A novel method for designing S-box based on chaotic map and Teaching–Learning-Based Optimization

A new method for obtaining strong S-boxes based on chaotic map and Teaching–Learning-Based Optimization (TLBO) is presented in this paper. Our method presents eight rounds; each round contains two transformations: row left shifting and columnwise rotation. The vectors for the transformations are different from one round to another, and they are controlled by two keys to the logistic map. These two keys are optimized by using TLBO which aims to construct a strong S-box that satisfies to the criteria set in advance. Test for the following criteria such as bijectivity, nonlinearity, strict avalanche criteria, equiprobable inputs/outputs XOR distribution is analyzed. Additionally, we will provide many comparisons with other S-boxes and test of the sensitivity to keys. The results of performance test show that the proposed design S-boxes presents good cryptography proprieties and can resist to several attacks.     

An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.     

A novel numerical algorithm based on Galerkin–Petrov time-discretization method for solving chaotic nonlinear dynamical systems

Nonlinear chaotic systems yield many interesting features related to different physical phenomena and practical applications. These systems are very sensitive to initial conditions at each time-iteration level in a numerical algorithm. In this article, we study the behavior of some nonlinear chaotic systems by a new numerical approach based on the concept of Galerkin–Petrov time-discretization formulation. Computational algorithms are derived to calculate dynamical behavior of nonlinear chaotic systems. Dynamical systems representing weather prediction model and finance model are chosen as test cases for simulation using the derived algorithms. The obtained results are compared with classical RK-4 and RK-5 methods, and an excellent agreement is achieved. The accuracy and convergence of the method are shown by comparing numerically computed results with the exact solution for two test problems derived from another nonlinear dynamical system in two-dimensional space. It is shown that the derived numerical algorithms have a great potential in dealing with the solution of nonlinear chaotic systems and thus can be utilized to delineate different features and characteristics of their solutions.     

An efficient Galerkin averaging-incremental harmonic balance method for nonlinear dynamic analysis of rigid multibody systems governed by differential–algebraic equations

Nonlinear Dynamics - An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed for steady-state nonlinear dynamic analysis of index-3 differential algebraic...     

Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

A numerical method for simulating gas–liquid–solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas–liquid two-phase problem, and the latter is a gas–liquid–solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.     

Phenomenological continuous contact–impact modelling for multibody simulations of pedestrian–vehicle contact interactions based on experimental data

Multibody modelling of pedestrian collisions requires the definition of contact–impact between the pedestrian and the vehicle. An examination of relevant impact test data reveals large rate-dependent components of the reaction force, permanent indentation, and concomitant energy loss. Contact–impact models previously used in simulations of pedestrian impacts typically have not adequately modelled one, two or all three of these phenomena. This paper presents a phenomenological contact–impact model based on the Hunt–Crossley model of impact, which includes rate-dependent damping, and is extended to include permanent indentation. The proposed model suitably characterises impact test data in a form that can also be implemented in the multibody simulation code MADYMO (TASS-Safe, Netherlands). The proposed contact–impact model was used to characterise the impact between a legform and the bumper of a vehicle, based on two impact tests conducted at different impact speeds. A single contact–impact definition in MADYMO closely reproduced the dynamics of both tests. The proposed model may be suitable in a wide range of impact conditions where the impact is modelled using multibody techniques and it is practicable to conduct impact tests as part of the modelling process.     

An ε-generalized gradient projection method for nonlinear minimax problems

In this paper, combining the techniques of ε-generalized gradient projection and Armjio’s line search, we present a new algorithm for the nonlinear minimax problems. At each iteration, the improved search direction is generated by an ε-generalized gradient projection explicit formula. Under some mild assumptions, the algorithm possesses global and strong convergence. Finally, some preliminary numerical results show that the proposed algorithm performs efficiently.     

