Eigenvalues of orthotropic continuous plates with two opposite sides simply supported

It is shown that the eigenvalue ω_mn of an orthotropic continuous plate with sides a and b can be obtained from the eigenvalue ω _mn^∗ of a corresponding isotropic continuous plate with sides a and b(D _x/H) ^{1}/{2} by the use of a reduction formula ω _mnω _mn^∗2+ {1}/{ρh ₀}D _y - {H ²}/{D _x}{n+1}/{b}π ^4{1}/{2} where ϱ is the mass density of both plates, h₀ is the thickness of both plates, and D_x, H and D_y are the flexural rigidities of the orthotropic one.