Analysis of the main parameters affecting the fundamental vibrating frequency of film/substrate bilayer beams of rectangular cross-section is discussed based on modeling and testing. Initially, the limits of validity of two analytical models to obtain the fundamental frequency of perfectly-bonded bilayer beams in cantilever configuration are determined by comparing the predicted frequencies to a finite element model developed herein. Using a selected analytical formulation, a modeling-assisted methodology is employed to investigate the parameters that are most influential on the determination of the elastic modulus of the film using a vibratory technique. Modeling suggests the use of thin compliant substrates for extracting the modulus of stiff (metallic) films. If the substrate is stiffer than the film, a thicker film is required to yield measurable shifts in the resonant frequency. The elastic modulus of a millimeter-thick thermosetting polymer extracted by this method agrees with the results obtained from conventional tensile testing of the polymer. Measurements carried out on a gold (100 nm)/polysulfone (130 µm) system yield an average elastic modulus of the gold film similar to the values reported in the literature.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.