Free vibrations of rotating CNTRC beams in thermal environment

Abstract

A study on the first natural frequency of rotating nanocomposite beams is addressed in this research. The beam has been reinforced with carbon nanotube. With the purpose of incorporating the shearability of the beam, the Reddy's third order shear deformation theory has been assigned. The motion equations are discretized in space employing the well-know Ritz-technique. For the sake of study on the first natural frequency, the nonlinear in time discretized equations of motion are linearized around the static deformation induced by the centrifugal force. The linearized discretized governing equations around the post-buckling state are exploited to find the first natural frequency after the buckling incidence. The outcomes reveal that although a stationary free-clamped(simply-clamped) beam and a stationary clamped-free(clamped-simply) beam treat similarly in the analyses, the associated rotating beams demonstrate a qualitative discrepancy. Moreover, the outcomes based upon the Reddy's third order shear deformation theory deviate from the results in regard of the Timoshenko beam theory approximately below the length to the height of the beam equal to 12 for CS FGX CNTRC beams. Nevertheless, for the FGO CNTRC beams the results in reference to the both mentioned theories approximately are consistent to each other.

Keywords

• Free vibrations
• Post-buckled natural frequency
• Rotating nanocomposite beams
• Carbon nanotube
• Boundary condition type