Nonlinear Vibration Analysis of Specially Orthotropic Micro-plates with Partial Crack and Varying Thickness Submerged in Fluid

Purpose This study investigates the non-linear vibrational response of partially cracked, specially orthotropic rectangular micro-plates with variable thicknesses, coupled with a fluid medium. Methods The classical plate theory has been revised by incorporating the modified couple stress theory to address size effects.A line spring model represents the partial crack at the center of the plate. Fluid interaction is incorporated using velocity potential and Bernoulli's equations to account for added mass effects in different immersion scenarios.Thickness variations along one and two dimensions are considered, and the governing equations are transformed into time-dependent modal coordinates using Galerkin's approach. Berger's approach introduces nonlinearity in the modal, and the multiple scales approximation solution method is utilized to solve the non-linear equations. Results The study explores the impact of crack length, size effect, various fiber orientations, thickness variations, taper parameters, fluid levels, and immersion depth on vibration behaviour, considering SSSS (Simply Supported on all sides) and CCSS (Clamped on two sides, Simply Supported on the others) boundary conditions. Key findings include the impact of taper constant and submergence depth on bending-hardening and bending-softening phenomena. Conclusion The findings demonstrate that taper constant and submergence depth significantly affect the vibrational characteristics of partially cracked orthotropic micro-plates, influencing bending-hardening and bending-softening behaviors. These results are valuable for the design and analysis of micro-plates in applications involving fluid-structure interactions and non-linear vibrations.