In this paper, a comprehensive model is presented to investigate the influence of surface elasticity and residual surface tension on the natural frequency of flexural vibrations of microbeams in the presence of rotary inertia and shear deformation effects. An explicit solution is derived for the natural oscillations of microscaled Timoshenko beams considering surface effects. The analytical results are illustrated with numerical examples in which two types of microbeams are configured based on Euler–Bernoulli and Timoshenko beam theory considering surface elasticity and residual surface tension. The natural frequencies of vibration are calculated for selected beam length on the order of nanometer to microns and the results are compared with those corresponding to the classical beam models, emphasizing the differences occurring when the surface effects are significant. It is found that the nondimensional natural frequency of the vibration of micro and nanoscaled beams is size dependent and for limiting case in which the beam length increases, the results tends to the results obtained by classical beam models. This study might be helpful for the design of high-precision measurement devices such as chemical and biological sensors.
Skip Nav Destination
Article navigation
5 October 2009
Research Article|
October 09 2009
Free vibration of microscaled Timoshenko beams
Saeed Abbasion;
Saeed Abbasion
a)
1Department of Mechanical Engineering,
Iran University of Science and Technology
, Tehran 16844, Iran
Search for other works by this author on:
Ahmad Rafsanjani;
Ahmad Rafsanjani
b)
1Department of Mechanical Engineering,
Iran University of Science and Technology
, Tehran 16844, Iran
Search for other works by this author on:
Reza Avazmohammadi;
Reza Avazmohammadi
2Department of Mechanical Engineering and Applied Mechanics,
University of Pennsylvania
, Philadelphia, Pennsylvania 19104-6315, USA
Search for other works by this author on:
Anoushiravan Farshidianfar
Anoushiravan Farshidianfar
3Department of Mechanical Engineering,
Ferdowsi University of Mashhad
, Mashhad 91775-1111, Iran
Search for other works by this author on:
a)
Electronic mail: s.abbasion@mecheng.iust.ac.ir.
b)
Electronic mail: rafsanjani@mecheng.iust.ac.ir. Tel.: +98-912-221-3711.
Appl. Phys. Lett. 95, 143122 (2009)
Article history
Received:
May 19 2009
Accepted:
September 17 2009
Citation
Saeed Abbasion, Ahmad Rafsanjani, Reza Avazmohammadi, Anoushiravan Farshidianfar; Free vibration of microscaled Timoshenko beams. Appl. Phys. Lett. 5 October 2009; 95 (14): 143122. https://doi.org/10.1063/1.3246143
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Sign in via your Institution
Sign in via your InstitutionPay-Per-View Access
$40.00