FREE VIBRATION ANALYSIS OF COMPRESSED SYMMETRICALLY LAMINATED RECTANGULAR PLATES

According to the differential equation of compressed symmetrically laminated rectangular plates in free vibration, various analytical solutions can be obtained to solve different boundary value problems. There exist two kinds of laminated plates. One is cross-ply, the directions of which are parallel with the coordinate axes. This belongs to the orthotropic plate. When the plate is simply supported on four edges, it can be solved by double sine series to obtain not only each frequency and its vibration mode while vibrating freely, but also each critical load and its buckling mode when compressed uniformly. The other is angle-ply, which belongs to anisotropic plate. When the plate is free on two adjacent edges and the other two are simply supported or fixed, it can be solved by complex series to obtain the lowest frequency, the vibration mode, the lowest critical load and the buckling mode. The roots of the characteristic equation are two pairs of complex ones, which can be expressed by trigonometric function and hyperbolic function that can satisfy the boundary conditions. Moreover, the solution composed by algebraic polynomial with double sine series is used to satisfy the corner conditions. The compressed or non-compressed vibration frequency and the critical loads for some example plates were calculated and compared with the results in other references.