Duality in the analysis of responses to nonlinear systems

The paper provides a new view on the averaging procedure and equivalent linearization in the study of nonlinear mechanics. It is shown that the duality of those techniques can be used to obtain better approximate solutions or to separate the original nonlinear systems subjected to periodic and random excitations into deterministic and stochastic ones

On the influence of second order non-linearity on random vibrations

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A selection of parameters of tuned mass damper for multi-degree-of-freedom systems subjected to second order coloured noise excitation

Among the fundamental concepts for structure control, passive control systems have a significant role since they do not require additional energies produced by actuator. The basic of passive control is to incorporate a secondary system into the primary structure in order to transfer a part of the vibration energy of the primary system into the secondary one. In the paper the design of an optimal tuned mass damper (TMD) for a structure subjected to second order coloured noise excitation is investigated in order to minimize the sum of response mean squares of components of the primary system with a given ranking priority

An approximate method for analysing non-linear systems subject to random excitation

A solution technique based on the representation of the response of the non-linear system by a polynomial of the response of the linearized system is presented. The relation between the original non-linear system and the linearized system is introduced by considering the so-called extended moment equations and their closed set is to be solved to determine unknowns. For the Vanderpol oscillator subject to white noise excitation, the technique gives good approximation to the response moments as well as the probability density function

Random oscillation in systems subject to the excitation of a class of coloured noises

In the paper the higher order stochastic averaging method is developed to a class of colored noise excitations when the corresponding forming filter has only finite negative eigenvalues. The second approximate probability density function to the Duffing system subject to the exponentially correlated process is obtained. Numerical application is carried out to investigate the independence of mean square amp1itude on the bandwidth parameter

An identification algorithm for feedback active control

The aim of the paper is to present a control law for feedback active controlled structures in which a control algorithm is proposed to identify the external excitation with a time delay. The time duration in which the external excitation acts on the structure is devised into subintervals. In each subinterval the external excitation is identified and is then selected with the opposite sign as the control force for the next subinterval. The realization of the identification control algorithm in the practical application mainly depends on the computing capacity of the involved computer. and requires an investigation with respect to its robustness and stabilization

Short Communication: A technique for investigating nonlinear vibrations

In this short communication the main ideas of the method of equivalent linearization and dual conception are further extended to suggest a new technique for solving nonlinear differential equations. This technique allows improving the accuracy when the nonlinearity is strong and getting nonlinear features of responses. For illustration the Duffing oscillator is considered to demonstrate the effectiveness of the proposed technique