H. Evirgen’s research while affiliated with Gazi University and other places

Layered spherical shells of arbitrary wall thickness subjected to uniform external and/or internal pressure and undergoing large elastic deformations are investigated. Layers are assumed to be made of neo-Hookean materials and perfectly bonded to one another along the interfaces. The stability of the finitely deformed state is studied using the theory of small deformations superposed on large elastic deformations where the secondary displacement field is assumed to be vibratory. The governing equations are solved numerically by a finite difference scheme to yield the frequencies of the small, free, asymmetric vibrations about the prestressed state. The loss of stability occurs when the superposed motions cease to be periodic.

Small, radial vibrations of layered spherical shells of arbitrary wall thickness and subjected to initial external and/or internal pressure causing finite radial deformations are investigated. The material of each layer is assumed to be of neo-Hookean type. The governing equations of both the finitely deformed static state and the superposed secondary dynamical state which are obtained, respectively, by the theory of finite elasticity and the theory of small deformations superposed on large, elastic deformations are solved analytically and in closed form to yield the frequency expression. Some numerical results are provided to study the effect of several parameters. On leave of absence from the Department of Civil Engineering, Faculty of Engineering and Architecture, Gazi University, Maltepe, Ankara, Turkey.