Vibration analysis of non-uniform orthotropic Kirchhoff plates resting on elastic foundation based on nonlocal elasticity theory

• Free vibration of non-uniform, non-local orthotropic Kirchhoff plates resting on elastic foundation is analyzed.
• Eringen's nonlocal elasticity theory is utilized.
• The Chebyshev collocation method is applied to discretize the governing equation of motion.
• Convergence analysis is carried out by numerical studies and demonstrated well.
• Plots of the natural frequencies versus different parameters are obtained.

The free vibration analysis of non-local orthotropic Kirchhoff plates has been investigated. Kirchhoff plates at the micro/nanoscale are modeled using Eringen's nonlocal elasticity theory, where the small scale effect is taken into consideration. The governing equations are derived using the nonlocal differential constitutive relations of Eringen. For this purpose, the resulted eigenvalue problem is solved numerically by applying the Chebyshev collocation method. The effects of the the Winkler modulus parameter, the shear modulus parameter, the aspect ratio, the taper, the nonlocal scale coefficient, and the boundary conditions on the natural frequencies have been studied.