Design of an optimal tuned mass damper for a system with parametric uncertainty

Structural control is becoming an attractive alternative for enhanced performance of civil engineering structures subject to seismic and wind loads. However, in order to guarantee stability and performance of structures when implemented with a passive or active control technique, there is a need to include information of uncertainty in the structural models due to the fact that civil engineering structures are time variant and nonlinear. These variations in the structure are often due to parameters such as variable live loads and inelastic behavior and, in cases, may be modeled as parametric uncertainty. The design of an optimal tuned mass damper (TMD) for a one degree-of-freedom (SDOF) system with parametric uncertainty is presented in this paper. The optimization of the connection between the absorber and the primary structure is cast as a constant feedback problem which is solved using structured singular value, μ, synthesis with D-K iteration and decentralized H _∞ design. Results are presented of the TMD that minimize the harmonic response of the primary structure represented by a set of systems within an uncertainty set.     

Shaking table tests of a plate-column structure with semi-active tuned mass damper

This paper presents selected results of experimental tests carried out on the three-storey plate-column structure, which is a physical model of a building. On the top floor the semi-active tuned mass damper (STMD) is installed. That device is a kind of harmonic oscillator with a variable stiffness characteristic. The tuning of STMD is possible in the frequency range from 0 to 5 Hz, which allows to counteract the resonant vibration of plate-column structure for the three basic frequencies. The model's vibration are kinematically excited by using the earthquake simulator. It is assumed that during an experimental tests the plate-column structure's vibration are only excited by horizontal component of base motion (dominant influence on building's vibration). The aim of the experimental analysis presented in this paper is to verify the effectiveness of the semi-active tuned mass damper in vibration's amplitude reduction of the main structure. The tested device is prototype of STMD, which uses a competitive constructional solution of stiffness parameter control. By reason of above, special attention is focused on the testing of vibration eliminator in two aspects: change of stiffness characteristic (the rate of change), and the accuracy of tuning to the resonant frequencies. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large time dynamics of a nonlinear spring–mass–damper model

In this paper we consider a nonlinear strongly damped wave equation as a model for a controlled spring–mass–damper system and give some results concerning its large time behaviour. It can be seen that the infinite dimensional system admits a two-dimensional attracting manifold where the equation is well represented by a classical nonlinear oscillations ODE, which can be exhibited explicitly. In contrast to other papers, this one applies Invariant Manifold Theory to a problem whose linear part is not self-adjoint.     

Numerical optimization of tuned mass absorbers attached to strongly nonlinear Duffing oscillator

We investigate the dynamics of the vertically forced Duffing oscillator with suspended tuned mass absorber. Three different types of tuned mass absorbers are taken into consideration, i.e., classical single pendulum, dual pendulum and pendulum-spring. We numerically adjust parameters of absorbers to obtain the best damping properties with the lowest mass of attached system. The modification of classical case (single pendulum) gives the decrease of Duffing system amplitude. We present strategy of parameters tuning which can be easily applied in a large class of systems.     

Dynamic performance analysis of non-linear tuned vibration absorbers

The main purpose of this study is to evaluate the dynamic characteristics of a damping controlled semi-active tuned vibration absorber (TVA). A base-excited, single-degree-of-freedom structure coupled with a TVA model is adopted as the baseline model for our analysis. A non-model based groundhook control (displacement-based on–off control or “on–off DBG”) was used to control the damping of the TVA. After developing numerical models of a non-linear TVA along with the on–off DBG control and a passive TVA, the optimal tuning parameters of both TVA models were obtained using an optimization routine. Using the two optimally tuned models, parametric studies were preformed by varying the values of both on and off-state damping to evaluate the dynamic performances of the TVAs using the peak transmissibility criteria. The results showed that the peak transmissibility of the semi-active TVA is nearly 21% lower than that of the passive, indicating that the semi-active TVA is more effective in reducing vibration levels. The results further showed that increases in off-state damping decreases the effectiveness of semi-active TVA in reducing maximum vibration levels.     

On the characteristics of a quasi-zero-stiffness vibration isolator with viscoelastic damper

Quasi-zero-stiffness (QZS) vibration isolators have been widely studied in previous literature, in which the viscous damping was adopted. In this paper, the QZS isolator with viscoelastic damper is studied, to seek an approach for further improving the isolation performance. The governing equation of the QZS isolator with viscoelastic damper (QZS-VED isolator) is formulated. The dynamic response is analyzed analytically and numerically. The transmissibility characteristics with varying key parameters are investigated, accompanied by comparison with the conventional QZS isolator, to demonstrate the advantages of the QZS-VED isolator. It is revealed that the damping ratio can be optimized to attain the lowest peak transmissibility and meanwhile the roll-off rate of high frequency transmissibility is twice that of the conventional QZS isolator, which implies superior isolation performance both around the resonant frequency and at high frequencies.     

