Thermal environmental effects on free vibration of functionally graded isosceles triangular microplates

Abstract

The free vibration of the functionally graded (FG) isosceles triangular microplates in thermal environment is investigated. The modified strain gradient theory (MSGT) together with the firstorder shear deformation theory (FSDT) of plates is adopted to formulate the problem. The material properties are assumed to be graded in the thickness direction. The Chebyshev-Ritz method is chosen as the solution procedure. After demonstrating the fast rate of convergence and accuracy of the method, the effects of temperature rise, length scale parameters, material gradient index, different boundary conditions, apex angle and width-to-thickness ratio on the free vibration of triangular microplates are studied.

Resonant frequency tuning of nanobeams by piezoelectric nanowires under thermo‐electro‐magnetic field: a theoretical study

“…In a few recent years, some scale‐dependent mathematical models have been proposed to formulate the vibrational response and stability behaviour of micro/nanoscale structures. Generally, modified continuum‐based theories such as the couple stress theory [6, 7] and the strain gradient elasticity [8, 9] have been applied to microscale structural elements while the dynamics and statics of nanostructures have been formulated with the help of the non‐local elasticity theory [10–14]. For instance, Malekzadeh et al [15] studied the effect of length scale on the frequency response of short nanotubes resting on an elastic foundation.…”