Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T07:22:25.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of Residual Stresses on the Vibration of a Circular Sensor Diaphragm with Surface Effects

Published online by Cambridge University Press:  17 August 2016

S.-S. Zhou ,
S.-J. Zhou ,
A.-Q. Li  and
B.-L. Wang
S.-S. Zhou
Affiliation:
School of Mechanical EngineeringShandong UniversityJinan, China
S.-J. Zhou*
Affiliation:
School of Mechanical EngineeringShandong UniversityJinan, China
A.-Q. Li
Affiliation:
School of Mechanical EngineeringShandong UniversityJinan, China
B.-L. Wang
Affiliation:
School of Civil EngineeringShandong UniversityJinan, China
*
*Corresponding author ([email protected])
Get access

Abstract

Resonant micro-biochemical sensors play important roles in a wide range of emerging applications to detect biochemical molecules. As the resonators of micro-biochemical sensors, the vibration characteristics of circular sensor diaphragms are important for the design of diaphragm-based resonant micro-biochemical sensors. In this paper, the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects is analyzed. Based on the Kirchhoff's plate theory and surface elasticity theory, the governing equation is presented. The material characteristic lengths for different surface effects are obtained. The influences of residual stresses on the effective flexural rigidity and natural frequency of the diaphragm with surface effects are discussed. Results show that the influence of residual stresses on the effective flexural rigidity becomes obvious with the increasing of residual stresses. The first order natural frequency increases rapidly when the tension parameter is larger than 30 for the stiffened surfaces, while for the softened surfaces the value is 10. Moreover, surface effects can influence the transition range of diaphragm from the plate behavior to membrane behavior in terms of the tension parameter. The transition range can be enlarged by the stiffened surface and be shortened by the softened surface. The analysis and results are helpful for the design of sensor diaphragm-based resonant micro-biochemical sensors and some related researches.

