Free transversal vibrations of rectangular plate with free edges

We consider a rectilinear-orthotropic rectangular plate described in the main central system of cartesian co-ordinates xOy , principal axes of elasticity of which are parallel to the sides a and b . We give a full unique analytical solution of homogeneous equation of the amplitudes in rectangular rectilinear-orthotropic domain S ≡ a × b of the plate for the simple (aliquant) roots of the proper characteristic equation. Free transversal vibrations of the rectilinear-orthotropic rectangular plate with the free edges along the whole perimeter (the plate floats in liquid with the density identical to itself) are considered in detail. The transcendental equations of free frequencies are obtained for the symmetric forms of normal transversal vibrations of rectilinear-orthotropic rectangular plate with the free edges. A formula for calculation of frequency P mn of the orthotopic rectangular plate is given.