Skip to main content


Weitere Artikel dieser Ausgabe durch Wischen aufrufen

29.10.2019 | Original Paper | Ausgabe 2/2020

Acta Mechanica 2/2020

A general dynamic theoretical model of elastic micro-structures with consideration of couple stress effects and its application in mechanical analysis of size-dependent properties

Acta Mechanica > Ausgabe 2/2020
Yilin Qu, Peng Li, Feng Jin
Wichtige Hinweise
Peng Li and Feng Jin have contributed equally to this article.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


A general and systematic theoretical framework of elastic micro-structures is established with the aid of modified couple stress theory for investigating the size-dependent property in small scale, in which the size-dependence is considered by introducing a material length scale parameter. Mathematically, dynamic governing equations and corresponding boundary conditions are derived and simplified by using single power series expansion for a micro-plate and double power series expansion for a micro-beam. It is demonstrated that this method exhibits extraordinary superiority, i.e., different vibration modes can be extracted easily from artificial truncations. This theoretical model can be reduced to some classical cases, including the Bernoulli–Euler beam, Timoshenko beam, Kirchhoff plate and Mindlin plate, if some specific assumptions are made. After validation, a systematic numerical investigation is carried out, which focuses on the couple stress effect on shear resonance of a cantilever micro-plate. Finally, a methodology for proposing the critical size that distinguishes micro-scale from macro-scale is illustrated in detail.

Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten

Über diesen Artikel

Weitere Artikel der Ausgabe 2/2020

Acta Mechanica 2/2020 Zur Ausgabe

Premium Partner


    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.