Subharmonic periodic solutions of order (1/2 ,1/4) to a weakly second order ordinary differential equation which governed the motion of a micro-dynamical system are studied analytically. Applying the method of multiple scales, we derive the modulation equation in the amplitude an...
Open access
Research Article10.9734/ARJOM/2017/32008
The frequency-locking area of harmonic and subharmonic ( 1/2, 1/3 ) solutions in a fast harmonic excitation Mathieu-Van der PolDuffing equation is studied. A perturbation technique is then performed on the slow dynamic near the harmonic and subharmonic ( 1/2, 1/3 ) solutions, to...
Open access
Research Article10.9734/JSRR/2017/32122
The superharmonic solutions of a weakly nonlinear second order differential equation governed the dynamic behavior of a microcantilever based on TM (Tapping mode) AFM (Atomic force microscopy) are studied analytically by applying the method of multiple scales (MMS). The modulatio...
Open access
Research Article10.9734/JSRR/2016/28140
The harmonic solution of a weakly non-linear second order differential equation governed the dynamic behavior of a micro cantilever based on TM (Tapping mode) AFM (Atomic force microscope) is investigated analytically by applying the method of multiple scales (MMS). The modulatio...
Open access
Research Article10.9734/BJMCS/2016/24725
In this paper, we investigated the periodic solutions of type superharmonic and subsuperharmonic of modified Duffing equation subjected to a bi-harmonic parametric and external excitations. The method of multiple scales is used to construct a first order uniform expansion of appr...
Open access
Research Article10.9734/BJMCS/2016/25684