In this current paper the Galerkin decomposition method is used to study the dynamic pull-in instability of clamped-clamped nanobeam-based N/MEMS switches under Casimir and van der Waals forces without electrostatic excitation. This model is nonlinear due to inherent nonlinearity of Casimir and van der Waals forces and geometrical nonlinearity such as midplane stretching of this elastic beam. First the Reduced Order Model (ROM) for a clamped-clamped nanobeam-based N/MEMS switches under Casimir and van der Waals forces is derived in consideration of elastic nonlinearity of nanobeam. Then the effect of nonlinear parameter on pull-in instability is investigated by a numerical method such as Runge-Kutta techniques. It is observed that increasing in midplane stretching causes increase in Casimir or van der Waals force required for occurring pull-in phenomenon and there is a linear relationship between them in investigated range. Both increasing in midplane stretching and damping coefficient causes increase in pull-in time. But the effect of damping is more than midplane stretching effect. Not only increasing in midplane stretching causes increase in Casimir or van der Waals force required for pull-in, but also the growth of damping coefficient has the same effect on them, however there is not a linear relationship between them in this manner.

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