Porosity, mass and geometric imperfection sensitivity in coupled vibration characteristics of CNT-strengthened beams with different boundary conditions

Structures face different types of imperfections and defects during the fabrication process, installation and working environment. In this paper, the imperfection effects in the coupled vibration behaviour of axially functionally graded carbon nanotube (CNT)-strengthened beam structures with different boundary conditions are analysed considering porosity as well as geometric and mass imperfections in the structure. Porosity is modelled using different types of formulations for simple-cell, open-cell and closed-cell porous structures. The porosity is assumed to be either uniform or by varying through the thickness of the hollow beam using different functions. Mass imperfection effect is added to the system by considering a concentrated mass in the system affecting the mass homogeneity of the structure. Geometry imperfection is also considered by having an initial deformation in the structure which could be caused by an improper fabrication process. Coupled axial and transverse equations of motion are obtained using Hamilton’s principle and the von Kármán geometrical nonlinearity. Governing equations are solved for different types of boundary conditions using a semi-analytical modal decomposition technique. It is shown that strengthening the base matrix with CNT fibres can improve the vibration behaviour of imperfect structures and the influence of CNT volume fraction and distribution through the length of the beam is discussed. The results provided in this paper may be used as a benchmark to validate future experimental results to prevent imperfection, delamination and stress singularities in the structures.