Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations

This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.

Nonlinear Dynamics and Stability of Neural Networks with Delay-Time

In this paper we study the dynamic properties and stabilities of neural networks with delay-time (which includes the time-varying case) by differential inequalities and Lyapunov function approaches. The criteria of connective stability, robust stability, Lyapunov stability, asymptotic atability, exponential stability and Lagrange stability of neural networks with delay-time are established, and the results obtained are very useful for the design, implementation and application of adaptive learning neural networks.

Nonlinear dynamics of flexible tethered satellite system subject to space environment

The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.

Evaluation on Stability of Stope Structure Based on Nonlinear Dynamics of Coupling Artificial Neural Network

The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-com- puting is a practical and advanced tool for solving large-scale underground rock engineering problems.

NONLINEAR DYNAMICS OF LATERAL MICRO-RESONATOR INCLUDING VISCOUS AIR DAMPING

The nonlinear dynamics of the lateral micro-resonator including the air damping effect is researched. The air damping force is varied periodically during the resonator oscillating, and the air damp coefficient can not be fixed as a constant. Therefore the linear dynamic analysis which used the constant air damping coefficient can not describe the actual dynamic characteristics of the mi-cro-resonator. The nonlinear dynamic model including the air damping force is established. On the base of Navier-Stokes equation and nonlinear dynamical equation, a coupled fluid-solid numerical simulation method is developed and demonstrates that damping force is a vital factor in micro-comb structures. Compared with existing experimental result, the nonlinear numerical value has quite good agreement with it. The differences of the amplitudes （peak） between the experimental data and the results by the linear model and the nonlinear model are 74.5% and 6% respectively. Nonlinear nu-merical value is more exact than linear value and the method can be applied in other mi-cro-electro-mechanical systeme （MEMS） structures to simulate the dynamic performance.

Low-speed instability analysis for hydraulic motor based on nonlinear dynamics

A nonlinear dynamics model and a mathematical expression were set up to investigatethe mechanism and conditions of vibration creep acceleration.The model showsthat hydraulic spring and nonlinear friction are major factors that can affect low-speed instability.The mathematic model was established to obtain the change rule of speed andinstantaneous acceleration of the hydraulic motor.Then, Matlab was used to simulate theeffect of nonlinear friction force and hydraulic motor parameters such as coefficient of leakand compression ratio, etc., under low speed.Finally, some measures were proposed toimprove the low-speed stability of the hydraulic motor.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom(DOF)nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics,including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

NONLINEAR DYNAMICS MODFLING OF MECHANICAL PERIODICITY OF END DIASTOLIC VOLUME OF LEFT VENTRICLE

The cardiovascular system with a lumped parameter model is treated, in which the Starling model is used to simulate left ventricle and the four-element Burattini & Gnudi model is used in the description of arterial system. Moreover, the feedback action of arterial pressure on cardiac cycle is taken into account. The phenomenon of mechanical periodicity (MP) of end diastolic volume (EDV) of left ventricle is successfully simulated by solving a series of one-dimensional discrete nonlinear dynamical equations. The effects of cardiovascular parameters on MP is also discussed.

Nonlinear dynamics in wurtzite InN diodes under terahertz radiation

We carry out a theoretical study of nonlinear dynamics in terahertz-driven n＋nn＋ wurtzite InN diodes by using time-dependent drift diffusion equations. A cooperative nonlinear oscillatory mode appears due to the negative differential mobility effect, which is the unique feature of wurtzite InN aroused by its strong nonparabolicity of the I＂1 valley. The appearance of different nonlinear oscillatory modes, including periodic and chaotic states, is attributed to the competition between the self-sustained oscillation and the external driving oscillation. The transitions between the periodic and chaotic states are carefully investigated using chaos-detecting methods, such as the bifurcation diagram, the Fourier spectrum and the first return map. The resulting bifurcation diagram displays an interesting and complex transition picture with the driving amplitude as the control parameter.

