https://northumbria-test.eprints-hosting.org/id/document/265204

A review of continuum mechanics models for size-dependent analysis of beams and plates

A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams

http://engweb.swan.ac.uk/~adhikaris/fulltext/journal/ft194.pdf

Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams

In this paper, the free vibration of magnetoelectro-elastic (MEE) nanoplates is investigated based on the nonlocal theory and Kirchhoff plate theory. The MEE nanoplate is assumed as all edges simply supported rectangular plate subjected to the biaxial force, external electric potential, external magnetic potential, and temperature rise. By using the Hamilton's principle, the governing equations and boundary conditions are derived and then solved analytically to obtain the natural frequencies of MEE nanoplates. A parametric study is presented to examine the effect of the nonlocal parameter, thermo-magneto-electro-mechanical loadings and aspect ratio on the vibration characteristics of MEE nanoplates. It is found that the natural frequency is quite sensitive to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the thermal loading.

Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory

Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory

Transverse vibration of nanotube-based micro-mass sensor via nonlocal Timoshenko beam theory

This article studies vibration of carbon nanotube (CNT)-based biosensor A CNT-based biosensor is modeled as a nonlocal Timoshenko beam made of multiwall CNT carrying a spherical nanoscale bio-object at the free end, and the influence of the rotary inertia of the bio-object itself is considered The fundamental frequencies are computed via the transfer function method The effects of the attached spherical bio-object's rotary inertia and mass, the length-to-diameter of the CNT on the natural frequencies are discussed If the nonlocal parameter is neglected, the frequencies for four possible cases are compared Obtained results show that the rotary inertia decreases the fundamental frequency, while an increase in the diameter of the attached bio-object reduces the natural frequency, but causes frequency shift to rise The mass sensitivity of biosensor can be improved for short CNTs used The rotary inertia of the attached bio-object has a strong effect on the natural frequencies and cannot be simply neglected The nonlocal Timoshenko beam model is more adequate than the nonlocal Euler-Bernoulli beam model for short CNT biosensors Obtained results are helpful to the design of micro-cantilevered resonator as atomic-resolution mass sensor or biosensor

Zhi-Bin Shen

Papers

Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory

Transverse vibration of nanotube-based micro-mass sensor via nonlocal Timoshenko beam theory

Nonlocal Timoshenko beam theory for vibration of carbon nanotube-based biosensor

Transverse vibration of circular graphene sheet-based mass sensor via nonlocal Kirchhoff plate theory

Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory.