This work utilizes the finite element technique to evaluate the dynamic buckling of nanobeams of varying thicknesses, supported by elastic foundations with variable stiffness. The calculation formulas are based on the novel shear deformation theory and integrate the size effect according to nonlocal theory. The beam’s substance, defined by micro-porosities, is allocated based on two separate rules, while its thickness fluctuates according to an exponential law and a trigonometric function. The buckling zone of the beam is determined according to Bolotin’s theory, highlighting the importance of this research. The calculation theory is corroborated by juxtaposing the reported ultimate load of the compressed beam with the results derived from both analytical and numerical methods. This study delineates the results of predicting the beam’s buckling domain across several situations, providing a scientific reference to aid designers in choosing appropriate parameters to meet real operational needs.
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