Effect Of Nonlinear Terms Research Articles

Effect of nonlinear terms in piston theory on characteristics of panel flutter

Currently, there is no systematic summary of the influence of the nonlinear terms in piston theory on the panel flutter. The two-dimensional nonlinear panel flutter equations under supersonic airflow based on the first, second, and third-order piston theories is established. The stability of the heated panel is analyzed by using the Lyapunov's indirect method, and the panel flutter equations are numerically solved based on the numerical analysis method to investigate the influence of the nonlinear terms in piston theory on the panel flutter. The results show that: ①Under a small temperature rise ratio, the panel response under the first-order piston theory only exhibits the convergent motion and single-period limit cycle flutter. While under higher-order piston theories, the panel response is more complex, exhibiting more complex nonlinear dynamic phenomena such as multi-period limit cycle flutter and chaotic motion in addition to the aforementioned characteristics. ②As the Mach number increases, the required dynamic pressure and temperature rise ratio decrease gradually when the dynamic response of the panel under the first-order piston theory and higher-order piston theories exhibit significant differences. ③The significant differences in the computational results of the second-order and third-order piston theory appear under the high Mach numbers and relatively high dynamic pressures, and the same phenomenon occurs underthe high temperature rise ratios. ④When the dynamic response characteristics of the panel are basically consistent, the displacement response peak calculated by using the higher-order piston theory is usually smaller than the result calculated by using the first-order piston theory, and the maximum error can reach about 16.66%. The present results have certain reference value for selecting the appropriate analysis method for the panel flutter under different conditions in practical applications.

Free wake panel method simulations of a highly flexible wing in flutter and gusts

This paper presents low speed fluid structure interaction simulations of a highly flexible wing at various flow conditions, including flutter and excitation from sinusoidal gusts. Such wings are becoming more relevant in recent years, due to their potential for improving aerodynamics and reducing weight, while their flutter characteristics are particularly challenging to address, as the modal properties of the wings change as deflections increase. Calculations are based on time domain coupling of a geometrically exact beam structural model and a 3D free wake panel method, modeling the outer surface of the wing, which allow for nonlinear effects in terms of geometrical deformations and the flow at low computational cost. Static and aeroelastic wing deflections are in line with experimental data of the Pazy wing, which is a benchmark for highly flexible wings from Technion. Two flutter mechanisms are predicted within 1 to 3 m/s of the experimental range. An analysis of the flutter modes is performed, showing that the second torsion mode plays a role in flutter, something that had not been published before. Limit cycle oscillations are achieved and are shown to compare well with reference data, with the frequency being within 1% of the experimental value. Finally, results of gust simulations of the Pazy wing are compared to data from experiments and corrections for the wind tunnel measurements are proposed, which should facilitate future validation efforts. This work serves as a contribution to the Pazy wing dataset and is a step towards mid-fidelity simulations for more complex configurations.

Chaotic Threshold of a Nonlinear Zener Systems Based on the Melnikov Method

Regarding a nonlinear Zener model with a viscoelastic Maxwell element as the research object, the complicated dynamic behaviors such as homoclinic bifurcation and chaos under harmonic excitation are investigated. At first, the analytically necessary condition for chaos in the sense of Smale horseshoe is derived based on the Melnikov method. Then, the system parameters that meet the analytical condition and the main resonance condition are selected for the numerical simulation. From the bifurcation diagrams and the largest Lyapunov exponents, it is found that the homoclinic orbit breaks, and the system goes to chaos in a crisis way when the excitation amplitude passes the first threshold. The system enters another new chaotic state in the form of period-doubling bifurcation with the increase of the excitation amplitude. At last, the effects of nonlinear term, stiffness coefficient and damping coefficient of Maxwell element on the analytically necessary condition for chaos are analyzed, respectively, and the correctness of the analytical result is proved by numerical simulation. The research result shows that the critical excitation amplitude decreases with the increase of nonlinear term. In addition, the chaotic threshold increases first and then tends to remain unchanged with the raise of stiffness coefficient. The chaotic threshold increases first and then decreases with the enhancement of damping. These results provide a theoretical basis for the research of nonlinear viscoelastic system in the future.

Dynamics of stocks prices based in the Black & Scholes equation and nonlinear stochastic differentials equations

The effect of non-linear terms on Itô–Langevin diffusion model with aim to analyze the change generated on long-tail distribution of the probability density of the returns and volatilities and long range memory is investigated. In particular, whether the model still obeys to stylized facts obeyed by the financial markets that is, the behavior of the long-tail distribution of the returns and volatilities and the correspondent scale law. More specifically, whether after inclusion of nonlinear terms in the model, it still satisfies to the inverse cubic law obeyed for quasi all markets and therefore, if the model still obey to the aspects or statistical regularities obeyed by the financial markets.

