## 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.

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.

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.