Axisymmetric Vibrations of Reinforced Orthotropic Shallow Spherical Caps

Axisymmetric vibrations of reinforced shallow. spherical caps manufactured from orthotropic materials are considered. The closed form solution is obtained for the natural frequency of the cap with a clamped and immovable circular edge by assuming that the motion component parallel to the cap boundary plane (in plane) is negligible. Parametric studies are performed to assess the effect of various geometric and structural parameters on the natural frequency of the cap and, most importantly, to identify the most influencing parameters of the problem. From the generated data, it is concluded that the national frequency increases with increasing extensional stiffness and eccentricity of reinforcements and to a lesser extent with increasing bending stiffness of reinforcements. Other important parameters include the base circle radius and the initial rise of the cap.