Determination of model constants for a specific clamped–clamped beam

Determine the values of the constants appearing in the forced, damped Duffing equation derived for the transverse vibrations of a specific clamped–clamped beam, using the beam’s actual physical parameters, so the model can be instantiated for a real device.

Background

The derived dynamics reduce to a Duffing-type equation with parameters such as natural frequency, damping, and cubic nonlinearity that depend on the beam’s geometry and material properties via integrals of eigenfunctions and other physical quantities.

The authors state that these constants have not yet been determined for a particular beam realization; they suggest obtaining them from literature tables or via finite-element simulations, highlighting the need to compute or measure device-specific parameter values to apply the model to an actual MEMS implementation.