Free vibrations of nanobeams under non-ideal supports based on modified couple stress theory

Abstract

Abstract In this study, free vibration analysis of nanobeams under various non-ideal supports have presented. Size effect of nanobeams has applied by utilizing modified couple stress theory. Hamilton’s principle has been used to derive the equation of motion. Governing equation has subjected to non-ideal boundary conditions which are modeled as linear functions including an introduced weighting factor (k). Obtained numerical results have verified by comparing with the published results. Results show that fundamental resonance frequencies of non-ideal clamped nanobeams are significantly decreased when it is compared to ideal supports. However, non-ideal simply supports creates a minor increase effect on fundamental frequencies with respect to clamped ones. Also, nano-size effect has investigated for non-ideal supports. It has found that, the smaller cross-sectional size of nanobeam causes increasing effect of non-ideal supports on fundamental frequencies.