From the point of view of practice engineering，three types of nonlinear dynamic vibration absorbers（NDVAs），which use the Euler-buckled beam as nonlinear stiffness element and take the effects of arrangements of the linear supporting spring and damper into account，are presented. Based on above established models，the analytical solutions of the coupling systems with different kinds of NDVAs are derived by using complexification-averaging method. Compared with amplitude frequency response curves of the main vibrational system，the vibration suppression performance of the NDVA with ungrounded elastic support is the best. At last，some design parameters，which contain initial deflection q0，length L and initial oblique angle θ，are selected and investigated. According to calculation results，it can be concluded that there are optimal values for all above three design parameters when resonant peak of the main vibrational system is used as the evaluation index in the whole calculation frequency region.