Boundary condition modelling and identification for cantilever-like structures using natural frequencies

The actual boundary conditions of cantilever-like structures might be non-ideally clamped in engineering practice, and they can also vary with time due to damage or aging. Precise modelling of boundary conditions, in which both the boundary stiffness and the boundary mass should be modelled correctly, might be one of the most significant aspects in dynamic analysis and testing for such structures. However, only the boundary stiffness was considered in the most existing methods. In this paper, a boundary condition modelling and identification method for cantilever-like structures is proposed to precisely model both the boundary stiffness and the boundary mass using sensitivity analysis of natural frequencies. The boundary conditions of a cantilever-like structure can be parameterized by constant mass, constant rotational inertia,constant translational stiffness, and constant rotational stiffness. The relationship between natural frequencies and boundary parameters is deduced according to the vibration equation for the lateral vibration of a non-uniform beam. Then, an iterative identification formulation is established using the sensitivity analysis of natural frequencies with respect to the boundary parameters. The regularization technique is also used to solve the potential ill-posed problem in the identification procedure.Numerical simulations and experiments are performed to validate the feasibility and accuracy of the proposed method. Results show that the proposed method can be utilized to precisely model the boundary parameters of a cantilever-like structure.