Nonlinear dynamic responses of beamlike truss based on the equivalent nonlinear beam model

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The main goal of this paper is to develop an equivalent nonlinear beam model (ENBM) for forced vibration analysis of the nonlinear beamlike truss (NBT) and its numerical implementation for describing the nonlinear behaviors of the periodic NBT. For the equivalent dynamic modeling method based on the energy equivalence principle of the truss structures, most of the existing approaches focus on studying the linear characteristic which cannot satisfy the nonlinear dynamic analytical requirement. Here, we extend the equivalent dynamic modeling to nonlinear forced vibration responses of the large NBT civil engineering structure with two pinned ends. We introduce the geometric nonlinearity into the equivalent dynamic model using the von Karman nonlinear strain-displacement relationship to imitate the nonlinear behaviors of the beamlike truss. On the basis of the Hamilton principle, the fourth-order governing partial differential equations of motion of the ENBM are obtained and solved utilizing the Galerkin method. It is shown that the ENBM accurately captures the nonlinear dynamic response of the beamlike truss subjected to external load by using the first four order modes. In order to showcase the efficiency and accuracy of the ENBM, time histories, phase maps and fast Fourier transform frequency spectra are investigated for the NBT and the ENBM under different external excitation magnitudes and frequencies. Comparisons between results of the ENBM and those obtained from the finite element simulations of the NBT show good agreements and identify the periodic motions of them. Furthermore, the effect of the external loading and damping parameters on the frequency-response and force-response curves is discussed. In addition, computing time of the proposed ENBM are compared with that of the full-scale finite element model in ANSYS so as to highlight the significant less computational cost of the equivalent nonlinear dynamic modeling. Particularly, the proposed ENBM can achieve the nonlinear mechanism of the NBT in analytical method and design the low-order control law conveniently.