TY - JOUR
T1 - Comprehensive exact solutions for free vibrations of thick annular sectorial plates with simply supported radial edges
AU - McGee, O. G.
AU - Huang, C. S.
AU - Leissa, A. W.
N1 - Funding Information:
Acknowledgement--This research was supported by the National Science Foundation, Award No. MSS-9157972.
PY - 1995/5
Y1 - 1995/5
N2 - The first known exact solutions are derived for the free vibrations of thick (Mindlin) annular sectorial plates having simply supported radial edges and arbitrary conditions along the circular edge. The general solutions to the Mindlin differential equations of motion contain non-integer order ordinary and modified Bessel functions of the first and second kinds, and six arbitrary constants of integration. Frequency determinant equations are derived for thick annular sectorial plates with circular edges having all nine possible combinations of clamped, simply supported, or free boundary conditions. Extensive amounts of nondimensional frequency parameters are presented for thickness ratio ( h a) values of ≅ 0,0.1, and 0.2; radii ( b a) values within the range of 0.1-0.7; and sector angle values of 180° ≤ α ≤ 360° for which, in the range of α > 180°, no previously published results are known to exist. Frequency results obtained for thick annular sectorial plates are compared to those determined for classically thin ( h a ≅ 0) ones. The frequencies for 360° annular sectorial plates (i.e. annular plates having a hinged crack) are compared with those for complete circular annular plates. The exact solutions presented herein are useful to researchers for determining the correctness of approximate numerical procedures and software packages for thick plate vibration analyses.
AB - The first known exact solutions are derived for the free vibrations of thick (Mindlin) annular sectorial plates having simply supported radial edges and arbitrary conditions along the circular edge. The general solutions to the Mindlin differential equations of motion contain non-integer order ordinary and modified Bessel functions of the first and second kinds, and six arbitrary constants of integration. Frequency determinant equations are derived for thick annular sectorial plates with circular edges having all nine possible combinations of clamped, simply supported, or free boundary conditions. Extensive amounts of nondimensional frequency parameters are presented for thickness ratio ( h a) values of ≅ 0,0.1, and 0.2; radii ( b a) values within the range of 0.1-0.7; and sector angle values of 180° ≤ α ≤ 360° for which, in the range of α > 180°, no previously published results are known to exist. Frequency results obtained for thick annular sectorial plates are compared to those determined for classically thin ( h a ≅ 0) ones. The frequencies for 360° annular sectorial plates (i.e. annular plates having a hinged crack) are compared with those for complete circular annular plates. The exact solutions presented herein are useful to researchers for determining the correctness of approximate numerical procedures and software packages for thick plate vibration analyses.
UR - http://www.scopus.com/inward/record.url?scp=0344053854&partnerID=8YFLogxK
U2 - 10.1016/0020-7403(94)00050-T
DO - 10.1016/0020-7403(94)00050-T
M3 - Article
AN - SCOPUS:0344053854
SN - 0020-7403
VL - 37
SP - 537
EP - 566
JO - International Journal of Mechanical Sciences
JF - International Journal of Mechanical Sciences
IS - 5
ER -