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In this paper, we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the problem, then we state and prove some convergence results, for which we provide the corresponding mechanical interpretation. Next, we turn to the numerical approximation of the problem based on a finite element scheme. We use a relaxation method to solve the discrete problems that we implement on the computer. Using this method, we provide numerical simulations which validate our convergence results. [ABSTRACT FROM AUTHOR]

Numerical models for vibro-acoustic analyses of complex mechanical systems are becoming more and more popular, in particular in the field of virtual product development. Therefore, reliable, comprehensive, and validated modeling methodologies remain crucial. However, system characteristics such as elasticities of the drive train components and nonlinear characteristics can lead to complex, and costly numerical models with a huge number of degrees of freedom. This may raise not only the need for novel and reasonable modeling strategies, but also exacerbates validation process, due to the wide scope in terms of operating conditions. In practice, structure-borne noise signals, for example, from accelerometers, are often used for the validation of mechanical systems. By choice of a sufficient number of measurement points, the interpretation becomes more complex. A lot of vibration response curves then need to be compared and interpreted over a wide operating range. In general, the interpretation focuses on deviations in quality and quantity. In this paper, to overcome these mentioned challenges, a validation methodology is proposed allowing a fast and transparent check of a number of captured signals. Therefore, it is shown how the original information can be reduced in a meaningful manner, making it possible to run a fast and accurate validation. The method is demonstrated on a real application with high mechanical complexity and it is shown that the chosen parameters are reliable. [ABSTRACT FROM AUTHOR]

The issue of synchronization between dynamical systems has attracted much attention, and the systems with integer-order dynamical networks have been well studied. The synchronous behavior of fractional-order dynamical systems is very interesting and importance, but has rarely been studied. In this paper, we studied the synchronization and anti-synchronization behavior between integer-order dynamical networks and fractional-order dynamical systems via a Takagi-Sugeno fuzzy model. Remarkably, there is synchronous behavior in such a system, and this is dramatically different from the behavior of integer-order dynamical networks. Moreover, we studied the impact of different coupling strengths on the dynamical process of synchronization and robustness of the designed controller to different coupling functions, different dimensions of dynamical equations and different fractional orders. Finally, we propose the theoretical analysis, which coincides well with the numerical simulations of five typical examples. [ABSTRACT FROM AUTHOR]

In this paper, a novel synchronization method of modified function projective lag synchronizations (MFPLS) between identical and nonidentical hyperchaotic complex nonlinear systems with parameter perturbations and external perturbations is proposed. In the method, the states of two hyperchaotic complex systems with parameter perturbations and external perturbations are asymptotically lag synchronized up to a desired scaling function matrix, and all the perturbations in the parameters asymptotically converge to zero. Base on the Lyapunov stability theory, the adaptive controller and updating laws of parameter perturbations are designed to achieve MFPLS between the drive and response systems. Theoretically the proof that the drive and response system will asymptotically lag synchronization and numerical simulations verify the feasibility and effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

The response of plate subjected to underwater explosion loading is of major concern in a variety of marine, ship and offshore platform applications. This paper first conducts the theoretical analysis of the shock loading acting on the plate exposed to underwater explosion. Thereafter, an effective numerical method is adopted to compute the central plastic deformation of the rectangular plates shocked by primary shock wave without regard to the modeling of surrounding water. Therefore numerical computation efficiency is highly improved. Due to the disregard of the gas bubble pulsation energy, numerical central deflections of the rectangular plates are less than the experimental results. Thus, an energy-modified method is advanced to modify the numerical results according to the energy distribution during underwater explosion. The comparison of two types of modified numerical predictions with experimental results piece-wise shows good agreement. [ABSTRACT FROM PUBLISHER]

In this paper we describe a new solution for stable haptic interaction with deformable object simulations featuring low servo rates and computational delays. The solution presented is a combination of the local model and the virtual coupling concepts proposed in the past. By varying the local model impedance depending on the local stiffness of the deformable object, the interaction between local model and simulation can always be made stable independently of low servo rates or computational delays. Moreover by using more complex local impedances that feature an integral term, we are able to control the steady-state error between the device and the surface of the deformable object This allows us to maximize the Z-width of the simulation, while obtaining overall stable behavior without using any added damping. The local model is always computed using the current deformable object surface, thus allowing for multi- point contact interaction, i.e., allowing multiple users to feel each other's influence on the object The proposed solution is presented and analyzed in a multirate setting. Experimental results employing a Phantom haptic interface are presented. [ABSTRACT FROM AUTHOR]