The natural vibration of rectangular plates with rounded corners is studied by using a family of homotopy shapes and an efficient Ritz method.

References

References
1.
Leissa
,
A. W.
,
1969
, “
Vibration of Plates
,” NASA, Washington, D.C., Report No. SP-160.
2.
Leissa
,
A. W.
,
1973
, “
The Free Vibration of Rectangular Plates
,”
J. Sound Vib.
31
(
8
), pp.
257
293
. 10.1016/S0022-460X(73)80371-2
3.
Leissa
,
A. W.
,
2005
, “
The Historical Bases of Rayleigh and Ritz Methods
,”
J. Sound Vib.
287
(
4–5
), pp.
961
978
. 10.1016/j.jsv.2004.12.021
4.
Gorman
,
D. J.
,
1978
, “
Free Vibration Analysis of the Completely Free Rectangular Plate by the Method of Superposition
,”
J. Sound Vib.
57
(
3
), pp.
437
447
.10.1016/0022-460X(78)90322-X
5.
Behnke
,
H.
, and
Mertins
,
U.
,
1995
, “
Eigenwertschranken fur das problem der frei schwingenden rechteckigen platte und untersuchungen zum ausweichphanomen
,”
Z. Angew. Math. Mech.
75
(
5
), pp.
343
363
.10.1002/zamm.19950750504
6.
Mochida
,
Y.
, and
Ilanko
,
S.
,
2008
, “
Bounded Natural Frequencies of Completely Free Rectangular Plates
,”
J. Sound Vib.
311
(
1–2
), pp.
1
8
.10.1016/j.jsv.2007.10.022
7.
Sato
,
K.
,
1973
, “
Free Flexural Vibrations of an Elliptical Plate With Free Edge
,”
J. Acoust. Soc. Am.
54
(
2
), pp.
547
550
.10.1121/1.1913618
8.
Beres
,
D. P.
,
1974
, “
Vibration Analysis of a Completely Free Elliptical Plate
,”
J. Sound Vib.
34
(
3
), pp.
441
443
.10.1016/S0022-460X(74)80322-6
9.
Singh
,
B.
, and
Chakraverty
,
S.
,
1991
, “
Transverse Vibration of Completely Free Elliptic and Circular Plates Using Orthogonal Polynomials in the Rayleigh Ritz Method
,”
Int. J. Mech. Sci.
33
(
9
), pp.
741
751
.10.1016/0020-7403(91)90069-F
10.
Irie
,
T.
,
Yamada
,
G.
, and
Sonoda
,
M.
,
1983
, “
Natural Frequencies of Square Membrane and Square Plate With Rounded Corners
,”
J. Sound Vib.
86
(
3
), pp.
442
448
. 10.1016/0022-460X(83)90588-6
11.
Wang
,
C. M.
,
Wang
,
L.
, and
Liew
,
K. M.
,
1994
, “
Vibration and Buckling of Super Elliptic Plates
,”
J. Sound Vib.
171
(
3
), pp.
301
314
. 10.1006/jsvi.1994.1122
12.
Ceribasi
,
S.
, and
Altay
,
G.
,
2009
, “
Free Vibration of Super Elliptical Plates With Constant and Variable Thickness by Ritz Method
,”
J. Sound Vib.
319
(
1–2
), pp.
668
680
.10.1016/j.jsv.2008.06.010
13.
Lim
,
C. W.
, and
Liew
,
K. M.
,
1995
, “
Vibrations of Perforated Plates With Rounded Corners
,”
J. Eng. Mech.
121
(
2
), pp.
203
213
. 10.1061/(ASCE)0733-9399(1995)121:2(203)
14.
Timoshenko
,
S.
, and
Woinowsky-Krieger
,
S.
,
1959
,
Theory of Plates and Shells
,
McGraw-Hill
,
New York
.
15.
Washizu
,
K.
,
1982
,
Variational Methods in Elasticity and Plasticity
,
Pergamon
,
Oxford, UK
.
You do not currently have access to this content.