Procedia IUTAM最新文献

Mathematical model of the rattleback is developed, where a special attention is payed to realistic and numerically effective modelling of the contact forces – friction forces and rolling resistance. In particular, special approximations of the resultant friction force and moment for non-point contact area are developed and applied. These reduced models allow to avoid necessity of use of the space discretization near the contact. The rattleback dynamics – regular and chaotic - is investigated numerically in the case of vibrations of the platform on which the object is located. Moreover, the interaction between a pair of magnets - the first situated inside the wobblestone and the second inside the platform – is modelled. The influence of the magnetic force on the system dynamics is investigated – especially in the context of possible use of the rattleback as energy harvesting system.

A two-ring network coupling by a transverse link is considered in this paper. Divide and conquer algorithm is used to analyze the stability and Hopf bifurcation values. Nonlinear waves (such as synchronization and reflection waves) are studied using the center manifold theorem and normal form theory. It is shown that appropriate settings of transverse coupling can guarantee the backup of the complicated dynamics from one ring to the other.

In the past few years, the energy harvester of piezoelectric beam has been extensively studied. In this paper, the bistable piezoelectric plate was adopted as the structure of energy harvester. The model consists of four parts including the substructure layer, the piezoelectric film, the protective layer and the magnet, which the material of the substructure layer and the piezoelectric layer are respectively carbon fiber and PVDF. The boundary conditions of the plate are simply supported by two opposite sides, which the other two sides are free. The base of the plate is subjected to the harmonic excitation. Based on von Karman large deformation theory and Hooke law, the partial differential equation for nonlinear vibration of the bistable piezoelectric system is derived by using Hamilton's principle. The Galerkin method is employed to discrete the partial differential equations to the ordinary differential equations. Then, the method of multiple scales is applied to perturbation analysis to obtain the nonlinear averaged equations in the polar form. Frequency-response curves of the piezoelectric plate are obtained by numerical simulations. The effects of the excitation amplitude, the damping coefficient, the piezoelectric parameters, the nonlinear parameters and the magnetic distance on nonlinear vibration of the bistable piezoelectric plate are studied.

The dampers (shock absorbers) installed in the suspensions of the towing car have some nonlinear property in road tests, like a practical piecewise-linear property. Its influence on the dynamic stability of car-trailer combinations are investigated in this paper. This nonlinearity is modeled by a Magic Formula damper model and then integrated into an extended single-track model with a tandem-axle trailer. Both the system local stability and global stability are analyzed with different theoretical methods. The results of system phase portrait show a limit cycle and the corresponding longitudinal velocity is identified as the system dynamic critical speed v_crit, which is ca. 147.2 km/h.

In the present paper, the interaction of surge, wave and tide on the north coast of Vietnamis assessed using a coupled model of surge, wave and tide. A series of storm surge simulations for Typhoons Frankie (1996) andWashi (2005) are carried out, considering the effects of the tide and the wave that combines a wave dependent drag and wave-induced radiation stress to find out a predominant factor in the storm surge generation. Typhoon Frankieis landfalled at the low tide while TyphoonWashi landfalled at the high tide. The results indicate that the effect of the wave is crucial to the storm surge simulation. In particular, the wave induced-surge improves the accuracy of the storm surge level up to 30 %. It also shows that the surge induced by wave radiation stress is dependant with the space resolution, and the finest resolution is improved and in close agreement with the observation. On the other hand, the influence of the tide is ignorable for the case of Typhoon Frankie and considerable in the case of Typhoon Washi.

The accurate prediction of surge height is vitally important in designing coastal defense structures. With the advancement of computation efficiency, many researchers have studied the wave-current interaction on surge height by coupling hydrodynamic and wave models. In this study, Deflt3D Flow model was interacted dynamically with Delft3D Wave model to simulate the storm surge process caused by typhoon Khanun to obtain the spatiotemporal properties on wave setup induced by storm wind. Simulations with and without wave model have been conducted, revealing that the spatiotemporally varying wave setup distribute along the coastal line when typhoon is in the open sea with large wave height and surge height around. The spatial distribution of nearshore wave setup at landfall moment was obtained. Nevertheless the contribution of wave effects on storm surge increases slightly under intensive storm wind, with the maximum wave setup near typhoon center accounting for 10% of the peak surge height.

The maximal Lyapunov exponent of a nonsmooth system is the lower bound for the proportional feedback gain necessary to achieve full state synchronization. In this paper, we prove this statement for the general class of nonsmooth systems in the framework of measure differential inclusions. The results are used to estimate the maximal Lyapunov exponent using chaos synchronization, which is illustrated on an impact oscillator.

The dynamical systems approach recently applied to understand subcritical transitions in wall-bounded shear flows is combined with the use of large-eddy simulations to investigate the nature of large-scale coherent motions in turbulent Couette and Poiseuille flows. Exact invariant solutions of the filtered Navier-Stokes (LES) equations are computed by using the Smagorinsky model to parametrize small-scale motions. These solutions can be continued into exact solutions of the Navier-Stokes equations, therefore providing a bridge between coherent large-scale motions in wall-bounded fully developed turbulent flows and invariant solutions appearing in transitional flows.

A procedure that allows us to describe the distribution patterns of atomic sites of the diamond type structure over the coordination spheres is presented. The spatial packing of the coordination spheres is formed by the vertices of the seven base polyhedra with cubic symmetry and the four polyhedra with tetrahedral symmetry. The former is given by a set of the seven regular or semi-regular polyhedra of Platonic and Archimedean solids such as the cube, the truncated cube, the octahedron, the cubic-, truncated-, rhomboidal-, and truncated cubic octahedrons. The latter is given by a set of four other shapes such as the tetrahedron, the rhombohedral-, truncated-, and truncated rhombohedral tetrahedrons.

This paper presents a study on the limits of stabilizability of unstable second-order dynamical systems by means of digital proportional-integral-derivative-acceleration (PIDA) feedback. Four different models are considered, which are all governed by the same dimensionless second-order differential equation. The mathematical model under analysis is a hybrid system involving terms with piecewise constant arguments due to the discrete sampling and actuation of the controller. Closed form formulas are derived for the domain of stability and for the limits of stabilizability as function of the system parameters, the sampling period and the control gains. It is concluded that while the acceleration term extends the limit of stabilizability, the integral term reduces stabilizability properties.