THE INFLUENCE OF CORNER STRESS SINGULARITIES ON THE VIBRATION CHARACTERISTICS OF RHOMBIC PLATES WITH COMBINATIONS OF SIMPLY SUPPORTED AND FREE EDGES

This paper offers accurate flexural vibration solutions for rhombic pl ates with simply supported and free edge conditions. A cornerstone her e is that the analysis explicitly considers the bending stress singula rities that occur in the two opposite, hinged-hinged and/or hinged-fre e corners having obtuse angles of the rhombic plates. These singularit ies become significant to the vibration solution as the rhombic plate becomes highly skewed (i.e. the obtuse angles increase). The classical Ritz method is employed with the assumed normal displacement field co nstructed from a hybrid set of (1) admissible and mathematically compl ete algebraic polynomials, and (2) comparison functions (termed here a s ''corner functions'') which account for the bending stress singulari ties at the obtuse hinged-hinged and/or hinged-free corners. It is sho wn that the corner functions accelerate the convergence of solutions, and that these functions are required if accurate solutions are to be obtained for highly skewed plates. Accurate nondimensional frequencies and normalized contours of the vibratory transverse displacement are presented for rhombic plates having a large enough skew angle of 75 de grees (i.e. obtuse angles of 165 degrees), so that the influence of th e stress singularities is large. Frequencies and mode shapes of isosce les triangular, hinged-free plates are also available from the data pr esented. (C) 1998 Published by Elsevier Science Ltd. All rights reserv ed.