Recently, the mechanical behavior of micro-/nano-structures has sparked an ongoing debate, which leads to a fundamental question: what steps can be taken to investigate the mechanical characteristics of these structures, and characterize their performance? From the standpoint of the non-classical behavior of materials, size-dependent theories of micro-/nano-structures can be considered to analyze their mechanical behavior. The application of classical theories in the investigation of small-scale structures can lead to inaccurate results. Many studies have been published in the past few years, in which continuum mechanics models have been used to investigate micro-/nano-structures with different geometry such as rods, tubes, beams, plates, and shells. The mechanical behavior of these systems under different loading – resulting in vibration, wave propagation, bending, and buckling phenomena – is the focus of the review covered in this work. The present objective is to provide a detailed survey of the most significant literature on continuum mechanics models of micro-/nano-structures, and thus orient researchers in their future studies in this field of research. 

https://dro.deakin.edu.au/articles/journal_contribution/A_review_of_size-dependent_continuum_mechanics_models_for_micro-_and_nano-structures/20639037/1/files/36844839.pdf

A review of size-dependent continuum mechanics models for micro- and nano-structures

Recently, the mechanical behavior of micro-/nano-structures has sparked an ongoing debate, which leads to a fundamental question: what steps can be taken to investigate the mechanical characteristics of these structures, and characterize their performance? From the standpoint of the non-classical behavior of materials, size-dependent theories of micro-/nano-structures can be considered to analyze their mechanical behavior. The application of classical theories in the investigation of small-scale structures can lead to inaccurate results. Many studies have been published in the past few years, in which continuum mechanics models have been used to investigate micro-/nano-structures with different geometry such as rods, tubes, beams, plates, and shells. The mechanical behavior of these systems under different loading – resulting in vibration, wave propagation, bending, and buckling phenomena – is the focus of the review covered in this work. The present objective is to provide a detailed survey of the most significant literature on continuum mechanics models of micro-/nano-structures, and thus orient researchers in their future studies in this field of research.

In this paper, the thermoelastic vibrations of a functionally graded thermo-piezoelectric rod of limited length are considered using the generalized theory of thermoelasticity. Both ends of the rod are fixed at zero voltage and are exposed to a movable axial heat source. Using the Laplace transform analysis, the problem was solved. The expressions for the displacements, temperature, stress, electric field and electric potential were obtained. To consider the influence of the properties of gradient materials, the moving heat source velocity and thermo-piezoelectric response, some comparisons were constructed for different distributions of the physical quantities. The non-homogeneity effect on the field variables is also discussed in some detail.

Analysis of a functionally graded thermopiezoelectric finite rod excited by a moving heat source

The main concern of this article is to deal with the thermoelastic interaction in a thick plate subjected to a moving heat source and being enlightened by memory-dependent derivative (MDD). Due to ...

Memory response on wave propagation in a thermoelastic plate due to moving band-type thermal loads and magnetic field

In this study, a mathematical model for rotating thermal nanobeams is presented. A system of equations is derived that describes the thermoelastic behaviour of rotating nanoscale beams. The proposed model is based on Eringen’s nonlocal elasticity theory, Euler–Bernoulli's assumptions, and generalized thermoelasticity with two different phase lags. The nanoscale beam material is completely surrounded by an axial magnetic field and exposed to a time-dependent variable temperature field. The Laplace transform in the state-space approach is employed to solve the problem studied. Because of the difficulty in finding the inversion of the Laplace transforms, it was obtained numerically using one of the techniques based on the technique of the Fourier series expansion. The significance of different parameters such as the rotational angular velocity, nonlocal parameter, temperature change, and magnetic field on the nanobeam response has been investigated. Moreover, the results obtained are verified with the corresponding results from the literature.

Modelling of vibrations of rotating nanoscale beams surrounded by a magnetic field and subjected to a harmonic thermal field using a state-space approach

Tianhu He

Papers

Investigation of generalized piezoelectric-thermoelastic problem with nonlocal effect and temperature-dependent properties.