  Within recent years, the field of nano-mechanics has diversified in a variety
of applications, ranging from quantum information processing to biological
molecules recognition. Among the diversity of devices produced these days, the
simplest (but versatile) element remains the doubly-clamped beam: it can store
very large tensile stresses (producing high resonance frequencies $f_0$ and
quality factors $Q$), is interfaceable with electric setups (by means of
conductive layers), and can be produced easily in clean rooms (with scalable
designs including multiplexing). Besides, its mechanical properties are the
simplest to describe. Resonance frequencies and $Q$s are being modeled, with as
specific achievement the ultra-high quality resonances based on ``soft
clamping'' and ``phonon shields''. Here, we demonstrate that the fabrication
undercut of the clamping regions of basic nano-beams produces a ``natural soft
clamping'', given for free. We present the analytic theory that enables to fit
experimental data, which can be used for $\{ Q , f_0 \}$ design: beyond Finite
Element Modeling validation, the presented expressions provide a profound
understanding of the phenomenon, with both a Q enhancement and a downwards
frequency shift.
