Response of self-excited three-degree-of-freedom systems to multifrequency excitations

An Experimental and Theoretical Investigation of a Micromirror Under Mixed-Frequency Excitation

“…The combination resonances look similar to what has been reported in [38,39] due to the presence of quadratic nonlinearity. However, in the present case, these resonances are activated due to both effects of quadratic nonlinearities, due to the electrostatic force, and due to the quadratic form of the voltage in the numerator of the electrostatic force expression.…”

Dynamics of Microbeams under Multi-Frequency Excitations

“…Down conversion for RF signals from 40–200 MHz and 27 MHz were demonstrated in [ 5 ]. The method of multiple scales was used to calculate the response of a three degrees of freedom system under multi-frequency excitation [ 9 ]. An integrated complementary metal–oxide–semiconductor (CMOS) mixer was designed based on clamped-clamped beams and two different approaches were used to implement both up and down conversion mixers [ 10 ].…”

Parametrically excited nonlinear systems: a comparison of two methods

“…Although problems involving single-frequency excitations have received considerable attention [1,11,12,13,15,17], limited problems involving multifrequency excitations have been studied in [2,19] for the case of one-degree-of-freedom systems and in [3,4,5,7,8,14,16,18] for the case of multidegree-of-freedom systems.…”

“…In [8], the method of multiple scales was used to studied harmonic, subharmonic, superharmonic, simultaneous sub/superharmonic and combination resonances of self-excited two coupled second-order system to multifrequency excitations. In [7], the response of self-excited three-degree-of-freedom systems to multifrequency excitations was analyzed.…”

“…7) where a i0 , θ i0 are the steady state values, and a i1 and θ i1 are infinitesimal timedependent perturbation. Inserting (3.7) into (2.12), using (2.16), and linearizing the resulting equations, we get…”