Abstract: In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.
Abstract: Axisymmetric vibration of an infinite Pyrocomposite
circular hollow cylinder made of inner and outer pyroelectric layer of
6mm-class bonded together by a Linear Elastic Material with Voids
(LEMV) layer is studied. The exact frequency equation is obtained
for the traction free surfaces with continuity condition at the
interfaces. Numerical results in the form of data and dispersion
curves for the first and second mode of the axisymmetric vibration of
the cylinder BaTio3 / Adhesive / BaTio3 by taking the Adhesive layer
as an existing Carbon Fibre Reinforced Polymer (CFRP) are
compared with a hypothetical LEMV layer with and without voids
and as well with a pyroelectric hollow cylinder. The damping is
analyzed through the imaginary parts of the complex frequencies.
Abstract: Vibrations of circular cylindrical shells made of
layered composite materials are considered. The shells are weakened
by circumferential cracks. The influence of circumferential cracks
with constant depth on the vibration of the shell is prescribed with the
aid of a matrix of local flexibility coupled with the coefficient of the
stress intensity known in the linear elastic fracture mechanics.
Numerical results are presented for the case of the shell with one
circular crack.