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The safety and reliability of high-speed trains rely on the structural integrity of their components and the dynamic performance of the entire vehicle system. This paper aims to define and substantiate the assessment of the structural integrity and dynamical integrity of high-speed trains in both theory and practice. The key principles and approaches will be proposed, and their applications to high-speed trains in China will be presented.

First, the structural integrity and dynamical integrity of high-speed trains are defined, and their relationship is introduced. Then, the principles for assessing the structural integrity of structural and dynamical components are presented and practical examples of gearboxes and dampers are provided. Finally, the principles and approaches for assessing the dynamical integrity of high-speed trains are presented and a novel operational assessment method is further presented.

Vehicle system dynamics is the core of the proposed framework that provides the loads and vibrations on train components and the dynamic performance of the entire vehicle system. For assessing the structural integrity of structural components, an open-loop analysis considering both normal and abnormal vehicle conditions is needed. For assessing the structural integrity of dynamical components, a closed-loop analysis involving the influence of wear and degradation on vehicle system dynamics is needed. The analysis of vehicle system dynamics should follow the principles of complete objects, conditions and indices. Numerical, experimental and operational approaches should be combined to achieve effective assessments.

The practical applications demonstrate that assessing the structural integrity and dynamical integrity of high-speed trains can support better control of critical defects, better lifespan management of train components and better maintenance decision-making for high-speed trains.

The paper shows that it is possible to reconstruct the dynamical attractors of demand at different levels of the supply chain by using time series duplication and techniques for normalisation. The objective of reconstructing dynamical attractors is to learn more about the long‐term dynamical behaviour of supply chains. Typical patterns that can be encountered through phase space reconstruction are discussed. Based on the analysis of real life supply chains first results are presented on how attractors can be used to better understand the dynamical behaviour of supply chains. The cases show that clear attractors can be identified for consumer and retailer demand. When this demand is compared with supply the phase space analysis becomes an effective tool for identifying distortion in the supply chain. The paper concludes by presenting two examples on how a better understanding of demand attractors have been used to improve operational and tactical planning.

High-rise tower structures supported by side frame structure and viscous damper in chemical industry can produce plasticity under dynamic loads, such as wind and earthquake, which will heavily influence the long-term safety operation. This paper aims to systematically study the optimization design of these structures by free vibration and dynamic shakedown analysis.

The transfer matrix method and Euler–Bernoulli beam vibration are used to study the free vibration characteristic of the simplified high-rise tower structure. Then the extended stress compensation method is used to construct the self-equilibrated stress by using the dynamic load vertexes and the lower bound dynamic shakedown analysis for the structure with viscous damper. Using the proposed method, comprehensive parametric studies and optimization are performed to examine the shakedown load of high-rise tower with various supported conditions.

The numerical results show that the supported frame stiffness, attached damper or spring parameters influence the free vibration and shakedown characters of high-rise tower very much. The dynamic shakedown load is lowered down quickly with external load frequency increasing to the fundamental natural frequency of the structure under spring supported condition, while changed little with the damping connection. The optimized location and parameter of support are obtained under dynamical excitations.

In this study, the high-rise tower structure is simplified as a cantilever beam supported by a short cantilever beam and a damper under repeated dynamic load, and linear elasticity for solid is assumed for free vibration analysis. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.

This study provides a comprehensive method for the dynamical optimization of high-rise tower structure by combining free vibration and shakedown analysis.

The purpose of this paper is to investigate internal forces in bridges induced by moving vehicles and compare them to earthquake loading.

Dynamic analysis of bridges is performed for moving support actions, for spectral method with Eurocode 8 parameters and for moving vehicle influence. Results from all three methods have been compared on two examples and conclusions have been made. Moving vehicle analysis could be based on the moving force and on the moving mass approach where the later one requires rather accurate knowledge of structural accelerations. It has been shown that the classical Newmark formulation produces accelerations of low accuracy and a novel impulse acceleration method has been devised.

It is found that the actions induced by the moving load could be comparable or larger than those caused by the earthquake on bridges whose mass is not too large in comparison to the vehicle mass.

The developed method will be applied to a broader choice of examples and more reliable conclusions made.

There are bridges where it would be appropriate to perform moving vehicle dynamic analysis, in which case the vertical earthquake actions could be neglected in the analysis.

In order to assess actions from moving vehicles, Newmark method has been generalized in a novel way. Paper describes vector formulation of Newmark method that permits free mixing of integration parameters that could vary from node to node. The method is advantageous for moving load analysis where loading conditions of nodes change in time.

Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important.

In this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.

Due to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops.

The presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities.

The motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems.

The treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development.

The proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed into the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes, which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.

Fractional calculus provides powerful tool to build more realistic and accurate mathematical models in economic field. This paper aims to explore a proposed fractional-order differentiated Cournot duopoly game and its discretized game.

Conditions for existence and uniqueness of the proposed game’s solution are derived. The existence of Nash equilibrium point and its local and global stability are obtained. Furthermore, local stability analysis of the discretized game is investigated. The effects of fractional-order on game’s dynamics are examined, along with other parameters of the game, via the 2D bifurcation diagrams in planes of system’s parameters are acquired.

Theoretical and numerical simulation results demonstrate rich variety of interesting dynamical behaviors such as period-doubling and Neimark–Sacker bifurcations, attractors’ crises in addition to chaotic attractors. The results demonstrated that the stability Nash equilibrium point of the game can be lost by period doubling or Neimark–Sacker bifurcations.

Oligopoly games are pivotal in the mathematical modeling of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also macroeconomic analysis of business cycles, innovation and growth.

Although the Cournot game and its variants have attracted great interest among mathematicians and economists since the time of its proposition till present, memory effects in continuous-time and discrete-time Cournot duopoly game have not been addressed yet. To the best of author’s knowledge, this can be considered as the first attempt to investigate this problem of fractional-order differentiated Cournot duopoly game. In addition, studying more realistic models of Cournot oligopoly games plays a pivotal role in the mathematical investigation and better understanding of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also in macroeconomic analysis of business cycles, innovation and growth.

Many engineering structures exhibit loss of stability under static and dynamic loading. Due to the significance of these phenomena in engineering design this topic has attracted considerable attention during the last decades. In recent years much effort has been made to devise algorithms within finite element analysis to investigate the static stability behaviour of structures. With these methods stable and unstable paths can be traced, and limit or bifurcation points can be computed efficiently. The associated arc‐length or branch‐switching procedures are today standard tools in existing finite element codes.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

It is well known that the real behaviour of joints lies between the ideal pinned or rigid joint responses. Additionally the influence of this behaviour on the global structural response has been widely studied in the past centred on the plastic resistance or the critical load. On the other hand, there are relatively few studies focusing on the dynamical response of these structures. This paper aims to discuss these issues.

Two types of structures with rigid and semi-rigid joints were considered. Their inelastic response was evaluated using the N2 conventional pushover method, and were later compared to the results from a full non-linear dynamic analysis.

The results indicated that increasing joint flexibility makes the structure less rigid, lengthening its fundamental period and enhancing its horizontal displacement. Furthermore, a parametric study showed that joint flexibility might be of paramount importance to low to medium rise buildings response.

The evaluation of the influence of joint flexibility on the inelastic behaviour of steel structures located in seismic zone is of paramount importance, and is tackled in this paper.