Nonlinear Interaction Problem Research Articles

Free movement of a near-wall particle in fluid of comparable density

The fundamental problem of nonlinear interaction between a freely moving particle and surrounding fluid flow is investigated for a density ratio of order unity, with potential applications to biomedical, environmental, and aerodynamic configurations. The interaction takes place near a fixed wall, with the particle being relatively thin. A mathematical model is presented, showing the fluid pressure forces to be dominant over the mass-acceleration effects in the particle motion (in contrast with previous analyses). The added mass due to the fluid motion, thus, greatly exceeds the body mass. Numerical simulations and asymptotic analysis reveal a range of possible particle motions. The main properties emerging are: (a) the distinction between collisions with the wall and fly-away responses; (b) the time scales involved in such behaviors; (c) the pressures and velocities induced at collision; (d) the occurrence of flow reversal in certain cases; and (e) the results being independent of the particle mass and moment of inertia as well as independent of the density ratio provided that the ratio is of order unity (0–7, say) or only slightly larger (8–30, say).

Experience in using ceramics (Si3N4) as a material for rolling bearings of high-speed machines

To analyse the influence of the material of the rolling elements (steel and ceramics) of a high-speed ball bearing on the stresses in the contact zone of the rolling elements and rings and on friction losses in the contact zone.The study considers the outer ring of an angular contact ball bearing, which is loaded with additional centrifugal force. A nonstationary nonlinear volumetric interaction problem between the ball and the raceway was solved to determine the contact angle using the “DYNA” application package. The values of contact stresses for ceramic and steel rolling elements of a hybrid ball bearing are determined, as well as the value of deformations of balls and raceways based on Hertz's theory. The specific friction power deals with the differential slipping of the rolling elements relative to the raceway was estimated.Analysis of the behaviour of the bearings at different rotation speeds showed that at rotational speeds of more than 7000 rad/s, bearings with ceramic rolling elements of the considered standard size have advantages in contact strength. In addition, it was found out that at high rotational speeds, the friction power of the ceramic rolling elements is almost two times less than the friction power of the steel rolling elements.The research results relate to rolling ball bearings operating at a speed parameter dn of up to 4∙106 mm∙rpm and the analysis of friction losses is limited to losses from differential slip, which suggests further research of other components of losses.The study can justify the choice of bearing type (steel or ceramic rolling elements) depending on the operating speed and the lubrication and cooling system, which depends on the level of heat generation in the bearing.The work obtained original results of contact stresses and friction loss components for a certain type of bearing in a wide range of rotation speeds.

An adaptive harmonic polynomial cell method for three-dimensional fully nonlinear wave-structure interaction with immersed boundaries

To accurately simulate wave-structure interaction based on fully nonlinear potential flow theory, a three-dimensional (3 D) high-order immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method is proposed. Both the free surface and body surface are immersed in background octree cells that are adaptively refined near the boundaries of interest, thereby dramatically reducing computational costs without loss of accuracy. We also propose an easy-to-implement IB strategy to deal with possible instabilities in the time-domain solution arising from the intersection of Dirichlet–Neumann boundaries. For a linearized problem of wave-wall interaction, a matrix-based stability analysis is performed, providing mathematical support for the robustness of the proposed IB strategy. In contrast to the two-dimensional HPC method, compressed cells are found to offer superior stability compared to stretched cells in the vertical direction, while equal mesh aspect ratio in the horizontal plane is superior. Cubic octree cells are, however, still preferred in practice. The free surface is primarily described by a set of massless background wave markers; however, to address the challenges of IB methods in tracking the free surface evolution near the structure, additional body-fitted wave markers are introduced close to the waterline. The information exchange between these two sets of wave markers is realized by radial basis function (RBF) interpolation. While standard RBF schemes have grid-size-dependent filtering performance, we propose a normalized RBF scheme, which is then optimized in terms of the number of neighboring nodes, a smoothing coefficient and the basis functions. Excellent accuracy properties of the proposed 3 D IB-AHPC method are demonstrated by studying fully nonlinear wave propagation. The method is further applied to study relevant fully nonlinear wave-structure interaction problems, including sloshing in 3 D rectangular tanks and wave diffraction of a bottom-mounted cylinder in regular waves. Satisfactory agreement is demonstrated with existing experimental and numerical results, suggesting that the proposed 3 D IB-AHPC method is a promising potential-flow method in marine hydrodynamics.

