this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...

The amplitude–frequency relationship is an important mathematical property for a nonlinear oscillator. He’s amplitude–frequency formulation and the Max–Min approach are used to handle the conservative nonlinear oscillator ẍ +  1 + ẋ2  x = 0 for the amplitude–frequency relationship. The obtained result is compared with those in the open literature, revealing the effectiveness of the used metho...