Abstract: The original 3D Lorenz-Haken equations -which describe laser dynamics- are converted into 2-second-order differential equations out of which the so far missing mathematics is extracted. Leaning on high-order trigonometry, important outcomes are pulled out: A fundamental result attributes chaos to forbidden periodic solutions, inside some precisely delimited region of the control parameter space that governs self-pulsing.
Abstract: The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.
Abstract: Sump can be defined as a reservoir which contains slurry; a mixture of solid and liquid or water, in it. Sump system is an unsteady process owing to the level response. Sump level shall be monitored carefully by using a good controller to avoid overflow. The current conventional controllers would not be able to solve problems with large time delay and nonlinearities, Fuzzy Logic controller is tested to prove its ability in solving the listed problems of slurry sump. Therefore, in order to justify the effectiveness and reliability of these controllers, simulation of the sump system was created by using MATLAB and the results were compared. According to the result obtained, instead of Proportional-Integral (PI) and Proportional-Integral and Derivative (PID), Fuzzy Logic controller showed the best result by offering quick response of 0.32 s for step input and 5 s for pulse generator, by producing small Integral Absolute Error (IAE) values that are 0.66 and 0.36 respectively.
Abstract: Hammerstein–Wiener model is a block-oriented model
where a linear dynamic system is surrounded by two static
nonlinearities at its input and output and could be used to model
various processes. This paper contains an optimization approach
method for analysing the problem of Hammerstein–Wiener systems
identification. The method relies on reformulate the identification
problem; solve it as constraint quadratic problem and analysing its
solutions. During the formulation of the problem, effects of adding
noise to both input and output signals of nonlinear blocks and
disturbance to linear block, in the emerged equations are discussed.
Additionally, the possible parametric form of matrix operations
to reduce the equation size is presented. To analyse the possible
solutions to the mentioned system of equations, a method to reduce
the difference between the number of equations and number of
unknown variables by formulate and importing existing knowledge
about nonlinear functions is presented. Obtained equations are applied
to an instance H–W system to validate the results and illustrate the
proposed method.
Abstract: The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.
Abstract: The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.
Abstract: To acquire accurate ship motions at the center of gravity, a single low-cost inertial sensor is utilized and applied on board to measure ship oscillating motions. As observations, the three axes accelerations and three axes rotational rates provided by the sensor are used. The mathematical model of processing the observation data includes determination of the distance vector between the sensor and the center of gravity in x, y, and z directions. After setting up the transfer matrix from sensor’s own coordinate system to the ship’s body frame, an extended Kalman filter is applied to deal with nonlinearities between the ship motion in the body frame and the observation information in the sensor’s frame. As a side effect, the method eliminates sensor noise and other unwanted errors. Results are not only roll and pitch, but also linear motions, in particular heave and surge at the center of gravity. For testing, we resort to measurements recorded on a small vessel in a well-defined sea state. With response amplitude operators computed numerically by a commercial software (Seaway), motion characteristics are estimated. These agree well with the measurements after processing with the suggested method.
Abstract: This paper summarizes the results of a survey on
smart non-structural element dynamic dissipation when installed
in modern high-rise mega-frame prototypes. An innovative glazed
curtain wall was designed using Shape Memory Alloy (SMA)
joints in order to increase the energy dissipation and enhance
the seismic/wind response of the structures. The studied buildings
consisted of thirty- and sixty-storey planar frames, extracted from
reference three-dimensional steel Moment Resisting Frame (MRF)
with outriggers and belt trusses. The internal core was composed of
a CBF system, whilst outriggers were placed every fifteen stories
to limit second order effects and inter-storey drifts. These structural
systems were designed in accordance with European rules and
numerical FE models were developed with an open-source code,
able to account for geometric and material nonlinearities. With
regard to the characterization of non-structural building components,
full-scale crescendo tests were performed on aluminium/glass curtain
wall units at the laboratory of the Construction Technologies
Institute (ITC) of the Italian National Research Council (CNR),
deriving force-displacement curves. Three-dimensional brick-based
inelastic FE models were calibrated according to experimental results,
simulating the fac¸ade response. Since recent seismic events and
extreme dynamic wind loads have generated the large occurrence of
non-structural components failure, which causes sensitive economic
losses and represents a hazard for pedestrians safety, a more
dissipative glazed curtain wall was studied. Taking advantage of the
mechanical properties of SMA, advanced smart joints were designed
with the aim to enhance both the dynamic performance of the single
non-structural unit and the global behavior. Thus, three-dimensional
brick-based plastic FE models were produced, based on the innovated
non-structural system, simulating the evolution of mechanical
degradation in aluminium-to-glass and SMA-to-glass connections
when high deformations occurred. Consequently, equivalent nonlinear
links were calibrated to reproduce the behavior of both tested and
smart designed units, and implemented on the thirty- and sixty-storey
structural planar frame FE models. Nonlinear time history analyses
(NLTHAs) were performed to quantify the potential of the new
system, when considered in the lateral resisting frame system (LRFS)
of modern high-rise MRFs. Sensitivity to the structure height was
explored comparing the responses of the two prototypes. Trends
in global and local performance were discussed to show that, if
accurately designed, advanced materials in non-structural elements provide new sources of energy dissipation.
