SS-V: 6010 Simply Supported Thin Square Plate - Periodic Forced Vibration Response

A simply supported thin square plate 10 x 10 x 0.05 m is subject to uniform pressure P=100 Pa which changes in time as the following function.(1)

$$P=100*\left(\sin \left(\omega \ast t\right)-\sin \left(3\omega \ast t\right)\right)$$

Where,

$\omega =2\ast PI\ast f$

$f=1.2Hz$

Excitation frequency.

The material properties are:

Properties

Value

Modulus of Elasticity

2.e+11 Pa

Poisson's Ratio

0.3

Density

8.e+3 kg/m³

The plate is simulated as a 3D solid body. Spot-lines were created at the mid-plane of the plate in order to apply hinge supports (Figure 1). In order to simulate periodic load changing according to the formula above, two pressure loads were applied to the plate:

• $P=100\ast \sin \left(\omega \ast t\right)$ to the top surface of the plate, and
• $P=-100\ast \sin \left(3\omega \ast t\right)$ to the bottom surface of the plate

Figure 1.

The following table contains typical values at steady-state portion of the dynamics solution (Figure 2).

Figure 2.