Stability Analysis of a Yawing Flat Plate Into the Water Current

2012 ◽  
Author(s):  
Mohammadmehdi Armandei ◽  
Antonio Carlos Fernandes
Keyword(s):  
Stability Analysis ◽  
Flat Plate ◽  
Least Square Method ◽  
Least Square ◽  
Water Current ◽  
Torsion Spring ◽  
Flutter Derivative ◽  
Liapunov Stable ◽  
The Stability ◽  
Derivatives Of

The present study deals with the stability analysis of an oscillating flat plate into the water current. The flat plate, which is attached to a torsion spring and located vertically in the water current, has only 1 DOF that is yawing motion. The experiments have shown that as the current velocity exceeds a special threshold, the flat plate becomes unstable and begins to oscillate. This oscillation can be utilized to extract energy. A free vibration experimental technique is used in this study. The experimental results are analyzed using the flutter derivative theory, in which the flutter derivatives of the motion are extracted using GLS (General Least-Square) method. The results confirm that the flat plate becomes dynamically unstable. Also, there is a Liapunov stable fixed point on the origin at the phase portrait of the yawing motion.

van der Pol-Duffing Modeling for Torsional Galloping

2014 ◽  
Author(s):  
Antonio Carlos Fernandes ◽  
Mohammadmehdi Armandei
Keyword(s):  
Stability Analysis ◽  
Flat Plate ◽  
Phenomenological Model ◽  
Current Speed ◽  
Water Current ◽  
Van Der Pol ◽  
Angular Oscillation ◽  
Torsion Spring ◽  
Aforementioned Study ◽  
Torsional Galloping

This study is a continuation of the study presented in OMAE 2012 entitled: “Stability Analysis of a Yawing Flat Plate into the Water Current”[1]. The structure in the aforementioned study consists of a rectangular flat plate with an elastic axis in its mid-chord length. The elasticity is provided by torsion spring. The flat plate has only one degree of freedom which is angular oscillation about its axis. It is observed that as the current speed exceeds a critical velocity, the flat plate becomes unstable. The instability leads to torsional galloping occurrence, as a result of which the flat plate begins to oscillate angularly about the elastic axis. Through the present study, a phenomenological model is developed based on van der Pol-Duffing equation, in order to explain the instability leading to the torsional galloping.

scholarly journals System-Level Temperature Compensation Method for the RLG-IMU Based on HHO-RVR

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Hao Liang ◽  
Yumin Tao ◽  
Meijiao Wang ◽  
Yu Guo ◽  
Xingfa Zhao
Keyword(s):  
Least Square Method ◽  
Absolute Error ◽  
Performance Comparison ◽  
Compensation Method ◽  
Least Square ◽  
System Level ◽  
Measurement Unit ◽  
Error Terms ◽  
The Stability ◽  
Stability Time

The ring laser gyro inertial measurement unit has many systematic error terms and influences each other. These error terms show a complex nonlinear drift that cannot be ignored when the temperature changes, which seriously affects the stability time and output accuracy of the system. In this paper, a system-level temperature modeling and compensation method is proposed based on the relevance vector regression method. First, all temperature-related parameters are modeled; meanwhile, the Harris hawks optimization algorithm is used to optimize each model parameter. Then, the system compensation is modeled to stabilize the system output to the desired temperature. Compared with the least square method, the fitting performance comparison and the system dynamic compensation experiment prove this method’s superiority. The root mean square error, the mean absolute error, the R -squared, and the variance of residual increased by an average of 35.27%, 39.29%, 2.29%, and 30.34%, respectively.

scholarly journals Solution of inverse heat conduction equation with the use of Chebyshev polynomials

2016 ◽  
Vol 37 (4) ◽  
pp. 73-88 ◽  
Author(s):  
Magda Joachimiak ◽  
Andrzej Frąckowiak ◽  
Michał Ciałkowski
Keyword(s):  
Inverse Problem ◽  
Chebyshev Polynomials ◽  
Direct Problem ◽  
Least Square Method ◽  
Least Square ◽  
Random Disturbance ◽  
Inverse Heat Conduction ◽  
Chebyshev Nodes ◽  
The Difference ◽  
The Stability

AbstractA direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials. Calculations were made for a grid consisting of Chebyshev nodes, what allows us to use orthogonal properties of Chebyshev polynomials. Temperature distributions on the boundary for the inverse problem were determined using minimization of the functional being the measure of the difference between the measured and calculated values of temperature (boundary inverse problem). For the quasi-Cauchy problem, the distance between set values of temperature and heat flux on the boundary was minimized using the least square method. Influence of the value of random disturbance to the temperature measurement, of measurement points (distance from the boundary, where the temperature is not known) arrangement as well as of the thermocouple installation error on the stability of the inverse problem was analyzed.

