The size-dependent vibration analysis of micro-plates based on a modified couple stress theory

✍ Scribed by E. Jomehzadeh; H.R. Noori; A.R. Saidi

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 313 KB
• Volume: 43
• Category: Article
• ISSN: 1386-9477
• DOI: 10.1016/j.physe.2010.11.005

✦ Synopsis

A microscale vibration analysis of micro-plates is developed based on a modified couple stress theory. The presence of the length scale parameter in this theory enables us to describe the size effect in microstructures. A variational approach based on Hamilton's principle is employed to obtain the governing equations of motion. To illustrate the new model, the free vibration analysis of a rectangular micro plate with two opposite edges simply supported and arbitrary boundary conditions along the other edges and a circular micro-plate are considered. The natural frequencies of micro-plates are presented for over a wide range of length scale parameters, different aspect ratios and various boundary conditions for both rectangular and circular micro-plates. The effect of length scale parameter on natural frequencies of micro-plates are discussed in details and the numerical results reveal that the intrinsic size dependence of material leads to increase the natural frequency.