A Ritz’s method based solution for the contact problem of a deformable rectangular plate on an elastic quarter-space

In this article, Ritz’s method is used to calculate with unprecedented accuracy the displacements related to a deformable rectangular plate resting on the surface of an elastic quarter-space. To achieve this required three basic steps. The first step involved the study of Green’s function describing the vertical displacements of the surface of an elastic quarter-space due to vertical force applied on its surface. For this case, an explicit formula was obtained by analytically resolving a complicated integral that did not previously have an analytical solution. The second step involved the study of the coupled system of a plate and an elastic quarter-space. This portion focused on determining reactive forces in the contact zone based on Hetenyi’s solution. After determination of the reactive forces, certain features were attributed to the plate’s edges. The final step involved the application of Ritz’s method to determine the deflections of the plate resting on the surface of the quarter-space. Finally, an example calculation and validation of results are given. This is the first semi-analytical solution proposed for this type of contact problem.     

A one-dimensional theory of wave-propagation in elastic rods based on the „method of internal constraints“

Conclusions The results obtained in this paper in the particular case of lateral vibrations of bars show an encouraging agreement between the values ofc/c ₀ andc _g/c₀ given by the approximate theory based on the assumption of internal constraints and the exact theory derived from the use of the equations of the Mathematical Theory of Elasticity.This approximate theory which will be referred to as the Theory of Internal Constraints is in the dynamic case completely contained in the constraint equation (1) and in the application ofHamiltons Principle. Accordingly the concept of Shear Coefficient is not used. In the general case of wave propagation in elastic straight rods this theory unifies a number of separate engineering treatments of the problem. Moreover, the same theory can be applied to the study of vibrations of curved bars taking into account the effects of shear and of rotatory inertia as has been shown in a previous paper.The mathematical simplicity of the theory and its degree of accuracy justify its use in dealing with engineering problems in vibrations of curved or straight bars for which more exact theories cannot be used because of their mathematical complexities.The author wants to express his best thanks to Mr.E. C. Zachmanoglou, student in the Department of Aeronautical Engineering, and to Mr.R. V. Milligan, graduate student in the Department of Mechanics, at Rensselaer Polytechnic Institute for the valuable help and assistance given to him in the preparation of the numerical tables and graphs which are presented in this paper.The material presented in this paper is based on an investigation which is being conducted under the sponsorship of the Office of Naval Research, Department of the U. S. Navy, Washington, D. C.; and is presented with the permission of the Office of Naval Research.     

Extended constraint enforcement formulations for finite-DOF systems based on Gauss’s principle of least constraint

Nonlinear Dynamics - This paper aims to contribute to formulations of mathematical models for finite-DOF systems based on the Gauss’s principle of least constraint. A new theorem allows to...     

Investigation on the effect of density ratio on the convergence behavior of partitioned method for fluid–structure interaction simulation

In order to investigate the effect of density ratio of fluid and solid on the convergence behavior of partitioned FSI algorithm, three strong-coupling partitioned algorithms (fixed-point method with a constant under-relaxation parameter, Aitken’s method and Quasi-Newton inverse least squares (QN-ILS) method) have been considered in the context of finite element method. We have employed the incompressible Navier–Stokes equations for a Newtonian fluid domain and the total Lagrangian formulation for a non-linear motion of solid domain. Linear-elastic (hyper-elastic) model has been employed for solid material with small (large) deformation. A pulsatile inlet-flow interacting with a 2D circular channel of linear-elastic material and a pressure wave propagation in a 3D flexible vessel have been simulated. Both linear-elastic and hyper-elastic (Mooney–Rivlin) models have been adopted for the 3D flexible vessel. From the present numerical experiments, we have found that QN-ILS outperforms the others leading to a robust convergence regardless of the density ratio for both linear-elastic and hyper-elastic models. On the other hand, the performances of the fixed-point method with a constant under-relaxation parameter and the Aitken’s method depend strongly on the density ratio, relaxation parameter selected for coupling iteration, and degree of deformation. Although the QN-ILS of this work is still slower than a monolithic method for serial computation, it has an advantage of easier parallelization due to the modularity of the partitioned FSI algorithm.     

Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization

The solutions to H _∞ and H ₂ optimization problems of a variant dynamic vibration absorber (DVA) applied to suppress vibration in beam structures are derived analytically. The H _∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the resonant vibration amplitude, as well as, the H ₂ optimum parameters to minimize the total vibration energy or the mean square motion of a beam under random force excitation as analytical formulas. The reduction in maximum amplitude responses and mean square motion of a beam using the traditional vibration absorber is compared with the proposed dynamic absorber. Numerical results show the non-traditional DVA under optimum conditions has better vibration suppression performance on beam structures than the traditional design of DVA. Furthermore, comparing H _∞ and H ₂ optimization procedures shows that for a beam under random force excitation, use of H₂ optimum parameters resulting in smaller mean square motion than the other optimization.     

