Curve veering in spherical reticulated shells: Numerical simulations and mechanism analysis

The phenomena of curve veering, encompassing frequency loci veering and modal jumping, are investigated in the context of spherical reticulated shells by incorporating random detuning parameters with a Gaussian distribution into the mass matrix. The Finite Element Method (FEM) is systematically employed to investigate the effects of the assumed mass detuning patterns on the natural frequencies and modal shapes exhibited by a spherical reticulated shell. Our findings reveal the presence of frequency loci veering in certain typical detuning scenarios. Subsequently, the Frequency Veering Index (FVI) is proposed to determine the position of veering points. In conjunction, the occurrence of the mode jumping phenomenon is observed in proximity to veering points. The Modal Assurance Criterion (MAC) is proposed as a metric to evaluate the mode jumping phenomenon, and the number of veering points is ascertained through statistical analysis. Ultimately, the matrix perturbation method is employed to validate the underlying mechanisms of frequency loci veering and mode jumping phenomena, while a simplified model is utilized to provide a deeper understanding of their intrinsic nature.