Natural Frequencies and Modes of Skew Membranes

Natural frequencies and mode shapes of a wide range of skew membranes are obtained by the Rayleigh‐Ritz method expressing the deflection as a double Fourier sine series in oblique coordinates. Since the eigenvalues of a polygonal simply supported plate are the squares of the eigenvalues of a polygonal membrane of the same geometry and the eigenfunctions are identical, the results of the present paper readily provide the vibration characteristics of simply supported skew plates as well. This detailed study revealed interesting features like the skew angle splitting the degenerate frequencies of rectangular membranes into distinct ones and the “frequency crossing” of some modes that belong to opposite symmetry groups of the skew membrane. With changing skew angle, the nodal patterns of some modes undergo a gradual change to other totally different patterns. Since, for some modes the diagonals happen to be the nodal lines, such modes can be interpreted as the appropriate modes of the corresponding triangular...