article · International Journal of Applied Mechanics
A quasi-three-dimensional nonlocal hyperbolic plate theory enables the analysis of free vibration and buckling behaviour in functionally graded nanoplates exposed to thermal environments. The formulation accounts for both shear and normal strains, incorporating shear deformation alongside thickness stretching. Governing equations of motion are derived through Hamilton's principle and solved using Navier's approach for simply-supported boundary conditions. Eringen's nonlocal theory captures the influence of nanoscale effects on the natural frequency and critical buckling loads of the structures. Numerical comparisons with existing published models demonstrate the accuracy of this theoretical approach. Additional numerical assessments evaluate how variations in the nonlocal coefficient, material power-law index, and structural dimensions affect the mechanical response of functionally graded nanoplates under thermal conditions.
Nanomaterials exposed to heat often experience mechanical stresses that can cause premature deformation or failure. Understanding how functionally graded nanoplates vibrate and buckle under thermal loads is essential for developing reliable microscale and nanoscale structural components. Accurately modelling thickness stretching and shear strains ensures that nanoscale structural behaviours can be predicted with higher mathematical precision.
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This paper presents the analyses of free vibration and buckling of functionally graded (FG) nanoplates in thermal environment by using a new quasi-3D nonlocal hyperbolic plate theory in which both shear and normal strains are included. The nonlocal equations of motion for the present problem are derived from Hamilton’s principle. For simply-supported boundary conditions, Navier’s approach is utilized to solve the motion equations. Eringen’s nonlocal theory is employed to capture the effect of the nonlocal parameter on natural frequency and buckling of the FGM nanoplates. Numerical results of the present formulation are compared with those predicted by other theories available in the open literature to explain the accuracy of the suggested theory that contains the shear deformation and thickness stretching. Other numerical examples are also presented to show the influences of the nonlocal coefficient, power law index and geometrical parameters on the vibration and buckling load of FGM nanoplates.
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DOI: 10.1142/s1758825117500089
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