Fluid Flow Effects on Size-dependent Dynamic Response of Cantilever Microbeams using Modified Strain Gradient and Hyperbolic Shear Deformation Beam Theory

An analytical study on fluid induced dynamics of cantilever microbeam is presented in this paper. Modified strain gradient theory has been used to consider the effect of small sizes. By considering the interaction between structure and fluid, the governing equations of motion are derived from hyperbolic beam theory. Governing equations of motion are discretized with the Galerkin method, and then the solution is found numerically. The dynamic response of the system and the amplitude-velocity curves of the fluid flow at different values of small size parameters and fluid flow velocity are determined and the effects of these parameters are examined. The results show that the hyperbolic beam theory provides more accurate results than classical Euler-Bernoulli and Timoshenko beam theories. Each of the three theories exhibits different lock-in regions and maximum amplitudes of the microbeam. It is also relevant to note that Euler-Bernoulli's theory predicts natural frequencies more than the other two theories, which ignores the rotational inertia of the beam's cross-section. Timoshenko beam theory predicts higher oscillation frequencies than hyperbolic beam theory, however, when the length is increased, the natural frequencies for the two theories are almost identical.