## 2. Cylindrical Panel

The eigenfrequencies and eigenmodes of a thin isotropic cylindrical panel are calculated. The purpose of the analysis is to examine the performance of the MITC shell elements combined to point mass elements (PMASS).

The panel is supported with four springs attached to the corners of the plate. Thus, the panel is not fully constrained and a shift of 1.0 has to be applied in order to be able to solve the eigenvalue problem. Figure 63. Curved panel model: Mesh consists of 10 by 14 Q4 elements or 5 by 7 Q8/Q9 elements.

The panel has a length a = 1.039_m, radius R = 1. m, an angle φ = 49.4 and a thickness t = 0. m. The springs have a height h =   and a cross section area of 1. m2. The materials are linear isotropic and the properties for the springs and the panel are listed below.

Table 5. Material properties

 Part Young's modulus [N/m2] Poisson number density ρ [kg] Panel 74.E9 0.3 2700. Springs 730. 0. 0.024

The free vibration analysis reveals that the first 6 eigenfrequencies are due to the vibration of the panel on its foundation. Therefore, only the 7th to 10th eigenfrequencies are listed in the table below:

Table 6. Computed eigenfrequencies

 Element Mode 7 Mode 8 Mode 9 Q4.S.MITC 9.94 12.9 22.6 Q8.S.MITC 9.93 12.7 22.4 Q9.S.MITC 9.91 12.7 22.4 Figure 64. Eigenmodes of the curved panel: Mode 7 (left) and 8 (right).