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Abstract Quasi-periodic (QP) solutions of a damped nonlinear QP Mathieu equation with cubic nonlinearity are investigated by using the incremental harmonic balance (IHB) method two time scales. The contains incommensurate excitation frequencies, one is small frequency while other nearly equals twice linear natural frequency. It found that Fourier spectra consist uniformly spaced sidebands due t...

one of the main steps within the geoid computation methodology without applying the stokes formula is downward continuation of the harmonic residual observables from the surface of the earth down to the surface of the reference ellipsoid. this downward continuation is done via the abel-poisson integral and its derivatives. this integral in which the unknowns, i.e. harmonic residual potential va...

In this study, the iterative harmonic balance method was used to develop analytical solutions of period-one rotations of a pendulum driven horizontally by harmonic excitations. The performance of the method was evaluated by two criteria, one based on the system energy error and the other based on the global residual error. As a comparison, analytical solutions based on the multi-scale method we...

This paper presents the influence of nonlinear terms of a previously proposed constitutive piezoelectric equation on the dynamics of a cantilever aluminium beam with a piezoelectric unimorph PZT (MIDE QP16N) attached to it. The system is subjected to different levels of base acceleration with the intention to evidence the limits of the linear model. To carry out the analysis, a one-dimensional ...

In this paper, a dynamical system, which consists of two linear mechanical oscillators, coupled with a nonlinear damping device is considered. First, the dynamic equations are derived, then, an analytical method such as harmonic balance method, is applied to obtain the response to a harmonic base excitation. The response of the system depends on the excitation characteristics. A parametric stud...

We consider oscillators consisting of a reactance circuit and a negative resistor. They may happen to have multi-mode oscillations around the anti-resonant frequencies of the reactance circuit. This kind of oscillators can be easily synthesized by setting the resonant and antiresonant frequencies of the reactance circuits. However, it is not easy to analyze the oscillation phenomena, because th...