Stability Analysis of TLP Tethers Under Vortex-Induced Oscillations

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
A. K. Banik ◽  
T. K. Datta
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Equation Of Motion ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
The Stability ◽  
Lock In ◽  
Continuation Technique ◽  
Mode Response ◽  
Stability Of The Solution

The vortex-induced oscillation of TLP tether is investigated in the vicinity of lock-in condition. The vortex shedding is caused purely due to current, which may vary across the depth of the sea. The vibration of TLP is modeled as a SDOF problem by assuming that the first mode response of the tether dominates the motion. Nonlinearity in the equation of motion is produced due to the relative velocity squared drag force. In order to trace different branches of the response curve and investigate different instability phenomena that may exist, an arc-length continuation technique along with the incremental harmonic balance method (IHBC) is employed. A procedure for treating the nonlinear term using distribution theory is presented so that the equation of motion is transformed to a form amenable to the application of IHBC. The stability of the solution is investigated by the Floquet theory using Hsu’s scheme.

scholarly journals Calculating periodic vibrations of nonlinear autonomous multi-degree-of-freedom systems by the incremental harmonic balance method

2004 ◽  
Vol 26 (3) ◽  
pp. 157-166
Author(s):  
Nguyen Van Khang ◽  
Thai Manh Cau
Keyword(s):  
Harmonic Balance ◽  
Floquet Theory ◽  
Monodromy Matrix ◽  
Harmonic Balance Method ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Van Der Pol ◽  
Incremental Harmonic Balance ◽  
The Stability

In this paper the incremental harmonic balance method is used to calculate periodic vibrations of nonlinear autonomous multip-degree-of-freedom systems. According to Floquet theory, the stability of a periodic solution is checked by evaluating the eigenvalues of the monodromy matrix. Using the programme MAPLE, the authors have studied the periodic vibrations of the system multi-degree van der Pol form.

Stability Analysis of an Articulated Loading Platform in Regular Sea

2007 ◽  
Vol 3 (1) ◽  
Author(s):  
A. K. Banik ◽  
T. K. Datta
Keyword(s):  
Harmonic Balance ◽  
Harmonic Wave ◽  
Harmonic Balance Method ◽  
Equation Of Motion ◽  
Damping Term ◽  
Incremental Harmonic Balance Method ◽  
Left Hand ◽  
Hydrodynamic Damping ◽  
Incremental Harmonic Balance ◽  
The Right

Stability of the response of an articulated loading platform under regular wave, modeled as a SDOF nonlinear oscillator, is investigated. Relative velocity square drag force for harmonic wave appearing in the right hand side of the equation of motion is mathematically treated to bring the velocity dependent nonlinear hydrodynamic damping term to the left hand side of the equation of motion. Use of these two techniques makes the equation of motion amenable to the application of method IHBC. In order to trace different branches of the response curve and investigate different instability phenomena that may exist, the commonly used incremental harmonic balance method (IHB) is modified and integrated with an arc-length continuation technique to develop into incremental harmonic balance continuation (IHBC) method. Further, a technique for treating the nonlinear hydrodynamic damping term using a concept of distribution theory has been developed. The stability of the solution is investigated by the Floquet theory using Hsu’s scheme. The stable solutions obtained by the IHBC method are compared with those obtained by the numerical integration of equation of motion wherever applicable.

scholarly journals Comparison of Common Methods in Dynamic Response Predictions of Rotor Systems with Malfunctions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongliang Yao ◽  
Qian Zhao ◽  
Qi Xu ◽  
Bangchun Wen
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Newmark Method ◽  
Incremental Harmonic Balance Method ◽  
Rotor Systems ◽  
Double Frequency ◽  
Frequency Domain Methods ◽  
Incremental Harmonic Balance

The efficiency and accuracy of common time and frequency domain methods that are used to simulate the response of a rotor system with malfunctions are compared and analyzed. The Newmark method and the incremental harmonic balance method are selected as typical representatives of time and frequency domain methods, respectively. To improve the simulation efficiency, the fixed interface component mode synthesis approach is combined with the Newmark method and the receptance approach is combined with the incremental harmonic balance method. Numerical simulations are performed for rotor systems with single and double frequency excitations. The inherent characteristic that determines the efficiency of the two methods is analyzed. The results of the analysis indicated that frequency domain methods are suitable single and double frequency excitation rotor systems, whereas time domain methods are more suitable for multifrequency excitation rotor systems.

scholarly journals A Modified Incremental Harmonic Balance Method for 2-DOF Airfoil Aeroelastic Systems with Nonsmooth Structural Nonlinearities

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Ying-Ge Ni ◽  
Wei Zhang ◽  
Yi Lv ◽  
Stylianos Georgantzinos
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Free Play ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Aeroelastic System ◽  
Structural Nonlinearity ◽  
Incremental Harmonic Balance

A modified incremental harmonic balance method is presented to analyze the aeroelastic responses of a 2-DOF airfoil aeroelastic system with a nonsmooth structural nonlinearity. The current method, which combines the traditional incremental harmonic balance method and a fast Fourier transform, can be used to obtain the higher-order approximate solution for the aeroelastic responses of a 2-DOF airfoil aeroelastic system with a nonsmooth structural nonlinearity using significantly fewer linearized algebraic equations than the traditional method, and the dominant frequency components of the response can be obtained by a fast Fourier transform of the numerical solution. Thus, periodic solutions can be obtained, and the calculation process can be simplified. Furthermore, the nonsmooth nonlinearity was expanded into a Fourier series. The procedures of the modified incremental harmonic balance method were demonstrated using systems with hysteresis and free play nonlinearities. The modified incremental harmonic balance method was validated by comparing with the numerical solutions. The effect of the number of harmonics on the solution precision as well as the effect of the free-play and stiffness ratio on the response amplitude is discussed.

Sign in / Sign up

Export Citation Format

Share Document