Consider a flat rectangular panel with sides of lengths a and b and simply supported along all four edges. The longitudinal axis is assumed to be parallel to the side of length a. The panel is...

Consider a flat rectangular panel with sides of lengths a and b and simply supported along all four edges. The longitudinal axis is assumed to be parallel to the side of length a. The panel is subjected to a uniform in-plane tension, N per unit length, such that

where ρm is the density of the plate material, h the plate thickness and D the flexural rigidity of the plate. Hence explain how you would proceed to obtain the first natural frequency and the damping ratio of the first mode of oscillation of the panel.