Partial stability analysis of nonlinear time-varying impulsive systems

2019 ◽  
Vol 12 (06) ◽  
pp. 1950066
Author(s):  
Boulbaba Ghanmi
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Time Varying ◽  
Impulsive Systems ◽  
Partial Stability ◽  
Stability Theorems ◽  
Time Varying Systems ◽  
The Stability ◽  
Derivatives Of ◽  
Theoretical Results

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite. With the help of the notion of stable functions, asymptotic partial stability, exponential partial stability, input-to-state partial stability (ISPS) and integral input-to-state partial stability (iISPS) are considered. Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

scholarly journals Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

2021 ◽  
Author(s):  
Aqeel ur Rehman ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stable Solution ◽  
Mhd Flow ◽  
Least Square Method ◽  
Dual Solutions ◽  
Least Square ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

scholarly journals Modeling and parameters estimation of a Spatial Predator-Prey distribution

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Denis Ndanguza ◽  
Jean Pierre Muhirwa ◽  
Anatholie Uwimana
Keyword(s):  
Stability Analysis ◽  
Synthetic Data ◽  
Simulated Data ◽  
Least Square Method ◽  
Parameters Estimation ◽  
Least Square ◽  
Coefficient Of Determination ◽  
Model Parameters ◽  
Predator Prey ◽  
Monte Carlo Algorithms

Predator prey interactions are important in ecology and most of time in the analysis, the two antagonists are assumed to be in a closed system. The aim of this study is to model the unclosed predator-prey system. The model is built and simulated data are computed by adding noise on deterministic solution. Therefore, model parameters are estimated using least square method. We compute the two critical points and the stability analysis is carried out and results show that the population is stable at one critical point and unstable at (0,0). The model fits the synthetic data with coefficient of determination R2 = 0.9693 equivalent to 96.93%. Using the residual analysis to test the validity of the model, it is shown that there is no pattern between residuals. To strengthen the validity of the model, the Markov Chain Monte Carlo algorithms are used as an alternative method in parameters estimation. Diagnostics prove the chains’ convergence which is the sign of an accurate model. As conclusion, the model is accurate and it can be applied to real data.Keywords: predator-prey, spatial distribution, parameters, Metropolis-Hastings algorithm, model diagnostic, stability analysis

Spectrophotometric Study of Cobalt (II) Chlorocomplexes in Methanol in the Visible Domain

2011 ◽  
Vol 324 ◽  
pp. 170-173 ◽  
Author(s):  
Soumia Boulefred ◽  
Abdelghani Chiboub-Fellah ◽  
Fatema Zohra Chiboub-Fellah ◽  
Mustayeen Ahmed Khan
Keyword(s):  
Structural Modification ◽  
Graphical Method ◽  
Visible Region ◽  
Least Square Method ◽  
Spectrophotometric Study ◽  
Least Square ◽  
Protic Solvent ◽  
Spectra Analysis ◽  
Overall Stability ◽  
The Stability

Cobalt(II) chlorocomplexes were studied in a polar protic solvent namely methanol at 25°C. The spectrophotometric technique in the visible region was used. The studied equilibrium is: Co2++ j Cl-CoClj↔(j-2)-. Formation of three chlorocomplexes and a structural modification (Oh → Td) were obtained from recorded spectra analysis. The stability of CoCl+was studied by the graphical method of Kruh and the overall stability constants were calculated with the SIRKO program based on the least-square method. Different models were tested and the model was retained for which the best values are: log β1 = 0.92, log β2 = 1.31 and log β3 = 1.08.

Sign in / Sign up

Export Citation Format

Share Document