Periodic Oscillation and Bifurcation Analysis of Pendulum with Spinning Support Using a Modified Continuous Piecewise Linearization Method

Abstract

The large-amplitude oscillation of a pendulum with spinning support was investigated using a modified continuous piecewise linearization method (CPLM). In contrast to previous studies, the present study investigated the response of the spinning support pendulum when the non-dimensional rotation parameter ( $$ {\Lambda} $$ ) is greater than one. The analysis showed that the natural frequency increased monotonically with Λ, while the oscillation history produced a distinct qualitative change as $$ {\Lambda} $$ increases from $$ {\Lambda} < 1 $$ to $$ {\Lambda} > 1 $$ , confirming the presence of a bifurcation at $$ {\Lambda} = 1 $$ . It was also observed that the response exhibits a bi-stable equilibrium and a double-well potential when $$ {\Lambda} > 1 $$ . Finally, the modified CPLM solution was shown to produce a maximum error of less than 0.30% for $$ {\text{A}} \le 179^\circ $$ and $$ {\Lambda} \le 1 $$ , which is better than other published results. This shows the potential of the modified CPLM to obtain accurate periodic solutions of complex nonlinear systems.