A new robust decentralized approach based on adaptive fuzzy backstepping method for microgrid secondary voltage control

Secondary microgrid voltage control is one of the most important parts of hierarchical control in islanded mode. By using of fuzzy and adaptive control methods, this paper presents a new method for secondary voltage control of islanded microgrid and also uses the rules of the backstepping method to obtain a control signal. The backstepping method has been used as a robust control technique to overcome the uncertainty and the effects of nonlinear terms, and the fuzzy method has been used to reduce its complexity. The adaptive method also gives fuzzy approximation coefficients. Considering the effect of neighbor agents on each other as uncertainty, a robust decentralized control method has been implemented in islanded microgrid. The simulation results in MATLAB environment show the controller’s ability to eliminate voltage deviations and the appropriate dynamic response.

Investigation of Wave Propagation Behavior of Partially Two-Layered Plates

Abstract In this study, the acoustic emission characteristics of a rectangular plate with a partially covered free damping viscoelastic layer excited by an acoustic source (Hsu-Nielsen) has been investigated. A partially covered plate configuration consisting of a base plate (aluminum) and free damping layer (polyethylene) is considered. An acoustic emission source generated different acoustic modes, which caused the plate to have in-plane and out-plane displacements. These plate displacements will be captured by acoustic sensors. To obtain the general form of plate displacements theoretically, Von Karman theory and a Kelvin-Voigt model were used and the equations of motion were derived using Galerkin’s method. The effects of nonlinear terms of the strain-displacement relation on wave propagation characteristics of plates were investigated. The main frequency ranges of signals and the propagation speed of acoustic modes and their attenuation are very important for source locating. These parameters depend on the acoustic source and transmitted medium. So, theoretically predicting the main frequency range of signals because of the acoustic source and propagation characteristics of different acoustic modes has an important role in an acoustic source–locating algorithm. For this purpose, acoustic emission experiments were carried out using two R15α sensors. Frequency domains of theoretical and experimental results were analyzed. A comparison of the obtained results showed good agreement between the experimental and theoretical Lamb velocities and main frequency ranges.

Effects of nonlinear terms and topography in a storm surge model along the southeastern coast of China: a case study of Typhoon Chan-hom

Based on Finite Volume Coastal Ocean Model (FVCOM), this study constructed a numerical model covering the Bohai Sea, Yellow Sea, and East China Sea. National Centers for Environmental Prediction’s Climate Forecast System Reanalysis (NCEP-CFSR) data were used to drive the model to simulate a large storm surge generated by Typhoon Chan-hom. The model was validated by multiple in situ observations of water levels taken at tidal gauge stations. The effects of the nonlinear terms and topography on the modeling of storm surges were then studied. First, the tide–surge interaction during the storm surge process was analyzed. The results show that the tide–surge interaction can suppress the storm surge at the climax of the astronomical tide and benefit the growth of the storm surge at the ebb of the astronomical tide. The tidal constituents M2, S2 and K1 were added to analyze the influences of the amplitudes and periods of tides on the nonlinear reaction. The results indicate that the nonlinear effect will be enhanced by an increased tidal height; additionally, the nonlinear interaction of semidiurnal tides is more significant than that of diurnal tides. The semidiurnal fluctuation that appears near the peak-value time is also attributed to the tide–surge interaction. Moreover, the tide–surge interaction can be influenced by the water depth and position of the area of interest. According to the numerical results, topography has a certain impact on the storm surge: The peak value of the storm surge will decrease with increasing slope. The existence of the Ryukyu Islands reduces the area influenced by the storm surge on the southeast coast of China but expands the high-value storm surge area.

Secondary control of islanded microgrid using robust finite time decentralized method based on adaptive fuzzy sliding mode controller

Secondary voltage control of islanded microgrid is one of the main needs of microgrid hierarchical control from one perspective and the realization of stable smart grids from another aspect. This article aims to achieve several goals simultaneously: First, it provides a decentralized structure for controlling and regulating the voltage of DGs, in which the effects of nonlinear terms on the dynamics of the microgrid system are considered without elimination or linearization. The fuzzy method has been used to approximate the uncertainties, the interactions of agents and nonlinear terms, and the adaptive method has been used to obtain the optimal fuzzy approximation gains. Sliding mode rules are also used to obtain a control signal and using Lyapunov's theory, the finite time and robust stability of the closed-loop control system is guaranteed. The finite time approach ensures the achievement of convergence in a finite and definite time, and the robust approach realizes the dynamic stability of the system against uncertainties and disturbances. The results of the microgrid system simulation show well the proposed controller capability in different operating conditions.

