A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges
Table 6
Frequency parameters for the multipoint-supported plate with different geometry parameters and numbers of clamped points.
geometry parameters
No. of clamped points
Model sequence
1
2
3
4
5
6
7
8
,
4
1.5833
1.6832
2.0553
2.0597
2.4456
2.7332
3.0820
3.1456
8
2.1798
2.4123
2.6437
3.2877
4.1133
5.1177
5.4172
5.5959
12
2.1833
2.4178
2.8495
3.4943
4.3430
5.3744
5.4539
5.6759
16
2.1834
2.4181
2.8503
3.4958
4.3451
5.3773
5.4542
5.6769
20
2.1834
2.4181
2.8503
3.4958
4.3451
5.3773
5.4542
5.6769
22
2.1834
2.4181
2.8503
3.4958
4.3451
5.3773
5.4542
5.6769
26
2.1834
2.4181
2.8503
3.4958
4.3451
5.3773
5.4542
5.6769
28
2.1834
2.4181
2.8503
3.4958
4.3451
5.3773
5.4542
5.6769
30
2.1834
2.4181
2.8503
3.4958
4.3451
5.3773
5.4542
5.6769
CC1
2.1810
2.4181
2.8536
3.4987
4.3445
5.3795
5.4602
5.6776
,
4
1.3105
1.4309
1.6865
1.7451
2.1095
2.1927
2.3602
2.4646
8
1.8389
2.0139
2.1817
2.6793
3.2958
4.0280
4.0619
4.1648
12
1.8424
2.0205
2.3551
2.8496
3.4791
4.1086
4.2146
4.2583
16
1.8426
2.0212
2.3569
2.8521
3.4824
4.1089
4.2180
4.2592
20
1.8426
2.0212
2.3569
2.8521
3.4824
4.1089
4.2180
4.2592
22
1.8426
2.0212
2.3569
2.8521
3.4824
4.1089
4.2180
4.2592
26
1.8426
2.0212
2.3569
2.8521
3.4824
4.1089
4.2180
4.2592
28
1.8426
2.0212
2.3569
2.8521
3.4824
4.1089
4.2180
4.2592
30
1.8426
2.0212
2.3569
2.8521
3.4824
4.1089
4.2180
4.2592
CC2
1.8449
2.0268
2.3604
2.8596
3.4840
4.1151
4.2190
4.2672
,
4
0.6581
0.8020
0.9433
0.9906
1.1117
1.1914
1.3123
1.4223
8
1.6839
1.7695
1.8092
1.8715
1.9115
2.0716
2.5176
2.5228
12
1.8057
1.8566
1.9511
2.0984
2.3047
2.5709
2.8942
3.2685
16
1.8058
1.8571
1.9521
2.1004
2.3074
2.5745
2.8979
3.2729
20
1.8058
1.8571
1.9521
2.1004
2.3074
2.5745
2.8979
3.2729
22
1.8058
1.8571
1.9521
2.1004
2.3074
2.5745
2.8979
3.2729
26
1.8058
1.8571
1.9521
2.1004
2.3074
2.5745
2.8979
3.2729
28
1.8058
1.8571
1.9521
2.1004
2.3074
2.5745
2.8979
3.2729
30
1.8058
1.8571
1.9521
2.1004
2.3074
2.5745
2.8979
3.2729
CC3
1.8097
1.8629
1.9553
2.1043
2.3078
2.5626
2.9013
3.2779
CC1: refers to the uniformly clamped plate with , and calculated by ABAQUS. CC2: refers to the uniformly clamped plate with , and calculated by ABAQUS. CC3: refers to the uniformly clamped plate with , and calculated by ABAQUS.
