Nonlinear natural frequencies and frequency veering of a beam with an arbitrary initial rise supported by flexible ends and resting on elastic foundation

The present study reports results for the effect of support flexibility on nonlinear natural frequencies and frequency veering phenomenon of an elastic euler-bernoulli beam resting on winkler elastic foundation with an initial arbitrary rise. also,it extends the analysis presented for the linear vibration analysis [1],to account for the effects of beam's ends flexibility and rise shape on; veering zones,and nonlinear natural frequencies. the beam is supported by translational and rotational springs at each end. the effect of the induced force due to mid-plane stretching is accounted for due to its importance and significance on the nonlinear dynamic and vibrational behavior of the beam,as it was proved and presented in earlier investigations and studies. the governing integro-partial differential equation is discretized using the assumed mode method galerkin's single mode approach and the resulting nonlinear temporal equation was solved using the harmonic balance method to obtain results for the nonlinear natural frequencies. the results are presented for the nonlinear natural frequencies of the first three modes of vibration,for a selected range of physical parameters,like rotational and translational springs at both ends of the beam,elastic foundation stiffness and initial rise shape and level. © 2017 jordan journal of mechanical and industrial engineering.