Thermally induced vibration of cross-ply laminated shallow arches

The dynamic response of simply supported cross-ply laminated shallow arches exposed to rapid heating is examined. The classical laminated arch theory, involving two coupled partial differential equations, is used. The equations of motion are converted into a linear system of ordinary differential equations using state variables. A closed-form solution for the induced flexural vibrations is obtained. As a demonstrative example, histories of deflection of graphite-reinforced aluminum arches are presented.