipe. Taking into account the extensibility assumption, the coupled nonlinear lateral–longitudinal equations of motion are derived using Hamilton's principle and discretized via Galerkin's method. The adaptive time step Adams algorithm is applied to extract the time response, and then the bifurcation, power spectral density and phase plane maps are plotted for some case studies. Effects of some geometrical parameters such as flow mass, pulsating flow frequency, gravity, nozzle mass and nozzle aspect ratio parameters are studied on the dynamics of such system and the validity of extensibility assumption is investigated and some conclusions are drawn.     

Differential quadrature method to stability analysis of pipes conveying fluid with spring support

It is a new attempt to extend the differential quadrature method (DQM) to stability analysis of the straight and curved centerline pipes conveying fluid. Emphasis is placed on the study of the influences of several parameters on the critical flow velocity. Compared to other methods, this method can more easily deal with the pipe with spring support at its boundaries and asks for much less computing effort while giving aceptable precision in the numerical results. Supported by National Key Project of China (No. PD9521907) and the National Science Foundation of China (No. 19872025).     

Dynamic analysis and regulation of the flexible pipe conveying fluid with a hard-magnetic soft segment

Applied Mathematics and Mechanics - The recently developed hard-magnetic soft (HMS) materials can play a significant role in the actuation and control of medical devices, soft robots, flexible...