Reference:

I.A. Birger, Ya.G. Panovko, Strength, Stability, Vibrations, Handbook in three volumes, Volume 3, Moscow, Mechanical engineering, 1968, p. 377.

Problem description:

Determine the natural frequencies of a square plate clamped around the perimeter.

Problem sketch:

Type of created problem:

Flat plate or grillage (Z, UX, UY).

Geometric characteristics:

a = 1 m; t = 0.01 m.

Material properties:

Elastic modulus: E = 2.1·10¹¹ Pa;

Poisson’s ratio: μ = 0.3;

Density: γ = 7800 kg/m³.

Boundary conditions:

On the perimeter: Z = UX = UY = 0.

Loads:

Dead load.

Model description:

The system is modeled using 100 finite elements of thin plate (FE type is 19) with additional nodes. To solve the problem, a modal analysis was performed.

Analytical solution:

Calculation results: