TY - JOUR
T1 - Free vibration analysis of circular plates by differential transformation method
AU - Yalcin, Hasan Serter
AU - Arikoglu, Aytac
AU - Ozkol, Ibrahim
PY - 2009/6/15
Y1 - 2009/6/15
N2 - This study analyses the free vibrations of circular thin plates for simply supported, clamped and free boundary conditions. The solution method used is differential transform method (DTM), which is a semi-numerical-analytical solution technique that can be applied to various types of differential equations. By using DTM, the governing differential equations are reduced to recurrence relations and its related boundary/regularity conditions are transformed into a set of algebraic equations. The frequency equations are obtained for the possible combinations of the outer edge boundary conditions and the regularity conditions at the center of the circular plate. Numerical results for the dimensionless natural frequencies are presented and then compared to the Bessel function solution and the numerical solutions that appear in literature. It is observed that DTM is a robust and powerful tool for eigenvalue analysis of circular thin plates.
AB - This study analyses the free vibrations of circular thin plates for simply supported, clamped and free boundary conditions. The solution method used is differential transform method (DTM), which is a semi-numerical-analytical solution technique that can be applied to various types of differential equations. By using DTM, the governing differential equations are reduced to recurrence relations and its related boundary/regularity conditions are transformed into a set of algebraic equations. The frequency equations are obtained for the possible combinations of the outer edge boundary conditions and the regularity conditions at the center of the circular plate. Numerical results for the dimensionless natural frequencies are presented and then compared to the Bessel function solution and the numerical solutions that appear in literature. It is observed that DTM is a robust and powerful tool for eigenvalue analysis of circular thin plates.
KW - Circular plate
KW - Differential transform method
KW - Free vibration
KW - Regularity conditions
UR - http://www.scopus.com/inward/record.url?scp=67349145979&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2009.02.032
DO - 10.1016/j.amc.2009.02.032
M3 - Article
AN - SCOPUS:67349145979
SN - 0096-3003
VL - 212
SP - 377
EP - 386
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 2
ER -