Approximate analytical methods have been used extensively for finding approximate solutions to nonlinear ordinary differential equations. In this paper we compare the recently developed direct normal form transformation with two other very well known and long standing methods, harmonic balance and the method of multiple scales. We will show that the direct normal form method combines some of th...

Two dimensions Mathieu equation containing periodic terms as well as the delayed parameters has been investigated in the present work. The present system represents to a generalized form of the one-dimension delay Mathieu equation. The mathematical difficulty for delay the coupled Mathieu equation has been overcome by using the matrices method. Properties of inverse complex matrices enable us t...

In this paper we deal with the performance analysis of harmonically forced nonlinear systems of Lur’e type. We use harmonic linearization to obtain a linear approximation of the nonlinear system, and provide a frequency domain condition that guarantees a unique positive real solution to the harmonic balance equation for a certain class of nonlinearities. Furthermore, we provide an estimate on t...

Professor Utkin in his discussion paper proposed an example showing that the amplitude of chattering caused by the presence of parasitic dynamics in systems governed by FirstOrder Sliding-Mode Control (FOSMC) is lower than the obtained using Super-Twisting Algorithm (STA). This example served to motivate this research reconsidering the problem of comparison of chattering magnitude in systems go...

The Bouc–Wen nonlinear hysteretic model has many control parameters, which been widely used in the field of seismic isolation. isolation layer is most important part system, can be effectively simulated by model, and system reflect different dynamic characteristics under parameters. Therefore, this paper mainly studies analyzes influence factors based on incremental harmonic balance method, pro...

Periodic solutions of a harmonically forced Duffing oscillator with time-delay state feedback are investigated using the incremental harmonic balance method. In process solving, explicit effect matrix time delay term was derived. The stability periodic determined by method which combines continuous approximation and multivariable Floquet theory. On this basis, frequency–amplitude response curve...