Research Projects

A framework for the free vibration response of FG Euler-Bernoulli (EB) nanobeam with single/multiple cracks is the main novelty of this study. According to the power law model, it is considered that the material gradation varies along the depth of the beam. Introduce the physical neutral axis instead of geometry central axis which includes the material nonlinearity in FG nanobeam due to unsymmetric material variation. The theory of EB beam model is employed to describe the kinematic field, and the constitutive relation of the stress-driven model is used to taken into account the influence of small-scale size. By employing this technique, the bending curvature at every cross-sectional area is expressed as an integral convolution of a kernel function that relies on a nonlocality and bending moment at entire cross-section. The nonlocal constitutive equation is presented in its integral form and then transformed into a separate spatial dependent and time dependent governing differential equations, under continuity and boundary conditions and at the locations where cracks are present in the nanobeam. Using the separable variable approach, it is necessary to solve the equation or motion at every segment of the beam between the crack by imposing the consistent continuity and boundary conditions. Further, to solve the nonlinear differential equation due to power law model, the method of multiple scales (MMS) approach is utilized to obtain the nonlinear natural frequencies and mode shapes of the graded nanobeam. This proposed model is validated with existing literature for intact nanobeam case when the length of crack is reduced to zero. The influence of power-law index, nonlocal parameter, boundary conditions, crack length and its location on response of free vibration of FG nanobeam will be examined.