A comprehensive review on the vibration analyses of small-scaled plate-based structures by utilizing the nonclassical continuum elasticity theories

In recent years, mechanical characteristics including vibration, bending, buckling and postbuckling, stability and instability, etc. of small-scaled structures (such as micro/nanowires, micro and nano plates, micro and nano tubes, micro and nano beams, carbon micro/nano-tubes, micro and nano shells, micro and nano probes, etc.) have been broadly investigated, because of recent advances in nanotechnologies and due to their astonishing characteristics. Also, these small-scaled structures are extensively applied in several areas. However, comprehending the mechanical characteristics of these small-scaled structures is of great prominence and yet a daunting task. To understand the mechanical behaviors and capture the effects (including small-scale effect) of these different advanced small-scaled structures (at micro and nano levels), it is very essential to implement them into classical/nonclassical continuum elasticity based on a suitable classical/nonclassical elasticity formulation or theory. Thus, this work searches the literature and hereby presents an ample literature review study with a special focus primarily on the novel progress of vibration analyses of microplates and nanoplates using nonlocal/nonclassical continuum theories of elasticity. Scopus and web of science databases were used as the primary scholarly-databases to acquire the documents reviewed in the current research. Furthermore, several perspectives of classifications are considered while reviewing and grouping these acquired documents. The main purpose was to illustrate existing research trends in the vibrational analysis of small -scaled plate-based structures utilizing nonlocal plate-based theories and nonclassical continuum elasticity theories, and to provide a foundation and guidance for future research on the mechanics of small-scaled plate-based structures.

Automated summary

This article provides a comprehensive review of the mechanical characteristics of small-scaled structures, focusing specifically on the novel progress in vibration analysis of microplates and nanoplates using nonlocal and nonclassical continuum elasticity theories. By searching the literature and considering various classification perspectives, the article aims to illustrate existing research trends and provide a foundation and guidance for future studies on the mechanics of small-scaled plate-based structures.