Equivalent Nonlinear Beam Model for Static and Free Vibration Analysis of the Beamlike Truss

Purpose: In this study, an equivalent nonlinear beam model (ENBM) of the beamlike truss considering the geometric nonlinearity is proposed based on the equivalent modeling approach. The ENBM can promote significantly computational efficiency and has the advantage of analytical solution for nonlinear dynamic analysis; moreover, the equivalent model provides great convenience for controller design of the beamlike truss. Methods: The ENBM contains nonlinear stretching force that can capture the large displacement effect of the beamlike truss, unlike most researches currently focus on equivalent beam model for linear beamlike truss (LBT). The novel equivalent nonlinear model is developed by introducing the von Karman nonlinear strain–displacement relationship in the equivalent linear beam model (ELBM). In effect, the nonlinear characteristic of the beamlike truss is related to nonlinearity of each member. Results: To check the validity of the proposed ENBM, two aspects including static deflection and free vibration response are investigated utilizing nonlinear finite-element method to establish the full-scale beamlike truss model. This paper employs the Hamilton principle to work out the governing partial differential equations of motion of the ENBM with two pinned ends. The governing partial differential equations are further discretized with the aid of the Galerkin approach. Conclusions: Comparisons between results of the ENBM and those obtained from the finite-element simulation of the nonlinear beamlike truss (NBT) show an excellent agreement, which confirms the validity and accuracy of the proposed method for imitating the static deflection and free vibration response of the original beamlike truss. The influences of the nonlinearity on the deflection and frequency of the equivalent beam model and the beamlike truss are discussed. In addition, the result of the calculation time demonstrates that the proposed approach can provide a more efficient nonlinear response analysis with significant less computational cost compared with the finite-element method.