Parameter identification for a class of nonlinear chaotic and hyperchaotic flows

Based on the stability theory, an accurate and fast parameter identification law of chaotic and hyperchaotic flows is created by selecting right initial values and suitable observers. The suitable observers are designed and used to identify any uncertain parameters of chaotic and hyperchaotic flows. Furthermore, the accuracy of parameter identification is very much improved by making use of wavelet de-noising. Theory analysis and numerical simulations of Lorenz and hyperchaotic Chen systems are implemented to verify the effectiveness and feasibility of the observers to identify the parameters.     

Impulsive generalized synchronization for a class of nonlinear discrete chaotic systems

The problem of impulsive generalized synchronization for a class of nonlinear discrete chaotic systems is investigated in this paper. Firstly the response system is constructed based on the impulsive control theory. Then by the asymptotic stability criteria of discrete systems with impulsive effects, some sufficient conditions for asymptotic H-synchronization between the drive system and response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Cryptanalyzing a nonlinear chaotic algorithm (NCA) for image encryption

This paper describes the security weakness of a recently proposed image encryption algorithm based on a logistic-like new chaotic map. We show that the chaotic map’s distribution is far from ideal, thus making it a bad candidate as a pseudo-random stream generator. As a consequence, the images encrypted with this algorithm are shown to be breakable through different attacks of variable complexity.     

Periodic optimal control for a degenerate nonlinear diffusion equation

This paper is concerned with the optimal control governed by a degenerate nonlinear diffusion equation. The existence and stability of the optimal control is established based on parabolic regularization and the weak convergence technique.     

Steady-state chaotic responses of a class of linear vibration absorbers

The steady state behavior of nonautonomous systems of two coupled nonlinear oscillators with small internal damping is analyzed by numerical integration of the motion equations, by varying the frequency of the periodical external excitation. A variety of periodic, quasi-periodic and chaotic oscillations are detected, whose properties are examined by means of Poincaré mappings, Lyapunov exponents spectra and fractal dimension measurements.     

Computation of optimal controls for a nonlinear stochastic third-order system

This paper deals with the computation of optimal feedback control laws for a nonlinear stochastic third-order system in which the nonlinear element is not completely specified. It is shown that, due to the structure of the system, the optimal feedback control law, whenever it exists, is not unique. Also, it is shown that, in order to implement an optimal feedback control law, a nonlinear partial differential equation has to be solved. A finite-difference algorithm for the solution of this equation is suggested, and its efficiency and applicability are demonstrated with examples.     

On Taylor series expansion for chaotic nonlinear systems

We study properties of Taylor series expansion for maps displaying chaotic behaviour. Analytical and numerical results are presented to illustrate that under certain conditions the trajectory of the map obtained by the expansion may not represent the original trajectory, even if the Taylor series converges.     

Synchronization conditions for chaotic nonlinear continuous neural networks

This paper deals with the synchronization problem of a class of chaotic nonlinear neural networks. A feedback control gain matrix is derived to achieve the state synchronization of two identical nonlinear neural networks by using the Lyapunov stability theory, and the obtained criterion condition can be verified if a certain Hamiltonian matrix with no eigenvalues on the imaginary axis. The new sufficient condition can avoid solving an algebraic Riccati equation. The results are illustrated through one numerical example.     

Two-material optimal design for nonlinear elastica

The work considers an optimal design problem in the context of nonlinear elastica. More specifically, we deal with finding the best way of mixing fixed amounts of two different elastic materials, so as to minimize the tip deflection of a cantilever beam loaded on its free extreme under the assumption of large deflections. Applying an optimality criteria method to the relaxed problem, simulations give us numerical evidence that the original design problem admits classical solutions (i.e. there is no microstructure) and those are the same as the respective ones for the case of small deflections.     

Direct training method for a continuous-time nonlinear optimal feedback controller

The solutions of most nonlinear optimal control problems are given in the form of open-loop optimal control which is computed from a given fixed initial condition. Optimal feedback control can in principle be obtained by solving the corresponding Hamilton-Jacobi-Bellman dynamic programming equation, though in general this is a difficult task. We propose a practical and effective alternative for constructing an approximate optimal feedback controller in the form of a feedforward neural network, and we justify this choice by several reasons. The controller is capable of approximately minimizing an arbitrary performance index for a nonlinear dynamical system for initial conditions arising from a nontrivial bounded subset of the state space. A direct training algorithm is proposed and several illustrative examples are given.This research was carried out with the support of a grant from the Australian Research Council.We thank the anonymous reviewers for their helpful comments.     

On nonlinear plane vibration of a moving threadline

We consider plane vibrations of a moving threadline described by the model equations obtained in [1]. We study the propagation of weak discontinuities and their interaction with shock waves. We show that the only possible shocks satisfying the Lax conditions [3] and the evolutionary condition of Brun [9] are the characteristic shocks.

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Riassunto Vengono considerate le vibrazioni piane di un filo flessibile descritte dalle equazioni ottenute in [1], Viene studiata la propagazione di onde di discontinuita' e la loro interazione con un'onda d'urto. Viene anche mostrato che gli unici urti possibili che soddisfano le condizioni di Lax [3] e la condizione di evoluzione di Brun [9] sono gli urti caratteristici.

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This work was supported by C.N.R. through G.N.F.M. and by M.P.I, through Fondi del 40% e 60% per la Ricerca Scientifica.