Nonlinear dynamics of a RLC series circuit modeled by a generalized Van der Pol oscillator

In this paper, nonlinear dynamics study of a RLC series circuit modeled by a generalized Van der Pol oscillator is investigated. After establishing a new general class of nonlinear ordinary differential equation, a forced Van der Pol oscillator subjected to an inertial nonlinearity is derived. According to the external excitation strength, harmonic, subharmonic and superharmonic oscillatory states are obtained using the multiple time scales method. Bifurcation diagrams displayed by the model for each system parameter are performed numerically through the fourth-order Runge–Kutta algorithm.

Recent advances in periodic vibrations of the middle ear with a floating mass transducer

The paper investigates periodic solutions of a nonlinear model of the middle ear with a floating mass transducer. A multi degree of freedom model is used to obtain a solution near the first resonance. The model is solved analytically by means of the multiple time scales method. Next, the stability of obtained periodic solutions is analysed in order to identify the parameters of the floating mass transducer that affect the middle ear dynamics. Moreover, some parameters of the middle ear structure are investigated with respect to their impact on obtained periodic solutions.

Multi-frequency excitation of microbeams supported by Winkler and Pasternak foundations

The multi-frequency excitation of a microbeam, resting on a nonlinear foundation, is investigated and the governing equation of motion of the microbeam system is developed. The viscoelastic-type foundation is considered by assuming nonlinear parameters for both Pasternak and Winkler coefficients. The well-known Galerkin approach is utilized to discretize the governing equation of motion and to obtain its nonlinear ordinary differential equations. The multiple time-scales method is employed to study the multi-frequency excitation of the microbeam. Furthermore, the resonant conditions due to the external excitation as well as the combination resonances for the first two modes are investigated. The influences of different parameters, namely the Pasternak and Winkler coefficients, the position of the applied force and the geometrical factors on the frequency response of the system are examined.