4. Isotropic Plate

The eigenfrequencies and eigenmodes of a thin flat rectangular isotropic plate are calculated for MITC shell elements with 4, 8, and 9 nodes. The plate has a length a = 10 [m], width b = 0.4 [m] and a thickness t = 0.002 [m]. The material is linear isotropic, with modulus of elasticity E = 72 109 [N/m2], Poisson number ν = 0.3, and density ρ = 2400 [kg/m3]. The edges I and III are simply supported. The other two edges are free. The plate is modelled using a regular 10 by 10 element mesh.

Flat isotropic plate (10 by 10 element mesh)

Figure 66. Flat isotropic plate (10 by 10 element mesh)

Analytical solutions can be obtained from various sources[27]. Computed values are not listed here (see __init__.py file). The figure below shows the second, third, and fourth eigenmode of the plate with respect to the undeformed shape.

Mode shapes for different eigenvalues

Figure 67. Mode shapes for different eigenvalues

Table 9. Analytical eigenfrequencies fi

f1 f2 f3 f4
5.0 17.1 20.2 38.6

[27] Robert D. Blevins, Krieger Publishing Company, Malabar Florida, 1993: Table 11-4.5 ,page 254.