Use of Tikhonov’s regularization method for solving identification problem for elastic systems

We present a method for solving nonlinear inverse problems, which also include identification problems for elastic systems. The problems whose initial data contain an error are usually solved by regularization methods [1–5]. In the present paper, we give preference to Tikhonov’s regularization method, which has been widely used in the recent years in practice to increase the stability of computational algorithms for solving problems in various areas of mechanics [6–9].     

Synchronization control for networked mobile robot systems based on Udwadia–Kalaba approach

This paper addresses the problem of synchronization control for networked multi-mobile robot systems from the perspective of analytical mechanics. By reformulating the task requirement as a constrained motion problem, a unified synchronization algorithm for networked multi-mobile robot systems with or without leaders is proposed in combination with algebraic graph theory and the Udwadia–Kalaba approach. With the proposed algorithm, the networked mobile robot system can achieve synchronization from arbitrary initial conditions for the leaderless case and realize accurate trajectory tracking with explicitly given reference trajectories for the leader-following case. Numerical simulations of a networked wheeled mobile robot system are performed under different network structures and various trajectory requirements to show the performance of the proposed control algorithm.

     

On the evolutions of the discontinuities of orders ⩾ m in solutions for quasi-linear systems of PDEs of order m,or for the linearizations of these systems

Summary One considers a system L[u]=0 of PDEs, quasi-linear (according to [1]) and of order m, which possesses a bicharacteristic line , as it happens in the hyperbolic case. For v=0, , –m (>0) let u(^v) be a discontinuity wave of order m+v that solves the system above and whose discontinuity hypersurface includes . The corresponding transport equations along are considered. Furthermore some interesting cases are pointed out, in which these equations turn out to be mutually equivalent in a suitable sense. Some theorems are stated to compare the transport equations for the discontinuities of the above kinds, that are connected with the systems d^hL[u]/dt^h=0 (h=0, , –m) and/or the linearization of the system L[u]=0 around any regular solution of it.

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Sommario Si considera un sistema L[u]=0 di equazioni alle derivate parziali, quasi lineare (secondo [1]) e di ordine m, il quale sia dotato di qualche bicaratteristica , come accade nel caso iperbolico. Per v=0, , –m(>0) sia u(^v) un'onda di discontinuità di ordine m+v risolvente il detto sistema e avente ipersuperficie di discontinuità contenente Si considerano le relative equazioni di trasporto lungo e si determinano casi interessanti in cui queste equazioni sono mutuamente equivalenti in senso opportuno. Si stabiliscono teoremi di confronto per il trasporto delle discontinuità del tipo suddetto, relative ai sistemi d^hL[u]/dt^h=0 (h=0, , –m) e/o alla linearizazione del sistema L[u]=0 attorno a qualche sua soluzione regolare.

     

Dynamic characteristics of self-acting gas bearing–flexible rotor coupling system based on the forecasting orbit method

This paper studies the nonlinear dynamic characteristics of a flexible rotor supported by self-acting gas bearings theoretically. The multiple degree freedom model of flexible rotor is established by the finite element method and analyzed coupled with the transient gas lubricated Reynolds equation by employing the forecasting orbit method. The Reynolds equation is solved by the alternating direction implicit method and the dynamic response of the rotor is calculated by the Newmark integral method. To settle the problem that the two kinds of transient solving processes (transient Reynolds equation for bearing and transient equation of motion for rotor) cannot be solved simultaneously, which arises from the fact that they need each other??s results as their initial values, the multi-field coupling algorithm based on the forecasting method is proposed and applied in this paper. By employing the numerical method, the rotor trajectory diagram, phase diagram, frequency spectrum, power spectrum, bifurcation diagram, and vibration mode diagram were obtained. It is to note that the dynamic characteristics of self-acting gas bearing?Crotor system and whirling instability of the system could be depicted successfully. This would establish the foundation for contributing to a further understanding of the gas bearing?Cflexible rotor system.