In this paper, the dynamic characteristics of clamped-clamped silicon microbeam subjected to electrostatic excitation and mechanical shock is investigated. The Euler-Bernoulli beam model based on the modified couple stress theory with von Kármán geometric non-linearity is utilized in theoretical formulation. Afterwards, squeeze-film damping effects of microstructures for small amplitude vibrati...

We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x) ≡ w(α,β)(x) = (1− x)α(1 + x)β (α, β > −1) we give a necessary and sufficient ...