Evaluation of support loss in micro-beam resonators: A revisit

• Published in: Journal of sound and vibration Vol. 411; pp. 148 - 164
• Main Authors: Chen, S.Y., Liu, J.Z., Guo, F.L.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 22.12.2017; Elsevier Science Ltd
• Subjects: Acoustics; Aspect ratio; Beamforming; Ceramic resonator oscillators; Computer simulation; Dissimilar materials; Elastic waves; Energy transmission; Flexural vibration; Fourier transforms; Green's function; Green's functions; Materials fatigue; Mathematical analysis; Mathematical models; Micro-beam resonator; Microbeams; Noise; Perfectly matched layers; Q factors; Quality factor; Resonators; Shear stress; Sound; Stress concentration; Support loss; Flexural vibration; Green's function; Micro-beam resonator; Support loss; Quality factor
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2017.08.048

This paper presents an analytical study on evaluation of support loss in micromechanical resonators undergoing in-plane flexural vibrations. Two-dimensional elastic wave theory is used to determine the energy transmission from the vibrating resonator to the support. Fourier transform and Green's function technique are adopted to solve the problem of wave motions on the surface of the support excited by the forces transmitted by the resonator onto the support. Analytical expressions of support loss in terms of quality factor, taking into account distributed normal stress and shear stress in the attachment region, and coupling between the normal stress and shear stress as well as material disparity between the support and the resonator, have been derived. Effects of geometry of micro-beam resonators, and material dissimilarity between support and resonator on support loss are examined. Numerical results show that ‘harder resonator’ and ‘softer support’ combination leads to larger support loss. In addition, the Perfectly Matched Layer (PML) numerical simulation technique is employed for validation of the proposed analytical model. Comparing with results of quality factor obtained by PML technique, we find that the present model agrees well with the results of PML technique and the pure-shear model overestimates support loss noticeably, especially for resonators with small aspect ratio and large material dissimilarity between the support and resonator. •Revisit support loss in micro-beam resonators.•Take account of distribution of normal and shear stresses in the clamped end.•Consider coupling effect between normal and shear stresses in the clamped end.•Employ Perfectly Matched Layer (PML) technique to validate the analytical model.