Spectrally stitched WDM nonlinear frequency division multiplexed transmission system

We present the concept and design of a 100 GHz PIC-based nonlinear frequency division multiplexed transmission system in which four b-modulated spectrally overlapping channels are spectrally stitched without frequency guard bands to obtain a continuous spectrum. Neural network-based equalizers are used at the receiver for improved performance. Simulations show that the proposed system alleviates the problem of nonlinear interaction between neighboring channels, that would, otherwise, be out of reach even for neural network equalization to solve on its own. The system achieves a 960 km transmission distance with a raw data rate of 333 Gbps per polarization and a BER well below the SD-FEC limit for every subcarrier.

Compressible Fluids Interacting with Plates: Regularity and Weak-Strong Uniqueness

In this paper, we study a nonlinear interaction problem between compressible viscous fluids and plates. For this problem, we introduce relative entropy and relative energy inequality for the finite energy weak solutions (FEWS). First, we prove that for all FEWS, the structure displacement enjoys improved regularity by utilizing the dissipation effects of the fluid onto the structure and that all FEWS satisfy the relative energy inequality. Then, we show that all FEWS enjoy the weak-strong uniqueness property, thus extending the classical result for compressible Navier–Stokes system to this fluid-structure interaction problem.

Low-frequency energy capture and water wave attenuation of a hybrid WEC-breakwater with nonlinear stiffness

Wave energy is attractive for its generous, sustainable and clean, the combination of floating breakwater (FB) and wave energy converter (WEC) is an economical approach to capture wave energy and attenuate waves. The conventional hybrid WEC-FB system is ineffective for low-frequency waves. To overcome this shortcoming, this paper proposed a novel WEC-FB with nonlinear stiffness mechanism to improve its wave attenuation and power capture performance. A hybrid semi-analytical nonlinear frequency-domain approach including the eigenfunction expansion matching method (EEMM) and multi-harmonic balance method (MHBM) is proposed to solve the nonlinear waves-structures interaction problem. The performance of the nonlinear WEC-FB is demonstrated by comparing with conventional linear counterpart, and the underlying reason for the effect of nonlinear mechanism is explored. The phase control mechanism for improving low frequency performance of wave elimination and energy capture is revealed by using the analytical method. This study shows that the introduction of the nonlinear mechanism can both improve the wave attenuation and energy absorption performance, especially in the low-frequency wave region.

Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which is filled with a fluid governed by the full Navier-Stokes-Fourier system. The fluid and the shell are fully coupled, giving rise to a novel nonlinear moving boundary fluid-structure interaction problem involving heat exchange. The existence of a weak solution is obtained by combining three approximation techniques – decoupling, penalization and domain extension. In particular, the penalization and the domain extension allow us to use the methods already developed for compressible fluids on moving domains. In such a way, the proof is more elegant and the analysis is drastically simplified. Let us stress that this is the first time the heat exchange in the context of fluid-structure interaction problems is considered.

Seismic response of nonlinear soil-structure interaction systems through the Preisach formalism: the Messina Bell Tower case study

In this paper the seismic response of linear behaving structures resting on compliant soil is addressed through the application of the Preisach formalism to capture the soil nonlinearities. The novel application of the Preisach model of hysteresis for nonlinear soil-structure interaction problems is explored through the study of the seismic response of a real structure. Through a harmonic balance procedure, furthermore, simplified nonlinear springs and dashpots are derived in closed form for a ready and accurate evaluation of the nonlinear soil-structure interaction response. The selected case study is the bell tower of the Messina Cathedral in Italy. The Bell Tower hosts the largest and most complex mechanical and astronomical clock in the world and it has been recently equipped by a permanent seismic monitoring system. A pertinent finite element (FE) model including the superstructure and the soil underneath, has been defined using authentic drawings and engineering design reports. The modal properties of the FE model have been compared with the experimental ones, identified from environmental noise recorded through the seismic monitoring system. Furthermore, the FE model has been validated by means of acceleration time histories recorded at different floors during two independent seismic events. A nonlinear incremental dynamic analysis of the Bell Tower has been also performed. The seismic response obtained by the complete FE analysis, has been compared with the proposed Preisach lumped parameter model, assembled with nonlinear springs and nonlinear dashpots. The results are well in agreement, offering an alternative promising strategy for the nonlinear soil-structure interaction studies.

