Rational variational approaches to strong nonlinear oscillations

This study considers two rational variational approaches to approximately achieve the frequency of nonlinear equations that governs the oscillations of conservative systems. These methods are the global error minimization and He’s variational approach (HVA) that trial functions have rational form. Three illustrative examples are demonstrated, the investigated cases are related to oscillators that the restoring force has cubic and irrational forms. as well as the large-amplitude oscillation of a system having inertia and static nonlinearities is included to examine the usefulness and merit of the proposed algorithms. comparisons based on the exact ones manifest strong agreement with outcomes from the rational HVA.

Nonlinear oscillation