Joule–Thomson expansion of a specific black hole in f(R) gravity coupled with Yang–Mills field

In this paper, we study the Joule–Thomson expansion of a specific black hole in f(R) gravity coupled with Yang–Mills field. Firstly, four-dimensional equation of state and the Joule–Thomson coefficient are derived from thermodynamic quantities, the critical temperature and the inversion temperature are obtained, and the isenthalpic curves and the inversion curves are plotted in the T − P plane. Then, by considering the higher dimensions black hole, the inversion temperature is obtained, the isenthalpic curves and the inversion curves are also plotted, and the effect of nonlinear term η and dimension for the Joule–Thomson expansion is demonstrated visually by depicting different curves. Finally, we compare the ratio of the inversion temperature to the critical temperatures with the van der Waals fluid and other black hole, which the ratio is not equal to 0.5, and it decreases with the dimensionality d.

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

Influence of nonlinear terms on dynamical behavior of graphene reinforced laminated composite plates

This research is focused on the effects of nonlinear terms on the dynamical behavior of graphene reinforced laminated composite plates. Firstly, the governing equations of the graphene reinforced composite thin plate subjected to transverse excitations are derived by using the Hamilton's principle and the von Karman deformation theory. Then numerical method is applied to investigate the nonlinear behaviors of graphene reinforced composite plates. Bifurcation diagram, waveform and phase portrait are demonstrated to analyze the nonlinear dynamics of the graphene reinforced laminated composite plates. Furthermore, the effects of nonlinear terms on the dynamical behavior are discussed in detail, where both the stronger and weaker nonlinear characteristics of lower modes of the plate are presented. Moreover, some interesting phenomena are obtained in numerical simulation.

Fully nonlinear and linear ship waves modelling using the potential numerical towing tank and NURBS

Waves induced by the ship advance in the calm water are simulated in a potential Numerical Towing Tank based on both the fully nonlinear approach and the linear theory. In the linear theory, a modified Green function, which was derived based on linearized free surface boundary conditions and the image method is used as a fundamental solution in the boundary integral equation. High-order boundary integral equation is used to solve the boundary value problem with Non-Uniform Rational B-Spline (NURBS) basis function. On the other hand, the time domain simulation of the fully nonlinear free surface flow due to the steady flow past over a ship model is conducted based on the Mixed Eulerian-Lagrangian approach. NURBS surface is used to describe the ship hull and the fully nonlinear free surface evolution. The numerical solutions are compared with a prior experimental study to verify both numerical models. In addition, the effect of nonlinear terms in fully nonlinear free surface boundary conditions is investigated. The wave making resistance as an essential criterion is compared with the experimental data and some numerical efforts to investigate the accuracy of both models. The capability of the modified Green function is also examined to simulate the ship waves in rectangular channels.

Transient approach for identification of the S-shape region of pump turbines

A new approach for identi cation of the S-shape region of pump turbines by means of transient tests is presented. The behavior of pump turbines is characterized by the S-shape region that is passed during load rejection. The mechanisms within the S-shape region are still part of basic research. Beside the known Thoma number dependency, further non-linear effects in terms of a hysteresis loop in the S-shape region are suspected. Since the S-shape region is passed in both directions during load rejection a hysteresis behavior would in uence the water way dynamics. The common approach by measuring various steady points is not able to capture this non-linear effect. Therefore, a transient approach for model tests is investigated. Within this paper the transient model test procedure is described and the results of the model test are shown. Since the transient behavior is superimposed by high frequent pressure uctuations, special focus is on the evaluation of the measurement data. Finally, the in uence of the hysteresis behavior on the simulation results of water way dynamic system is shown.

Nonlinear dynamic behavior of single-layer graphene under uniformly distributed loads

An atomistic-continuum multiscale approach is used to simulate the nonlinear dynamic behavior of simply-supported single layer graphene sheets subject to a uniformly distributed out-of-plane load. The dynamic equation of motion is derived and solved by the Newmark-β method. The evolution of surface morphology and the nonlinear effects in terms of geometrical and material nonlinearities can be captured by iteratively updating the system stiffness. It is found that the natural frequencies of simply-supported graphene sheets almost remain constant when the external load is in a small range. The present solutions are in good agreement with those results obtained from the linear vibration analysis by a semi-analytical method. As the applied load increases continuously, this gives rise to an elongation of graphene to increase the natural frequency. Based on the numerical approach, the surface morphology evolution of graphene can be visualized and explored.

