Nonlinear longitudinal forced vibration of a hysteretic bar: An analytical solution

► A novel constitutive relation for hysteretic materials is introduced. ► The nonlinear response contains higher harmonics of odd order only. ► These have amplitude proportional to the square of the applied stress, Σ ► The shift of the resonance frequency is proportional to Σ. ► Q-1 depends on Σ½against earlier theoretical predictions.