Hygrothermal and imperfection effects on FG nanobeam vibration via a refined integral shear theory

In this study, a higher-order approach incorporating a new polynomial-exponential integral shear strain field is established to examine the vibration response of functionally graded (FG) nanobeams subjected to hygrothermal loading and material composition imperfections. The formulation employs a displacement field with undetermined integral terms and considers four hygrothermal environments: uniform, linear, nonlinear, and sinusoidal distributions. The nanobeam respites on a Winkler-Pasternak elastic foundation, and three porosity patterns based on cosine-type functions are examined. A power-law scheme describes the disparity of constituent materials across the thickness, including temperature-dependent mechanical properties. The analysis explores the influence of environmental conditions, material gradation, porosity profiles, nonlocal impacts, and foundation stiffness on natural frequencies. The outcomes deliver a comprehensive context for future research on the dynamic behavior of advanced graded nanostructures.