Vibration and resonance reliability analysis of non-uniform beam with randomly varying boundary conditions based on Kriging model

In order to prevent the function failure of the structure due to resonance in the working process. The vibration responses and resonance reliability of non-uniform beam (NUB) with randomly varying boundary conditions (RVBCs) are investigated in this paper. The natural frequencies calculated by Adomian decomposition method (ADM) are used to establish the sample space, based on which the Kriging model is obtained through learning. The influences of boundary support spring stiffness (BSSS) and taper ratio on natural frequencies, vibration responses, and resonance reliability are then studied. The numerical results show that within the range of studied parameters, when the BSSS of the NUB change simultaneously during vibration, the influences and trends of the BSSS on each order's natural frequency are different and challenging to predict. Due to the geometric nonuniformity of the NUB, the influence of the spring at the left end with a smaller cross-section on the resonance failure probability is more significant than that on the other side. With the increase in taper ratio, the amplitude, maximum strain, and resonance failure probability increase first and then decrease. The method can also be used to solve the vibration characteristics and resonance reliability of NUBs with randomly varying elastic modulus, density and dimensions, which can provide a reference for the data monitoring and use maintenance of the nonuniform beam in vibration.