No abstract

In this present work the geometrical non-linearity in free in-plane vibration of inextensible functionally graded circular arch with uniform cross-section and pinned-pinned at both ends has been studied. For simplification, the complicating effects such as rotary inertia and shear deformation will be ignored. The sixth order differential partial equation of motion has been obtained after the inextensibility assumption. This study is based on Euler Bernoulli theory and Von Karman's assumptions. The kinetic and total strain energies due to the axial strain and bending have been discretized into a series of a finite spatial functions and derived by applying the Hamilton's principle energy. The non-linear algebraic equations were obtained and solved numerically using an approximate explicit method developed previously the so-called second formulation. A numerical results have been obtained to examine the effects of the volume fraction index on non-linear behavior of the arch. Comparison is made with the available results for the case of isotropic homogeneous circular arches: good agreement is obtained.