Low-dimensional dynamic modeling for planar truss structures using assumed mode weighting

Planar truss structures, composed of numerous slender beams, exhibit complex coupling and nonlinear behavior under external excitations. Accurate, low-dimensional dynamic models are essential for analyzing their nonlinear behavior and controlling vibrations. This study presents a novel analytical modeling approach, the Truss Analytical Mode Method (TAMM), for planar truss structures. The TAMM, based on mode coordinate assembly and assumed mode weighting, addresses the high-degree-of-freedom challenges in FEM and overcomes the limitations of the Equivalent Modeling Method (EMM) in capturing local vibrations and modeling variable-height truss structures. Each beam and connection point is individually numbered, and two translational springs and one rotational spring are used to simulate the constraints between beams at each node. The kinetic and potential energies and the corresponding mass and stiffness matrices of each beam and elastic constraint are derived using the unconstrained modes. These matrices are then assembled to form the overall mass and stiffness matrices, resulting in the truss structure's Assumed Mode (AM) model. The global modes are obtained by solving the eigenvectors of the AM model and are further used to establish the nonlinear dynamic model considering the geometric nonlinearities in slender components. The solution of the dynamic model established by the FEM is used to verify the validity of the proposed approach. The computation time required by the TAMM to calculate the natural frequencies is reduced by 88 % compared to that of the FEM. Numerical simulations of typical engineering examples show that the global modes capture the truss structure's overall and local vibration characteristics. While the rotational stiffness of elastic connections has little effect on global vibration, it significantly influences local behavior.