The Effects of Porosity on the Vibration Behaviors of the Functionally Graded Spherical Nanoshells Using General Higher-Order Shear Deformation Theory

This study examines the dynamic behavior of functionally graded spherical shallow nanoshells with taking into acount the effects of porosity. Eringen’s nonlocal elasticity theory was utilized to adjust for the small-scale effects on the free vibration behaviors of the functionally graded spherical shallow nanoshells. The governing equations are derived from a higher-order shear deformation theory and Hamilton’s preincple. These equations are subsequently solved by Navier’s closed-form method to produce a reliable and accurate model. The present model’s accuracy and dependability are confirmed through in-depth case studies. This work is remarkable in that it presents a thorough understanding of the free vibration responses in functionally graded spherical shallow nanoshells, all while paying close attention to small-scale effects. The subsequent parameter study researches the impacts of some factors on the free vibration characteristics of functionally graded spherical shallow nanoshells, including aspect ratio, thickness ratio, graded index, and nonlocal parameter. This work advances the discipline by providing a unique viewpoint on structural dynamics at the nanoscale. This work is distinguished by the careful considering the impacts of the nonlocal parameter, which advances the understanding of these complex systems and opens up new avenues for future advancements in micro/nanostructure design, testing, analysis, and optimization.