Detection and characterization of local nonlinearity in a clamped‐clamped beam with state space realization

Abstract The state space representation of linear and nonlinear systems is widely used in the literature for system characterization, system identification, and model‐based control synthesis. In the case of systems with local nonlinearity, the realization of a state space model where the states are physically interpretable as a requirement has been a challenging task. This requirement becomes more emphasized, especially in the scope of industrial high‐precision systems. Consequently, the class of black‐box system identification approaches becomes less attractive. In the scope of this paper, we are interested in modeling systems with dominant local nonlinearity where employing linear models can only cover a limited range of system dynamics. More specifically, geometric nonlinearities which are present in the joints (bolted) of structural interfaces are analyzed. The main goal is to provide systematical modeling of such systems without using a sparse nonlinear representation. Such a low‐order nonlinear model can improve the simplicity of analyzing the nonlinear system and can be used for structural vibration and noise control. In order not to neglect the sophisticated linear modeling technique, the linear model is proposed to be extended by means of smooth nonlinear terms. The systematic approach contains the modeling of the linear counterpart followed by the localization and characterization steps in the well‐known three‐step paradigm. For the characterization step, this work relies on the acceleration surface method (ASM). The experimental setup under study, as a benchmark, is a set of two beams of different lengths and thicknesses connected by a screw that is excited by a mechanical shaker. The axes are oriented in the transverse direction of the beams, while the boundaries are realized as imperfect clamped‐clamped boundary conditions at two ends in the model. Consequently, by selecting the excitation amplitude, we can control the dominant dynamics at lower excitation amplitudes and invoke the local nonlinearity at higher amplitudes. For higher excitation levels using sine sweep signals, the phase space information of the shaker and accelerometer sensors is used to detect the local nonlinearities along the clamped‐clamped beam. The detected and characterized nonlinearities are incorporated into the linear system as a systematic approach for modeling such a structurally nonlinear system.