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The carbon nanotube (CNT) reinforced functionally graded materials (FGM) are expected to be the new generation materials having wide range of unexplored potential applications in various technological areas such as aerospace and structural and chemical industry. The present work deals with the finite element modeling and free vibration analysis of CNT based functionally graded beam using three-dimensional Timoshenko beam theory. It has been assumed that the material properties of CNT based FG beam vary only along the thickness and these properties are evaluated by rule of mixture. The extended Hamilton principle has been applied to find out the governing equations of CNT based FG beam. Finite element method is used to solve governing equation with the exact shape functions. Initial analysis deals with CNTs assumed to be oriented along the length direction only. But practically it is not possible. So, further work deals with the free vibration analysis of functionally graded nanocomposite beams reinforced by randomly oriented straight single walled carbon nanotubes (SWCNTs). The Eshelby-Mori-Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. Results are presented in tabular and graphical forms to show the effects of carbon nanotube orientations, slenderness ratios, and boundary conditions on the dynamic behavior of the beam.

In this paper, the inverse problem of the nonlinear vibration of pile foundations has been studied. The methodology proposed by Novak is used to identify the parameters of the soil-pile system from the measured response displaying nonlinear features. A comprehensive study involving both vertical dynamic testing of piles and theoretical analysis is described. The dynamic tests are carried out on single and 2 × 2 group piles in the field under varying levels of vertical harmonic load. From the measured nonlinear response curves, the effective pile-soil system mass, stiffness and damping are determined using the methodology of Novak assuming nonlinear restoring force and linear damping force. It is found that the stiffness of pile-soil system markedly decrease with increasing exciting intensity but the damping increase with exciting moments. Finally the dynamic responses of piles are back-calculated using the estimated nonlinear parameters. It is found that theoretical nonlinear response curves agree well with that obtained from vertical vibration tests.

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