Abstract: This paper presents modeling and control of a highly nonlinear system including, non-interacting two spherical tanks using iterative learning control (ILC). Consequently, the objective of the paper is to control the liquid levels in the nonlinear tanks. First, a proportional-integral-derivative (PID) controller is applied to the plant model as a suitable benchmark for comparison. Then, dynamic responses of the control system corresponding to different step inputs are investigated. It is found that the conventional PID control is not able to fulfill the design criteria such as desired time constant. Consequently, an iterative learning controller is proposed to accurately control the coupled nonlinear tanks system. The simulation results clearly demonstrate the superiority of the presented ILC approach over the conventional PID controller to cope with the nonlinearities presented in the dynamic system.
Abstract: Finite Element Models (FEMs) are widely used in order to study and predict the dynamic properties of structures and usually, the prediction can be obtained with much more accuracy in the case of a single component than in the case of assemblies. Especially for structural dynamics studies, in the low and middle frequency range, most complex FEMs can be seen as assemblies made by linear components joined together at interfaces. From a modelling and computational point of view, these types of joints can be seen as localized sources of stiffness and damping and can be modelled as lumped spring/damper elements, most of time, characterized by nonlinear constitutive laws. On the other side, most of FE programs are able to run nonlinear analysis in time-domain. They treat the whole structure as nonlinear, even if there is one nonlinear degree of freedom (DOF) out of thousands of linear ones, making the analysis unnecessarily expensive from a computational point of view. In this work, a methodology in order to obtain the nonlinear frequency response of structures, whose nonlinearities can be considered as localized sources, is presented. The work extends the well-known Structural Dynamic Modification Method (SDMM) to a nonlinear set of modifications, and allows getting the Nonlinear Frequency Response Functions (NLFRFs), through an ‘updating’ process of the Linear Frequency Response Functions (LFRFs). A brief summary of the analytical concepts is given, starting from the linear formulation and understanding what the implications of the nonlinear one, are. The response of the system is formulated in both: time and frequency domain. First the Modal Database is extracted and the linear response is calculated. Secondly the nonlinear response is obtained thru the NL SDMM, by updating the underlying linear behavior of the system. The methodology, implemented in MATLAB, has been successfully applied to estimate the nonlinear frequency response of two systems. The first one is a two DOFs spring-mass-damper system, and the second example takes into account a full aircraft FE Model. In spite of the different levels of complexity, both examples show the reliability and effectiveness of the method. The results highlight a feasible and robust procedure, which allows a quick estimation of the effect of localized nonlinearities on the dynamic behavior. The method is particularly powerful when most of the FE Model can be considered as acting linearly and the nonlinear behavior is restricted to few degrees of freedom. The procedure is very attractive from a computational point of view because the FEM needs to be run just once, which allows faster nonlinear sensitivity analysis and easier implementation of optimization procedures for the calibration of nonlinear models.
Abstract: The different seismic behavior of liquid storage tanks rather than conventional structures makes their responses more complicated. Uplifting and excessive settlement due to liquid sloshing are the most frequent damages in cylindrical liquid tanks after shell bucking failure modes. As a matter of fact, uses of liquid storage tanks because of the simple construction on compact layer of soil as a foundation are very conventional, but in some cases need to retrofit are essential. The tank seismic behavior can be improved by modifying dynamic characteristic of tank with verifying seismic loads as well as retrofitting and improving base ground. This paper focuses on a typical steel tank on loose, medium and stiff sandy soil and describes an evaluation of displacement of the tank before and after retrofitting. The Abaqus program was selected for its ability to include shell and structural steel elements, soil-structure interaction, and geometrical nonlinearities and contact type elements. The result shows considerable decreasing in settlement and uplifting in the case of retrofitted tank. Also, by increasing shear strength parameter of soil, the performance of the liquid storage tank under the case of seismic load increased.
