Quantum mechanics

Composite number

Engineering

Materials science

Boundary value problem

Vibration

Thermodynamics

Physics

Finite element method

Mathematics

Ritz method

Shell (structure)

Mathematical analysis

Composite material

Structural engineering

Stiffness

Mechanics

Engineering Analysis with Boundary Elements

Rotating cylindrical shells have been widely used in rotating machinery. The vibration characteristics of rotating composite cylindrical shells have a significant influence on the rotor dynamics. This paper provides a useful approach for the vibration analysis of a rotating functionally graded (FG) graphene nanoplatelets (GPLs) reinforced composite (GPLRC) cylindrical shell with matrix cracks. GPLs and matrix cracks are distributed in multilayer FG-GPLRC shells. The modified Halpin-Tsai model and self-consistent model are employed to determine the effective materials properties and stiffness degradation of the composite shell. The energy functional of rotating FG-GPLRC cylindrical shells are obtained using the first-order shear deformation theory (FSDT). Based on the improved moving least-squares Ritz (IMLS-Ritz) approximation, the discrete vibration equations of rotating FG-GPLRC cylindrical shells are derived. The accuracy of the IMLS-Ritz results is examined by comparing the natural frequencies with those presented in the previously published papers. Then the effects of crack density parameter, rotating speed, GPLs parameters, weight fraction, size and geometry, as well as the geometry of the cylindrical shell and boundary conditions on the critical rotating speed and natural frequency are examined comprehensively.

On the dynamics of rotating matrix cracked FG-GPLRC cylindrical shells via the element-free IMLS-Ritz method