Stability characteristic of bi-directional FG nano cylindrical imperfect composite: Improving the performance of sports bikes using carbon nanotubes

Classical and first-order nonlocal beam theory are employed in this study to assess the thermal buckling performance of a small-scale conical, cylindrical beam. The beam is constructed from functionally graded (FG) porositydependent material and operates under the thermal conditions of the environment. Imperfections within the non-uniform beam vary along both the radius and length direction, with continuous changes in thickness throughout its length. The resulting structure is functionally graded in both radial and axial directions, forming a bi-directional configuration. Utilizing the energy method, governing equations are derived to analyze the thermal stability and buckling characteristics of a nanobeam across different beam theories. Subsequently, the extracted partial differential equations (PDE) are numerically solved using the generalized differential quadratic method (GDQM), providing a comprehensive exploration of the thermal behavior of the system. The detailed discussion of the produced results is based on various applied effective parameters, with a focus on the potential application of nanotubes in enhancing sports bikes performance.