This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equati...

This paper presents a unified approach to vibration analysis of functionally graded beams with transverse open-edge cracks based on the so-called shape obtained as general solution equations in frequency domain. The crack is modeled by pair translational and rotational springs stiffness computed from depth dependence upon material parameters. frequency-dependent functions allow one not only obt...

Soft materials such as rubberlike and biological tissues are usually modeled incompressible. Mechanical properties of polymeric can be controlled either by exposing them to ultraviolet light for different time durations or changing their molecular structure. A challenge is find the spatial variation moduli fully utilize material. One way achieve this have a uniform distribution stress component...