This work concerns with free vibration analysis of piezoelectric Nano beam resting on nonlinear Winkler –Pasternak foundation. Based on Hamilton principle, governing equations of the problem are derived. Three differential quadrature techniques are employed to reduce the problem to an Eigen-value problem. The obtained nonlinear algebraic system is solved by using iterative quadrature technique. That is solved for different materials and boundary conditions. The natural frequencies of Nano elastic beam based on nonlocal elasticity theory and Timoshenko beam theory are obtained. Numerical analysis is introduced to explain influence of computational characteristics of the proposed schemes on convergence, accuracy and efficiency of the obtained results. The obtained results agreed with the previous analytical and numerical ones. Furthermore, a parametric study is introduced to investigate the influence of linear and nonlinear elastic foundation, temperature change, external electric voltage, nonlocal parameter and length-to-thickness ratio on the values of natural frequencies and mode shapes of the piezoelectric Nano beam.
Ragab, Ola; Mohamed, Mokhtar; and Matbuly, M. S.
"QUADRATURE ANALYSIS OF ELASTICITY SUPPORTED PIEZOELECTRIC NANO BEAM,"
Delta University Scientific Journal: Vol. 3:
1, Article 6.
Available at: https://digitalcommons.aaru.edu.jo/dusj/vol3/iss1/6