Free Vibrations of Functionally Graded Porous Hanging and Standing
Cantilever Beams
Abstract
The free oscillations of a functionally graded (FG) porous vertical
cantilever beam in the frame work of Euler-Bernoulli beam theory. The
beam is subjected to the gravity-load and the properties of the FG
material such as the modulus of elasticity and the density are supposed
to change through the thickness of the beam according to power-law
relations. The equation of motion is derived using Newton’s second law.
The Numerical Chebyshev collocation method is utilized to determine the
transverse frequencies of the FG porous hanging and standing cantilever
Euler-Bernoulli beams. A parametric study is conducted to determine the
effects of various factors such as the transverse functionally graded
index, the porosity factor, and the elastic and the mass density ratios
on the natural frequencies and the mode shapes of the FG porous vertical
hanging and standing cantilever thin beams under their self-weight. The
accuracy of the proposed numerical method is evaluated through
comparisons of the frequencies obtained from the present approach with
those available in previous literature.