Keywords

Sensor diaphragmResidual stressesSurface effects
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 3 , June 2017 , pp. 323 - 329
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Lee, H. J., Park, K. K., Kupnik, M., Melosh, N. A. and Khuri-Yakub, B. T., “Mesoporous thin-film on highly-sensitive resonant chemical sensor for relative humidity and CO2 detection,” Analytical Chemistry, 84, pp. 3063–3066 (2012).Google Scholar
2. Calleja, M., Kosaka, P. M., San Paulo, A. and Tamayo, J., “Challenges for nanomechanical sensors in biological detection,” Nanoscale, 4, pp. 4925–4938 (2012).Google Scholar
3. Ilic, B., Yang, Y. and Craighead, H. G., “Virus detection using nanoelectromechanical devices,” Applied Physics Letters, 85, pp. 2604–2606 (2004).CrossRefGoogle Scholar
4. Eom, K., Park, H. S., Yoon, D. S. and Kwon, T., “Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles,” Physics Reports, 503, pp. 115–163 (2011).Google Scholar
5. Johnson, B. N. and Mutharasam, R., “Biosensing using dynamic-mode cantilever sensors: A review,” Biosensors and Bioelectronics, 32, pp. 1–18 (2012).CrossRefGoogle ScholarPubMed
6. Li, S. Q., Li, Z. M., Chin, B. B. and Cheng, Z. Y., “Development of biosensor based on micro-diaphragm,” Conference on Smart Electronics, MEMS, BioMEMS, and Nanotechnology, San Diego, U.S. (2004).Google Scholar
7. Olfatnia, M., et al., “Medium damping influences on the resonant frequency and quality factor of piezoelectric circular microdiaphragm sensors,” Journal of Micromechanics and Microengineering, 21, 045002 (2011).Google Scholar
8. Olfatnia, M., Xu, T., Ong, L. S., Miao, J. M. and Wang, Z. H., “Investigation of residual stress and its effects on the vibrational characteristics of piezoelectric-based multilayered microdiaphragms,” Journal of Micromechanics and Microengineering, 20, 015007 (2010).Google Scholar
9. Lee, S., et al., “Stress influences on the ultrasonic transducers,” Sensors Actuators A, 119, pp. 405–411 (2005).CrossRefGoogle Scholar
10. Muralt, P., Kholkin, A., Kohli, M. and Maeder, T., “Piezoelectric actuation of PZT thin-film diaphragms at static and resonant conditions,” Sensors Actuators A, 53, pp. 398–404 (1996).CrossRefGoogle Scholar
11. Sheplak, K. and Dugundji, J., “Large deflection of clamped circular plate under initial tension and transitions to membrane behavior,” Journal of Applied Mechanics, 65, pp. 107–115 (1998).Google Scholar
12. Yu, M. and Balachandran, B., “Sensor diaphragm under initial tension: linear analysis,” Experimental Mechanics, 45, pp. 123–129 (2005).CrossRefGoogle Scholar
13. Ibach, H., “The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures,” Surface Science Reports, 29, pp. 193–263 (1997).Google Scholar
14. Muller, P. and Saul, A., “Elastic effects on surface physics,” Surface Science Reports, 54, pp. 157–258 (2004).Google Scholar
15. Miller, R. E. and Shenoy, V. B., “Size-dependent elastic properties of nanosized structural elements,” Nanotechnology, 11, pp. 139–147 (2000).Google Scholar
16. Lu, P., He, L. H., Lee, H. P. and Lu, C., “Thin plate theory including surface effects,” International Journal of Solids and Structures, 43, pp. 4631–4647 (2006).Google Scholar
17. Sharma, P., Ganti, S. and Bhate, N., “Effect of surfaces on the size-dependent elastic state of nanoinhomogeneities,” Applied Physics Letters, 82, pp. 535–537 (2003).Google Scholar
18. Wang, G. F., Wang, T. J. and Feng, X. O., “Surface effects on the diffraction of plane compressional waves by a nanosized circular hole,” Applied Physics Letters, 89, 231923 (2006).Google Scholar
19. He, L. H., Lim, C. W. and Wu, B. S., “A continuum model for size-dependent deformation of elastic films of nano-scale thickness,” International Journal of Solids and Structures, 41, pp. 847–857 (2004).Google Scholar
20. Assadi, A. “Size dependent forced vibration of nanoplates with consideration of surface effects,” Applied Mathematical Modelling, 37, pp. 3573–3588 (2012).Google Scholar
21. Liu, C. and Rajapakse, R. K. N. D., “A size-dependent continuum model for nanoscale circular plates,” IEEE Transcctions on Nanotechnology, 12, pp. 13–20 (2013).Google Scholar
22. Lim, C. W. and He, L. H., “Size-dependent nonlinear response of thin elastic films with nanoscale thickness,” International Journal of Mechanical Sciences, 46, pp. 1715–1726 (2004).Google Scholar
23. Ansari, R. and Sahmani, S., “Surface stress effects on the free vibration behavior of nanoplates,” International Journal of Engineering Science, 49, pp. 1204–1215 (2011).CrossRefGoogle Scholar
24. Gurtin, M. E. and Murdoch, A. I., “A continuum theory of elastic material surfaces,” Archives of Rational Mechanics and Analysis, 57, pp. 291–323 (1975).Google Scholar
25. Gurtin, M. E. and Murdoch, A. I., “Addenda to our paper a continuum theory of elastic material surfaces,” Archives of Rational Mechanics and Analysis, 59, pp. 389–390 (1975).Google Scholar
26. Assadi, A. and Farshi, B., “Vibration characteristics of circular nanoplates,” Journal of Applied Physics, 108, 074312 (2010).Google Scholar
27. Wang, G. F. and Feng, X. Q., “Effects of surface elasticity and residual surface tension on the natural frequency of microbeams,” Applied Physics Letters, 90, 231904 (2007).CrossRefGoogle Scholar
28. Lu, P., Lee, H. P., Lu, C. and O’Shea, S. J., “Surface stress effects on the resonance properties of cantilever sensors,” Physical Review. Series B, 72, 085405 (2005).Google Scholar