Influence of size effect on flapwise vibration behavior of rotary microbeam and its analysis through spectral meshless radial point interpolation

In this paper, by utilizing the modified couple stress theory, influence of size effect on flapwise vibration behavior of rotary microbeam is analyzed based on Bernoulli–Euler beam model. It should be mentioned that this theory contains the size effect by considering the material length scale parameter unlike the classical continuum theories. Governing equation and boundary conditions are derived by using Hamilton’s principle. Governing equation is solved for cantilever and propped cantilever boundary conditions by applying spectral meshless radial point interpolation (SMRPI) method. SMRPI is based on meshless methods and benefits from spectral collocation ideas. The point interpolation method with the help of radial basis functions is proposed to construct shape functions which have Kronecker delta function property. Evaluation of high order derivatives is possible by constructing and using operational matrices. The computational cost of the method is modest due to using strong form equation and collocation approach.