The Origin of Nonlinear Dynamics Involving Complexity in Modern Sciences

This paper reveals the origin of nonlinear dynamics and presents a solution for nonlinear systematic problems based on other science. Generally, physical phenomena are divided into linear static logical problems and nonlinear dynamic systematic problems, but all scientists have solved both problems using the same algebraic logical solution in statistical physics based on determinism such as chaos theory. Surprisingly, this is a contradiction and a serious mistake because there is a perfect solution such as the system analysis theory existing in other science. Unfortunately, it has developed in the 20th century by engineers. Thus, classical physicists could not solve it. Meanwhile, the author achieved the systematic solution for many unsolved nonlinear systematical, further, proved the research result through simulation using specially designed simulation device. Thus, this is a revolutionary achievement because it can easily solve the unsolved nonlinear dynamics that exists in all fields of science. Ironically most determinists do not welcome and reject it. However, it has no matter, it will be separated from current physics and other scientists studied it in the second physics. Therefore, it would be contributed to solve the unsolved nonlinear dynamics in complex science.

Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic （DEA） shock waves and double layers in an unmagnetized, col- lisionless, complex or dusty plasma system are carried out. The plasma system is assumed to be composed of inertial and viscous cold electron fluids, nonextensive distributed hot electrons, Maxwellian ions, and negatively charged stationary dust grains. The standard reductive perturbation technique is used to derive the nonlinear dynamical equations, that is, the nonplanar Burgers equation and the nonplanar further Burgers equation. They are also numerically analyzed to investigate the basic features of shock waves and double layers （DLs）. It is observed that the roles of the viscous cold electron fluids, nonextensivity of hot electrons, and other plasma parameters in this investigation have significantly modified the basic features （such as, polarity, amplitude and width） of the nonplanar DEA shock waves and DLs. It is also observed that the strength of the shock is maximal for the spherical geometry, intermediate for cylindrical geometry, while it is minimal for the planar geometry. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.

Nonlinear dynamics and coupling effect of libration and vibration of tethered space robot in deorbiting process

In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the tethered combination system in the post-capture phase was established with the consideration of the attitudes of two spacecrafts and the quadratic nonlinear elasticity of the tether.The motion law of the tethered combination in the deorbiting process with different disturbances was simulated and discussed on the premise that the platform was only controlled by a constant thrust force.It is known that the four motion freedoms of the tethered combination are coupled with each other in the deorbiting process from the simulation results.A noticeable phenomenon is that the tether longitudinal vibration does not decay to vanish even under the large tether damping with initial attitude disturbances due to the coupling effect.The approximate analytical solutions of the dynamics for a simplified model are obtained through the perturbation method.The condition of the inter resonance phenomenon is the frequency ratio λ_1=2.The case study shows good accordance between the analytical solutions and numerical results,indicating the effectiveness and correctness of approximate analytical solutions.

STUDY ON NONLINEAR DYNAMICS OF TCP-RENO TRAFFIC UNDER RED

A discrete time feedback control system model based on a multi-router network has been presented. The model can be described by a set of recurrence equations. The numerical examples about the bifurcation of average and instantaneous queue size along with the variety of RED control parameter are shown. The simulate experiments about those of the RED control parameters are also presented. All of these results show that instability in TCP-Reno traffic under RED can be induced by the inherent nonlinear behavior of the network.

Nonlinear Dynamics of Nervous Stomach Model Using Supervised Neural Networks

The purpose of the current investigations is to solve the nonlinear dynamics based on the nervous stomach model(NSM)using the supervised neural networks(SNNs)along with the novel features of Levenberg-Marquardt backpropagation technique(LMBT),i.e.,SNNs-LMBT.The SNNs-LMBT is implemented with three different types of sample data,authentication,testing and training.The ratios for these statistics to solve three different variants of the nonlinear dynamics of the NSM are designated 75%for training,15%for validation and 10%for testing,respectively.For the numerical measures of the nonlinear dynamics of the NSM,the Runge-Kutta scheme is implemented to form the reference dataset.The attained numerical form of the nonlinear dynamics of the NSM through the SNNs-LMBT is implemented in the reduction of the mean square error(MSE).For the exactness,competence,reliability and efficiency of the proposed SNNs-LMBT,the numerical actions are capable using the proportional arrangements through the features of the MSE results,error histograms(EHs),regression and correlation.

