Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory

In this study, analytical and numerical solution procedures are proposed for vibration of an embedded microbeam under action of a moving microparticle based on the modified couple stress theory (MCST) within the framework of Euler–Bernoulli beam theory. The governing equation and the related boundary conditions are derived by using Hamilton’s principle. The closed form solution of the transverse deflections of the embedded microbeam is obtained using the finite Fourier sine transformation. In the numerical solution, the dynamic deflections are computed by using the Lagrange’s equations in conjunction with the direct integration method of Newmark. The static deflections are also obtained analytically. A detailed parametric study is conducted to study the influences of the material length scale parameter, the Poisson’s ratio, the velocity of the microparticle and the elastic medium constant as well as the solution procedures on the dynamic responses of the microbeam. For comparison purpose, static deflections and free vibration frequencies of the microbeam are obtained and compared with previously published studies. Good agreement is observed. The results show that the above mentioned effects play an important role on the dynamic behavior of the microbeam.