APPROXIMATE ANALYTIC SOLUTIONS OF THE PROBLEM ON PLANE FORMS OF FREE OSCILLATIONS FOR A RECTANGULAR PLATE WITH UNFIXED EDGES

摘要

We consider a linear problem on the plane forms of free oscillations of a rectangular orthotropic plate with unfixed edges which are free of stresses. With the help of the method proposed in [1], using the combinations of double and single trigonometric functions as basic ones, we construct approximating functions for displacements which strictly satisfy the boundary conditions for the free edge of the plate. On this base, using the variational equations of the Bubnov method, whose structure depends on that of the constructed approximating functions for displacements, we obtain analytic solutions to the problem under consideration. Some of them coincide with exact analytic solutions obtained in [1], the other ones arc approximate by definition. We prove that certain approximate solutions, as a special case, contain exact analytic solutions obtained in [1].