System identification of excited beam immersed in granular materials: A multifrequency data-based method in a variational framework

Abstract

Granules and immersed structures coupling vibration systems are common in civil, pharmaceutical, mining, and metallurgical fields. These systems present frequency-dependent physical parameters and nonlinear dynamic characteristics owing to the multiphase, cross-scaled, and highly nonlinear discrete media. The research on such coupling vibration systems has just started in recent years, mainly focusing on simulations and experiments, and the theoretical model has not been publicly reported. In order to obtain the general form of the dynamic equation of the granules and immersed beam coupling vibration systems, in this paper, the integral variational equation of the granules-beam system was first constructed based on the variational principle. A deflection curve reconstruction method was introduced to obtain the flexural function of the beam through data captured by a few strain measuring points. Furthermore, the coupling mechanism between the mass and stiffness data of the system with single-frequency responses was explained under an integral variational framework, and a multifrequency data-based method was proposed to identify the granules and immersed beam coupling vibration system. Numerical studies were conducted on the effectiveness and robustness of the proposed method, including the measurement noise and number of strain measuring points. Experimental studies on the granules and immersed beam coupling vibration system were based on dynamic strain testing techniques. The identification results further verified the feasibility of the proposed method, and the general form of the dynamic equation of the system and variations in the system parameters with excitation frequencies were obtained. The frequency-dependent characteristics generated new peak and jump phenomena, respectively, below and slightly above the first-order natural frequency of the beam.