State-of-the-Art of Vibration Analysis of Small-Sized Structures by using Nonclassical Continuum Theories of Elasticity

Abstract

Recently, small-sized structures including micro/nanobeams, micro/nanoplates, micro/nanotubes, micro/nanowires, etc. have received great attention among researchers in the fields of nanotechnology and nanodevice because of their tremendous applications. These nanostructures are extensively applied in areas involving nano and micro scaled devices and systems including nano electromechanical systems, biosensors, nano actuators, nano probes, etc. Consequently, the stability, vibration, buckling and postbuckling behaviors of these small-sized structures have been studied extensively. Also, understanding the mechanical characteristics of these nanostructures is of a critical significance. In this work, we have reviewed the literature and hereby present a comprehensive state-of-the-art review study on the advances of vibrational analyses of small-sized structures (primarily with a special focus on small-sized beam-like structures) using nonlocal/nonclassical continuum theories. For this purpose, Scopus database is used as the scholarly database in acquiring the reviewed articles. The acquired and reviewed documents are grouped taking several perspectives into account. Summary-based approaches and a detailed-based approach were considered while classifying these documents. In the detailed-based approach, we categorized the studies based on; nonclassical continuum theories and theories applied; small-sized-structure/model investigated; static and dynamic mechanical analyses; issues/challenges addressed or investigated; methodologies and assumptions considered; governing equations of motion formulation methods; governing equations of motion solution techniques; and the parameters investigated. The objective was to present the current research trends in vibration analysis of these small-sized structures, and to deliver some guidance and foundation for future research directions.