Abstract: A Fourier series based learning control (FSBLC)
algorithm for tracking trajectories of mechanical systems with
unknown nonlinearities is presented. Two processes are introduced to
which the FSBLC with PD controller is applied. One is a simplified
service robot capable of climbing stairs due to special wheels and
the other is a propeller driven pendulum with nearly the same
requirements on control. Additionally to the investigation of learning
the feed forward for the desired trajectories some considerations on
the implementation of such an algorithm on low cost microcontroller
hardware are made. Simulations of the service robot as well as
practical experiments on the pendulum show the capability of the used
FSBLC algorithm to perform the task of improving control behavior
for repetitive task of such mechanical systems.
Abstract: In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.
Abstract: In this paper, we study the optical nonlinearities of
Silver sulfide (Ag2S) nanostructures dispersed in the Dimethyl
sulfoxide (DMSO) under exposure to 532 nm, 15 nanosecond (ns)
pulsed laser irradiation. Ultraviolet–visible absorption spectrometry
(UV-Vis), X-ray diffraction (XRD), and transmission electron
microscopy (TEM) are used to characterize the obtained nanocrystal
samples. The band gap energy of colloid is determined by analyzing
the UV–Vis absorption spectra of the Ag2S NPs using the band
theory of semiconductors. Z-scan technique is used to characterize
the optical nonlinear properties of the Ag2S nanoparticles (NPs).
Large enhancement of two photon absorption effect is observed with
increase in concentration of the Ag2S nanoparticles using open Zscan
measurements in the ns laser regime. The values of the nonlinear
absorption coefficients are determined based on the local nonlinear
responses including two photon absorption. The observed aperture
dependence of the Ag2S NP limiting performance indicates that the
nonlinear scattering plays an important role in the limiting action of
the sample. The concentration dependence of the optical liming is
also investigated. Our results demonstrate that the optical limiting
threshold decreases with increasing the silver sulfide NPs in DMSO.
Abstract: In this paper, we considered and applied parametric
modeling for some experimental data of dynamical system. In this
study, we investigated the different distribution of output
measurement from some dynamical systems. Also, with variance
processing in experimental data we obtained the region of
nonlinearity in experimental data and then identification of output
section is applied in different situation and data distribution. Finally,
the effect of the spanning the measurement such as variance to
identification and limitation of this approach is explained.
Abstract: The exact theoretical expression describing the
probability distribution of nonlinear sea-surface elevations derived
from the second-order narrowband model has a cumbersome form
that requires numerical computations, not well-disposed to theoretical
or practical applications. Here, the same narrowband model is reexamined
to develop a simpler closed-form approximation suitable
for theoretical and practical applications. The salient features of the
approximate form are explored, and its relative validity is verified
with comparisons to other readily available approximations, and
oceanic data.
Abstract: Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.
Abstract: The tension leg platform (TLP) is a vertically moored structure with excess buoyancy. The TLP is regarded as moored structure in horizontal plan, while inherit stiffness of fixed platform in vertical plane. In this paper, a numerical study using modified Morison equation was carried out in the time domain to investigate the influence of nonlinearities due to hydrodynamic forces and the coupling effect between surge, sway, heave, roll, pitch and yaw degrees of freedom on the dynamic behavior of TLP's. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables and the nonlinear equations of motion were solved utilizing Newmark’s beta integration scheme. The effect of tethers length and wave characteristics such as wave period and wave height on the response of TLP's was evaluated.
Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether length, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations about that is significantly dependent on tether length.
Abstract: An exploration in the competency of the optical
multilevel Mapping Multiplexing Technique (MMT) system in
tolerating to the impact of nonlinearities as Self Phase Modulation
(SPM) during the presence of dispersion compensation methods. The
existence of high energy pulses stimulates deterioration in the chirp
compression process attained by SPM which introduces an upper
power boundary limit. An evaluation of the post and asymmetric prepost
fiber compensation methods have been deployed on the MMT
system compared with others of the same bit rate modulation formats.
The MMT 40 Gb/s post compensation system has 1.4 dB
enhancements to the 40 Gb/s 4-Arysystem and less than 3.9 dB
penalty compared to the 40 Gb/s OOK-RZsystem. However, the
optimized Pre-Post asymmetric compensation has an enhancement of
4.6 dB compared to the Post compensation MMT configuration for a
30% pre compensation dispersion.
Abstract: This paper presents three-phase evolution search methodology to automatically design fuzzy logic controllers (FLCs) that can work in a wide range of operating conditions. These include varying load, parameter variations, and unknown external disturbances. The three-phase scheme consists of an exploration phase, an exploitation phase and a robustness phase. The first two phases search for FLC with high accuracy performances while the last phase aims at obtaining FLC providing the best compromise between the accuracy and robustness performances. Simulations were performed for direct-drive two-axis robot arm. The evolved FLC with the proposed design technique found to provide a very satisfactory performance under the wide range of operation conditions and to overcome problem associated with coupling and nonlinearities characteristics inherent to robot arms.