On the non-classical transfer matrix method for free vibration behaviour of multi-rigid-elastic unit microsystem

Abstract

The free vibration behaviour of multi-rigid-elastic unit microsystem is crucial for microminiaturization design. Classical transfer matrix method (CTMM) without material length-scale parameters fails to explain size-dependent free vibration response. In this paper, we revisit the theoretical framework for size effects, construct state vector, transfer matrix, transfer equation with material length-scale parameters, and develop isotropic non-classical transfer matrix method (NCTMM). Then, we derive the non-classical transfer matrix of typical microcomponent. The transfer matrix of torsion vibrating strain gradient microbar and transverse vibrating flexoelectric/flexomagnetic-elastic bilayer microbeam are developed based on the general flexomagnetic elasticity (GFME), respectively. Subsequently, we establish system transfer equation of multi-rigid-elastic unit chain microsystem. The microsystem free vibration problem is solved. It is found that the natural frequency of non-classical model increases gradually with decrease of the ratio of characteristic size and material length-scale parameter. When the ratio increases, the natural frequency of non-classical model is close to that of classical model. Moreover, the contribution from strain gradient elasticity, material length-scale parameter and slant edge crack type to electric/magnetic mode shape is further clarified. Compared with classical transfer matrix method (CTMM), the non-classical transfer matrix method (NCTMM) can perform system-level multi-body microscale analysis more appropriately.