Cubic Quintic Septic Duffing oscillator: An analytical study

This paper deals with a particular arrangement of a statically balanced system using 3 springs of prescribed material stiffness and critical geometrical parameter. The dynamics is described by a nonlinear differential equation upto septic power following odd nonlinearity for small disturbance from static equilibrium position. The governing differential equation is solved analytically by the combination of the linearisation of the equation with the method of Harmonic Balancing to observe the low natural frequency at fixed point and a finite displacement range in the neighbourhood of the equilibrium point where the dynamic stiffness is low. By this approximation method, the behaviour of the displacement with increase in time as well as the phase-plot of Cubic Quintic Septic Duffing equation for a set of parameter values is studied at the equilibrium position and its neighbourhood.