Steady-state response of a fluid-conveying pipe with 3:1 internal resonance in supercritical regime

Abstract

The forced vibration response of the pipe conveying fluid, with 3:1 internal resonance, is studied here for the first time. The straight equilibrium configuration becomes bent while the velocity of the fluid exceeds the critical value. As a result, the original mono-stable system transforms to a bi-stable system. Critical excitation which can cause global responses is solved out from the potential equation of the unperturbed system. The condition of 3:1 internal resonance is established after the partial differential equation is discretized. Global bifurcations are studied in simulation ways. By the method of multiple scales, local responses around the bent configuration are investigated. The analytical results are verified by simulations. Responses at the second mode bifurcate out another branch near the resonance frequency. It is very different with the triply harmonic responses without internal resonance. The triply harmonic response is a resonant excitation to the second mode. Responses will change largely with the detuning relationship between these two modes. Influences of the excited amplitude are also studied. Based on the analytical method, critical excited conditions of jumping and hysteretic phenomena are determined. The responses will have up-and down-bifurcations in the special region.

Magneto Electro Elastic Modelling and Nonlinear Vibration Analysis of Bi Directional Functionally Graded Beams

“…x hh (7) where the superscripts c and b respectively refer to the properties of the CoFe2O4 and BaTiO3 materials, ce represents the distance between the physical and geometric centers, the calculation of which is obtained in the previous literature [52]. In addition, n denotes the thickness FG index, which estimates the volume fraction exponent along the beam thickness orientation.…”

“…Due to its complexity, the investigation on the nonlinear dynamics of the engineering structures is a challenging subject. As the development of the theories of nonlinear dynamics, the nonlinear free vibration [1,2], nonlinear primary resonance [3,4], nonlinear parametric resonance [5,6], nonlinear internal resonance [7,8] and nonlinear isolation [9] have been widely studied by using some developed approaches such as the method of multiple scales [10,11], harmonic balance method [12], the Galerkin truncation method [14], the differential quadrature method [15], the finite difference method [16,17]. The predictions and understanding become possible for complicated nonlinear phenomena in the dynamic system, such as jumping, saturation, bifurcations and chaotic behaviors [17][18][19][20] to be beneficial for the application of the engineering devices.…”

Chaotification in an internal-resonance-based electromagnetic vibration energy harvester

“…Internal resonance, which is one of the unique phenomena in the multi-DOF nonlinear dynamics, occurs when the linear natural frequencies of the first two vibration modes are in commensurate or nearly commensurate ratio, i.e., 1:2 or 1:3, etc. There are several significant investigations on the internal resonance：fluid-conveying pipe [11], marine riser [12], arch beams [13], composite plates [14], nanoscale rods [15], rotor systems [16], magnetic resonance force microscopy [17], and the unique phenomenon such as mode interaction was revealed by Galerkin truncation, multi-scale method, harmonic balance method, etc. Nonlinear behaviors such as bifurcation and chaos were detected as well.…”

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].…”