part 20 - modal and buckling analysis of a rectangular pla )...critical buckling load = 0.7591 n/mm...
TRANSCRIPT
Modal and Buckling Analysis of a
Rectangular Plate with FEM-System
MEANS V10
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Modal and Buckling Analysis of a Rectangular Plate 1
Modal and Buckling Analysis of a Rectangular Plate with FEM-System MEANS V10
Rectangular Plate
A rectangular plate of steel with fixed edges in Z direction ist loaded with a line load of 2.5 N/mm. How big are the eigenfrequencies and buckling loads without rib, with a rib reinforcemet and with a beam girder reinforcement?
Plate without rib
Plate with a rib reinforcement
Plate with beam girder reinforcement
Modal and Buckling Analysis of a Rectangular Plate 2
Plate dimensions and material dates:
a = 2 m b = 1 m Plate Thickness h = 0.001 m E-Modulus E = 2.1 E+11 N / m² Poisson-Number v = 0.3 Density p = 7850 kg / m³ Constant Line Load q = 2.5 N/mm
Eigenfrequencies with the Kirchhoffschen Plate Theory
with the plate stiffness B = E * t ³ / (12 * ( 1 - v² )) = 19.23 Nm = 1.57 * 1.25 * ( 19.23 / 7.85 ) 0.5 = 3.07 Hz f1 = 3.07 Hz (first bending frequency)
Critical Buckling Load with constant line load Critical Buckling Load = 4 * pppp² * B / b ²
with the plate stiffness B = E * t ³ / (12 * ( 1 - v² )) = 19230 Nmm
= 4 * 9.867 * 19230 Nmm / 1000 mm * 1000 mm = 0.7591 N/mm Critical Buckling Load = 0.7591 N/mm Critical Buckling Factor = Critical Buckling Load / Line Load = 0.30
Result comparison
The results of the eigenfrequencies and the buckling loads between the plate theory and FEM system MEANS V10 show a very good agreement. Plate Theory MEANS V10 Eigenfrequency No 1 3.07 Hz 3.07 Hz Critical Buckling Faktor No 1 0.30 0.29 Critical Buckling Load for Line Load 0.75 N/mm 0.7250 N/mm
Modal and Buckling Analysis of a Rectangular Plate 3
Plate without Rib Eigenfrequencies and Eigenforms Buckling Factor and Buckling Forms
Eigenfrequency No. 1 = 3.07 Hz
Buckling Factor No. 1 = 0.29
Eigenfrequency No. 2 = 4.92 Hz
Buckling Factor No. 2 = 0.34
Eigenfrequency No. 3 = 8.0 Hz
Buckling Factor No. 3 = 0.38
Eigenfrequency No. 4 = 10.45 Hz
Buckling Factor No. 4 = 0.47
Modal and Buckling Analysis of a Rectangular Plate 4
Plate with a Rib Reinforcement
Eigenfrequencies and Eigenforms Buckling Factor and Buckling Forms
Eigenfrequency No. 1 = 5.85 Hz
Buckling Factor No. 1 = 0.36
Eigenfrequency No. 2 = 5.93 Hz
Buckling Factor No. 2 = 0.36
Eigenfrequency No. 3 = 12.83 Hz
Buckling Factor No. 3 = 0.52
Eigenfrequency No. 4 = 13.02 Hz
Buckling Factor No. 4 = 0.64
Modal and Buckling Analysis of a Rectangular Plate 5
Plate with Beam Girder Reinforcement
Eigenfrequencies and Eigenforms Buckling Factor and Buckling Forms
Eigenfrequency No. 1 = 6.01 Hz
Buckling Factor No. 1 = 0.38
Eigenfrequency No. 2 = 6.07 Hz
Buckling Factor No. 2 = 0.38
Eigenfrequency No. 3 = 13.05 Hz
Buckling Factor No. 3 = 0.7
Eigenfrequency No. 4 = 13.84 Hz
Buckling Factor No. 4 = 0.71