Free vibration of radially graded hollow cylinders subject to axial force via a higher-order shear deformation beam theory

Abstract

The dynamic behavior of radially functionally graded tubes is studied when subjected to axial tensile and compressive forces. Differing from the Euler–Bernoulli/Timoshenko beam theories, a higher-order shear beam deformation model that does neither require a shear correction factor nor need a planar cross-section assumption after deformation. The cross-section’s warping is constructed to meet the shear-free condition on tube’s inner and outer surfaces. A governing partial differential equation is derived. Exact characteristic equations for determining the natural frequencies are given. For typical end supports including hinged-hinged, clamped–clamped, clamped-free, and clamped-hinged ends, the natural frequencies are calculated. By letting the frequency vanish, the critical buckling loads under compression can be exactly determined by solving the characteristic equation. A comparison of the present buckling loads and the natural frequencies with the classical ones and with finite element results is made and verifies the efficiency of the proposed model. The frequency-load interaction is plotted for typical boundary conditions. Axial tensile force causes the natural frequencies to increase and axial compressive force decreases the natural frequencies. The effects of the radial gradient, tube’s thickness and length, and the cross-sectional warping shape on the buckling loads and the natural frequencies are elucidated.