Vibration of a standing plate with simply supported vertical sides and weakened by a horizontal hinge

A rectangular standing plate under self weight has simply supported vertical sides and weakened by a horizontal internal hinge. Using Levy separation, the governing equations reduce to an ordinary differential equation with non-constant coefficients. The difficult boundary value problem is then turned into two deterministic initial value problems. Fundamental frequencies for four kinds of common edge conditions are determined. It is found that the hinge, similar to self weight, decreases the frequency, and in certain cases promotes buckling.