Part 20 - Modal and Buckling Analysis of a rectangular pla )...Critical Buckling Load = 0.7591 N/mm Critical Buckling Factor = Critical Buckling Load / Line Load = 0.30 Result comparison

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