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The dynamical and stationary behaviors of a fourth-order evolution equationwith clamped boundary conditions and a singular nonlocal reaction term, whichis coupled to an elliptic free boundary problem on a non-smooth domain, areinvestigated. The equation arises in the modeling of microelectromechanicalsystems (MEMS) and includes two positive parameters $\lambda$ and $\varepsilon$related to the applied voltage and the aspect ratio of the device,respectively. Local and global well-posedness results are obtained for thecorresponding hyperbolic and parabolic evolution problems as well as acriterion for global existence excluding the occurrence of finite timesingularities which are not physically relevant. Existence of a stable steadystate is shown for sufficiently small $\lambda$. Non-existence of steady statesis also established when $\varepsilon$ is small enough and $\lambda$ is largeenough (depending on $\varepsilon$).

A free boundary problem modeling electrostatic MEMS: I. Linear bending effects