The Analysis of Large Deformation of Beam by Functionally Graded Material (FGM) Under Uniform Transverse Loading

In this paper, we study the analysis of the large beam deformation (FGM) under the uniform transverse loading. The mechanical properties of the beam including the modulus of elasticity and the Poisson coefficient are a function of the thickness of the beam (The Power Distribution Law). Principle equations for the FG-beams are obtained using the Von-Carmen theory for large deformities. The results are obtained by minimizing the total potential energy and solving it. The numerical examples are presented for this method. In this paper, the effect of material properties on the stress basin is examined from a thickness perspective. It discusses the effects of nonlinear terms in strain-relational relations.

Effect of a Nonlinear Term in a Strain-Displacement Relationship on the Load-Displacement Path of Von Mises Truss

Von Misses truss is one of the best examples to explain different theoretical approaches, nature of non-linear solution, define the snap-through, illustrate interactive buckling, etc. The presented paper compares two nonlinear approaches to the problem. Effect of nonlinear terms in strain-displacement relationship on the load level in critical point of nonlinear solution is analyzed. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used. Corresponding levels of the total potential energy are defined. The peculiarities of the effects of the initial imperfections are investigated. Custom FEM computer program has been used for analysis. Full Newton-Raphson procedure, in which the stiffness matrix is updated at every equilibrium iteration, has been applied. Obtained results are compared with results of the nonlinear analysis using ANSYS system, element type BEAM3 is used. The arc-length method is chosen for analysis, the reference arc-length radius is calculated from the load increment. Only fundamental path of nonlinear solution has been presented.

Technique for Reducing the Effects of Nonlinear Terms on Electric Field Measurements of Electric Field Sensor Arrays on Aircraft Platforms

AbstractA generalized technique has been developed that reduces the contributions of nonlinear effects that occur during measurements of natural electric fields around thunderstorms by an array of field mills on an aircraft. The nonlinear effects can be due to nearby charge emitted by the aircraft as it acquires and sheds charge, but the nonlinear effects are not limited to such sources. The generalized technique uses the multiple independent measurements of the external electric field obtained during flight to determine and remove nonlinear contaminations in the external vector electric field. To demonstrate the technique, a simulated case with nonlinear contaminations was created and then corrected for the nonlinear components. In addition, data from two different field programs utilizing two different aircraft and field mill configurations, each containing observable and different nonlinear effects, were also corrected for the significant nonlinear effects found in the field mill outputs. The expanded independent measurements in this new technique allow for the determination and correction of components in the field mill outputs from almost any measurable source. Alternate utilization of the technique can include removing effects in the aircraft charging such as aircraft altitude, cloud properties, engine power settings, or aircraft flap deployment. This technique provides a way to make more precise measurements of the true external electric field for scientific studies of cloud electrification.

Nonlinear vibrations of spring-supported axially moving string

In this study, multi-supported axially moving string is discussed. Supports located at the ends of the string are simple supports. A support located in the middle section owns the features of a spring. String speed is assumed to vary harmonically around an average rate. Hamilton’s principle has been used to figure out the nonlinear equations of motion and boundary conditions. These equations and boundary conditions are dimensionless. Considering the nonlinear effects caused by the string extensions, nonlinear equations of motion are obtained. By using multi-timescaled method, which is one of the perturbation methods, approximate solutions have been found. The first term in the perturbation series causes the linear problem. With the solution of the linear problem, exact natural frequencies have been calculated for different locations of the supports on the middle, various spring coefficients and, with the spring support in the middle of the different location, different spring coefficient and axial speed values. Nonlinear terms on second order add correction terms to the linear problem. Effect of nonlinear terms on the natural frequency has been calculated for various parameters. The cases when the changing frequency of speed is equal to zero, close to zero and close to two times of the natural frequency have been analyzed separately. For each case, the stable and unstable areas in the solutions have been identified by stability analysis.

Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory

Abstract Based on the strain gradient and Eringen’s piezoelasticity theories, wave propagation of an embedded double-walled boron nitride nanotube (DWBNNT) conveying fluid is investigated using Euler–Bernoulli beam model. The elastic medium is simulated by the Pasternak foundation. The van der Waals (vdW) forces between the inner and outer nanotubes are taken into account. Since, considering electro-mechanical coupling made the nonlinear motion equations, a numerical procedure is proposed to evaluate the upstream and downstream phase velocities. The results indicate that the effect of nonlinear terms in motion equations on the phase velocity cannot be neglected at lower wave numbers. Furthermore, the effect of fluid-conveying on wave propagation of the DWBNNT is significant at lower wave numbers.

On non-linear dynamics of a coupled electro-mechanical system

Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steady-state response of the electro-mechanical system exposed to a harmonic close-resonance mechanical excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a) detuning (i.e. a natural frequency variation) and (b) damping (i.e. a decay in the amplitude of vibration), are analyzed further. An applicability range of the mathematical model is assessed.