The objective of this study is to establish the effectiveness of four different time-frequency representations (TFRs)--the reassigned spectrogram, the reassigned scalogram, the smoothed Wigner-Ville distribution, and the Hilbert spectrum--by comparing their ability to resolve the dispersion relationships for Lamb waves generated and detected with optical techniques. This paper illustrates the utility of using TFRs to quantitatively resolve changes in the frequency content of these nonstationary signals, as a function of time. While each technique has certain strengths and weaknesses, the reassigned spectrogram appears to be the best choice to characterize multimode Lamb waves.

Analytical expressions are provided for the energy loss from vibrating mechanical resonators into their support structures for two limiting cases: supports that can be treated as plates, and supports that act as semi-infinite elastic media, with effectively infinite thickness. The former case is applicable to many microscale resonators, while the latter is appropriate for nanoscale devices. General formulations are given, applicable to a wide range of resonator geometries. These formulations are then applied to two geometries commonly used in microelectromechanical systems and nanelectromechanical systems applications: cantilevered beams and doubly fixed beams. Experimental data are presented to validate the finite-thickness support theory, and the predictions of the theory are also compared to data from existing literature for a microscale rectangular paddle oscillator.

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