Research Article

Free Vibration Exploration of Rotating FGM Porosity Beams under Axial Load considering the Initial Geometrical Imperfection

Table 3

The first nondimensional frequencies of the beam resting on the two-parameter elastic foundation, , S-S.

a/h = 100
nModeExact [47]This work
6 elements8 elements10 elements12 elements14 elements

Without the elastic foundation

015.4835.4835.4835.4835.4835.483
221.93321.93121.92421.92221.92121.921
349.35049.38949.31849.29649.28849.284
114.2214.2204.2204.2204.2204.220
216.88416.88416.87916.87716.87616.876
337.98938.03037.97537.95837.95237.949
213.8523.8513.8513.8513.8513.851
215.40715.40815.40315.40215.40115.401
334.66634.70734.65734.64134.63534.633
With the elastic foundation

016.0156.0146.0146.0146.0146.014
222.44522.44222.43622.43422.43322.433
349.85849.89149.82449.80349.79649.792
115.0085.0075.0075.0075.0075.007
217.66617.66417.66017.65917.65817.658
338.7738.80138.75338.73838.73238.729
214.7524.7524.7524.7524.7524.752
216.31616.31516.31116.31016.31016.309
335.57735.60635.56435.55035.54535.543