Computation of vibration solution for functionally graded carbon nanotube-reinforced composite thick plates resting on elastic foundations using the element-free IMLS-Ritz method

Abstract

This paper explores the element-free IMLS-Ritz method for computation of vibration solution of thick functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates resting on elastic foundations. The shear deformation effect is incorporated through the first-order shear deformation theory (FSDT). The cubic spline weight function and linear basis are utilized in the approximation. Regular node arrangements and cell background meshes are employed in the numerical integration. The penalty method is adopted to impose the essential boundary conditions. Numerical stability and applicability of the IMLS-Ritz method are examined through solving a few numerical example problems. The influence of Winkler modulus parameters on the vibration behavior of FG-CNTRC plates is studied. Besides, the effects of CNT volume fraction, CNT distribution, plate thickness-to-width ratio, plate aspect ratio on FG-CNTRC plates are investigated under different boundary conditions. The vibration frequencies and mode shapes of the FG-CNTRC plates on different Winkler foundations are presented.