Abstract
Investigated herein is the free vibrations of beams based on the strain gradient Timoshenko beam theory with the method of initial values. For the vibration of strain-gradient Timoshenko beam (SGTB), the sixth-order ordinary differential equation and three boundary conditions at each end have been obtained by using the Hamilton principle. The effect of the characteristic length on the frequencies of free vibrations is shown. The frequencies of the SGTB are compared to the frequencies of the strain gradient Euler beam (SGEB), classical Timoshenko beam (CTB) and classical Euler beam (CEB). It has been observed that the high-frequency values of conventional and strain-gradient beams are very different. This result can be used to determine the value of the material characteristic length for a nanobeam for which lengthscale effects are believed to be dominant.
Original language | English |
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Pages (from-to) | 835-852 |
Number of pages | 18 |
Journal | Microsystem Technologies |
Volume | 26 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Mar 2020 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
Funding
The work reported here is supported by the Alexander von Humboldt Foundation.
Funders | Funder number |
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Alexander von Humboldt-Stiftung |