Attachment losses of high Q oscillators

Attachment losses can play a role in limiting the quality factors of micro/nanomechanical oscillators. The existing theoretical results in this regard are applicable to highly idealized scenarios. The theory has been extended in two important directions: the width of the cantilever is considered to be small relative to a wavelength as opposed to large, and the base is allowed to have finite thickness. These extensions result in significant, in many cases order of magnitude, changes in the estimates of attachment loss. Simple formulas for Q(-1) covering most of the parameter range are given.