Multi-Stages Iterative Process for Conservative Economic Finite-Difference Schemes Realization for the Problem of Nonlinear Laser Pulse Interaction with a Medium

We consider a problem of laser pulse interaction with a nonlinear medium which is accompanied by different nonlinear phenomena. Among them, we highlight the laser pulse self-action, optical bistability realization, formation of laser-induced complicated spatio-temporal structures. For computer modeling of these strongly nonlinear effects, using robust conservative numerical methods is required. Well-known, there are two widely applied approaches for the construction of numerical method: the conservative finite-difference schemes and additive finite-difference schemes (the split-step methods or decomposition methods). The first ones are non-economic, as a rule, while the second type of the methods is economic ones, however they possess well-known disadvantages. In our study, we joint advantages of both approaches by developing an original multi-stage iterative process for the conservative finite-difference scheme realization. Using computer simulation results, we demonstrate the feasibility of the proposed approach for investigating certain nonlinear optical phenomena.

Steady state harmonic response of nonlinear soil-structure interaction problems through the Preisach formalism

Steady state harmonic response of nonlinear soil-structure interaction problems is addressed in this paper. Due to well-known stiffness degradation phenomenon, the steady-state study is referred to small-medium strain condition whereas no significant pore water pressure change is observed (e.g. clayey soils and sands in drained conditions). A novel cyclic hysteretic model based on the Preisach formalism is proposed to describe the cyclic behavior of soil-foundation interaction. Through a harmonic balance procedure, furthermore, the steady state response of nonlinear soil-structure interaction problems is determined. Equivalent amplitude-dependent stiffness and damping have been derived in closed form to reliably describe the nonlinear soil-structure interaction phenomenon. Those expressions are function of the elastic foundation soil stiffness, the maximum attainable horizontal force and the moment capacity of the foundation. Furthermore, handy expressions of the equivalent fundamental period and damping, also dependent from the level of the excitation, are also derived. The proposed hysteretic model, moreover, has the advantage to be easily calibrated to match the modulus reduction and damping curves determined either from numerical or experimental tests. Numerical applications and comparisons with more advanced models and experimental data available in literature are also presented.

Decentralized event-triggered adaptive control for interconnected nonlinear dynamics of constrained air supply and thermal management systems of PEMFCs

This paper investigates a decentralized event-triggered adaptive control problem for uncertain interconnected air supply and thermal management nonlinear dynamics of proton exchange membrane fuel cells (PEMFCs). In addition, the constraint problems of the oxygen excess ratio (OER) and stack temperature (ST) are addressed for preventing oxygen starvation, parasitic loss, membrane dehydration, and electrode flooding of PEMFCs. First, the practical nonlinear interaction problem between the air pressure of the air supply subsystem and the ST of the thermal management subsystem is formulated. Then, a decentralized adaptive control design strategy is established to guarantee the constraint satisfaction of each subsystem and the asynchronously event-triggered regulation of the OER and ST. In contrast to the previous studies on the control of PEMFCs, this study first addresses the nonlinear interaction problem of the air supply and thermal management systems and their decentralized control design in the control field of PEMFCs. Based on the Lyapunov stability theorem, the stability of the resulting overall control scheme is analyzed.

Need to Control the Ionosphere Perturbation under the Powerful Radiowaves Influence.

Abstract Possible consequences of the ionosphere perturbation under the powerful radiowaves influence are considered. The main effects arising from nonlinear interaction of radiation with the propagation medium are described. Special attention is paid to the analysis of the problem of nonlinear interaction of concentrated wave beams for threshold and saturable nonlinearities. Under certain parameters, this interaction can lead to the complete destruction of the concentrated wave fields, as well as to the fusion of wave beams into a solitary wave of high power. To avoid this unsafe situation, it is necessary to automatically control the radio emission power.

Weak solution to the incompressible viscous fluid and a thermoelastic plate interaction problem in 3D

In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate. The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models. We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that, via operator splitting, decouples the system into two sub-problems, one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure. To prove the convergence of the approximate quasilinear elastic force, we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.

Bridge-Vehicle Dynamic Interaction Modeling and Solution - An Overview

The dynamic interaction between the bridge and the passing vehicle or train is considered a point of interest concerning the railway bridge design and maintenance, and the interest becomes greater for the bridges serving as links on high-speed lines. In this paper, the interaction problem is presented through the different models used to describe the phenomenon and the different techniques adopted to solve the non-linear interaction problem. The models describing the problem vary greatly from very simple 2D models with moving loads over beams to complex 3D models with multiple degrees of freedom (DOFs) for both the bridge and vehicle and with precise definition of various parts and parameters affecting the response such as the type of bridge element, the track structure and the bridge elastic supports. The solution algorithms of the non-linear interaction problem also vary from simple analytic solutions and non-direct techniques to more sophisticated iterative techniques in finite element (FE) domains.

