Stiffness identification of beam structures with elastic foundations through the global mode method and time-domain nonlinear subspace method

Dynamic modeling for beam structures with elastic foundations has received considerable attention, as foundations may affect the dynamic characteristics of beam structures significantly. However, the identification of the stiffnesses between beam structures and foundations remains a challenge. This paper focuses on the stiffness identification problem of beam structures with elastic foundations by proposing a combined approach comprising the global mode method and time-domain nonlinear subspace identification (TNSI) method. The nonlinear dynamic model of beam structures with nonlinear elastic foundations and boundaries is first established by the global mode method. Subsequently, we propose a novel approach to identify the locations and linear terms of the foundations’ stiffnesses based on global natural frequencies by introducing global frequency surfaces. Furthermore, the TNSI method is employed to separate the underlying linear system from the nonlinear system and identify the nonlinear terms of the foundations’ stiffnesses. Numerical and experimental validations are finally carried out and identification results demonstrate the feasibility and accuracy of the proposed approach on the linear and nonlinear stiffness identification of beam structures with elastic foundations.