Stroke patients with hemiparesis often exhibit an asymmetrical weight distribution, with the paretic leg providing less support and less weight-shift activity than the sound leg does. For upper-limb hemiparesis constraint-induced movement therapy (CIMT), where the sound limb is constrained and the patient is forced to use the paretic limb, has proven to be one of the most effective rehabilitati...

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 letter, an application of energy balance method is applied to solve the nonlinear oscillators with un force. Comparison is made between the modification of harmonic balance method and energy balance method. The results reveal that the energy balance method is very effective and simple. Energy balance method is very effective and convenient and quite accurate to both linear and nonlinear...

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...

A model of laminated cylindrical shells with discontinuous piezoelectric layer is proposed. Based on the first-order shear nonlinear shell theory, vibration control point-supported elastic boundary condition analyzed. In this model, a series artificial springs are introduced to simulate arbitrary conditions. And elastic-electrically coupled differential equations obtained by Chebyshev polynomia...

The aim of this comment is to extend the study of the dynamics of a finite extensibility nonlinear oscillator conducted by Febbo [M. Febbo, A finite extensibility nonlinear oscillator, Applied Mathematics and Computation 217 (2011) 6464-6475]. We show that the linearized harmonic balance method is not sufficiently adequate for this oscillator and that the harmonic balance method without lineari...

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...