OpenMP parallelism in computations of three-dimensional potential numerical wave tank for fully nonlinear simulation of wave-body interaction using NURBS

The open multi-processing parallelism was implemented into a serial code to compute a high-order boundary integral equation based on the second Green's identity. on symmetric multiprocessing computer platforms. The parallel code is augmented to a three-dimensional potential numerical wave tank for fully nonlinear wave-body interaction problems in the time domain. The non-uniform rational B-Spline surface was manipulated to define the geometry of the computational boundaries and the distribution of boundary values either as a high-order iso-geometric formulation. The material node approach and fourth-order Runge-Kutta time integration method were compounded for time marching the fully nonlinear free surface boundary. The propagation of a fifth-order Stokes wave was simulated to examine the scalability of the parallel constructs implementation. Afterwards, the second-order Stokes wave interaction with a cylindrical pile was modeled as a practical case study to show the benefits of the parallel code. The results were compared with former experiments and numerical studies.

Convergence analysis and error estimate of finite element method of a nonlinear fluid-structure interaction problem

In this paper, a semi-discrete finite element method for the nonlinear fluid-structure interaction problem interacts between the Navier-Stokes fluids and linear elastic solids, is studied and developed. A classical mixed variational principle of the weak formulation is given, and the corresponding finite element method is defined. As for the nonlinearity arising from the nonlinear interaction problem, we consider in time of a solution for suitably small data, and uniqueness hypothesis. This approach is fairly robust and adapts to the important case of interface with fractures or cracks. Convergence and estimate of the finite element method are also obtained for the nonlinear fluid-structure interaction problem. Finally, numerical experiments are presented to show the performance of the proposed method.

Numerical Modelling of Interaction between Solitary Wave and Sloped Seawall

A numerical model for solving interaction between solitary wave and a sloped seawall is established. The CIP (Constrained Interpolation profile) scheme is employed to solve the flow field. THINC (Tangent of Hyperbola Interpolation for Interface Capturing) method is applied for capturing the free surface. Hydrodynamic forces is calculated by integrating the pressure and friction along the seawall surface. First, convergence tests with respect to mesh resolution and time step are examined, and the solitary wave profile is validated by experimental data from the published paper. Then, time series of the free surface elevation at specific location with different heights of incident solitary wave are presented. Finally, hydrodynamic forces acting on the weather side of the seawall are analyzed. The conclusion can be drawn that this numerical model has applicability for strongly nonlinear wave-body interaction problems.

Frequency-domain method for multistage turbomachine tone noise calculation

A method of frequency-domain calculation of the multistage turbomachinery tone noise is presented. The method is based on the kinematic relations featuring dependence of flow fields in a turbomachine on time and circumferential angle. It solves the flow in several blade passages inside each row and can be used in conjunction with nonlinear equations. The method is developed at Central Institute of Aviation Motor and implemented in the Three Dimensional Acoustics Solver in-house solver. The multi-passage method is verified on two numerical problems. One is the tone noise generation by a 2D two stage turbine. The other is the problem of nonlinear interaction of circumferential modes in a 2D cylindrical channel.

An effective nonlinear susceptibility model for general three-wave mixing in quasi-phase-matching structure

We develop an effective nonlinear susceptibility model (ENSM) to solve analytically the general three-wave mixing nonlinear optical interaction problem under the quasi-phase-matching (QPM) scheme. The nonlinear processes including sum-frequency generation, difference-frequency generation and second harmonic generation are discussed in both periodic poled lithium niobate (PPLN) and chirped PPLN (CPPLN) structures. The analytical ENSM results show great consistency with rigorous numerical simulation based on direct solution of the nonlinear coupled-wave equations. This indicates that the ENSM is a brief, convenient, accurate, and efficient theoretical tool to quantitatively evaluate the performance of various three-wave mixing interactions in general QPM structures such as PPLN and CPPLN and to design and optimize the QPM structures for many specific functionalities of nonlinear frequency conversion.

Novel algorithm for modeling combined laser and induction welding respecting keyhole effect

Numerical model of combined laser and induction welding is presented and solved. From the physical viewpoint, the process represents a coupled problem of nonlinear and nonstationary interaction of the magnetic and temperature fields respecting the phase change and evaporation of heated molten metal (keyhole effect). A specific algorithm was developed for manipulation with the space and time variation of interface between solid and molten metal. Selected results are compared with the realized experiment.