A Review of the Nonlinear Dynamics of Intraseasonal Oscillations

In recent years,significant progress has been made regarding theories of intraseasonal oscillations (ISOs) (also known as the Madden-Julian oscillation (MJO) in the tropics).This short review introduces the latest advances in ISO theories with an emphasis particularly on theoretical paradigms involving nonlinear dynamics in the following aspects:(1) the basic ideas and limitations of the previous and current theories and hypotheses regarding the MJO,(2) the new multi-scale theory of the MJO based on the intraseasonal planetary equatorial synoptic dynamics (IPESD) framework,and (3) nonlinear dynamics of ISOs in the extratropics based on the resonant triads of Rossby-Haurwitz waves.

Application of Nonlinear Dynamics in Studying Flashover Fire in a Small Open Kitchen

Open kitchen designs are found in small units in tall residential buildings of Asian-Oceania regions for better space utilization. As many combustibles are stored in small residential units, fire originated in the open kitchen can grow and spread fast. Consequently, flashover can occur to give a big fire and result in severe casualties and property damage. Nonlinear dynamics can be applied to predict critical heat release rate to flashover in the unit with an open kitchen and will be illustrated in this paper. Based on a two-zone model, temperature of the hot smoke layer was taken as the system state variable. An evolution equation was developed with selective control parameters. Onsetting of flashover using a nonlinear dynamical system was demonstrated in the example residential units. Effects of the floor dimensions, the radiation feedback coefficient and thermal properties of wall material on the onset of flashover were then examined and analyzed. The developed nonlinear dynamical model for studying the onset of flashover gives a better understanding of the various control parameters.

Controlling Nonlinear Dynamics in Continuous Crystallizers

Crystallization is used to produce vast quantities of materials. For several applications, continuous crystallization is often the best operation mode because it is able to reproduce better crystal size distributions than other operation modes. Nonlinear oscillation in continuous industrial crystallization processes is a well-known phenomenon leading to practical difficulties such that control actions are necessary. Nonlinear oscillation is a consequence of the highly nonlinear kinetics, different feedbacks between the variables and elementary processes taking place in crystallizers units, and the non-equilibrium thermodynamic operation. In this paper the control of a continuous crystallizer model that displays oscillatory behavior is addressed via two practical robust control approaches： （i） modeling error compensation, and （ii） integral high order sliding mode control. The controller designs are based on the reduced-order model representation of the population balance equations resulting after the application of the method of moments. Numerical simulations show good closed-loop performance and robustness properties

New Systems Solution for Resolving Nonlinear Dynamics Based on Systems Thinking

This study describes a new solution for resolving nonlinear dynamics. Surprisingly, it has been resolved and completed by non-physicists on behalf of physicists in 2021. It is a revolutionary solution like the Copernican Theory, which is perfectly different from the existing chaos theory. In the past, nonlinear dynamics has been analyzed using logical solutions, such as chaos theory, based on logical thinking. However, it is not perfect systematic solution, hence;the new solution has been analyzed and resolved by systematic analytical tool in other sciences. Then, the result is more perfect and precise than the old chaos theory. Regrettably, most physicists do not welcome this advancement, because they have primitive solutions such as chaos theory. If the new solution is true, it is very disadvantageous to them like Galileo’s heliocentric theory. Therefore, they do not welcome it and deny and reject it. Hence, they wish it to fail;moreover, they want to remain in safe zone. Unfortunately, they became outsiders because they have no ability to review new solutions. Unfortunately, we have no obligation to follow physicists. If so, non-physicists, bypassing physicists, must study independently nonlinear dynamics based on systems thinking, and have to share the findings other scientists. It means that the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the future.