Bending Deflections and Natural Frequencies of Micro/Nanobeams Using a Third Order Single Variable Nonlocal Beam Theory

Abstract

AbstractIn this paper, the bending deflections and natural frequencies of micro/nanobeams have been evaluated using a third order single variable nonlocal beam theory. The beam theory used herein contains only one governing differential equation involving a single displacement variable. Also, governing equation of the theory has strong similarity to that of nonlocal Euler–Bernoulli beam theory. In this work, the beam bending and free vibration analysis of simply supported micro/nanobeams with rectangular cross-section have been carried out. In case of bending analysis, the deflections of the beams are evaluated by using two methods, namely Navier’s method and by direct integration of the governing differential equation. Similarly, the free vibration analysis of rectangular cross-section has been carried out, and the corresponding frequency characteristic equation is obtained by using Navier’s method. The bending deflections and natural frequencies have been evaluated for the case of beams with different thickness/length ratios and various values of nonlocal parameters. The results for beam deflections and natural frequencies have been presented in the tabular form as well as in the graphical form. Results obtained by using the present beam theory are compared with those of other beam theory results available in the literature. The results for deflection and natural frequencies obtained herein are found to be accurate.KeywordsBending deflectionNatural frequenciesMicro/NanobeamsNonlocal theorySimply supported beam