Reference:

M.V. Barton, “Vibration of rectangular and skew cantilever plates”, Journal of Applied Mechanics, vol. 18, 1951, p. 129 – 134.

Problem description:

Determine the natural frequencies of a restraint-free square plate.

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:

Elastic links of low stiffness in all nodes of the calculation scheme: R_Z = 0.001 N/m.

Loads:

Dead load.

Model description:

The system is modeled using 400 finite elements of thin plate (FE type is 19). To solve the problem, a modal analysis was performed.

Calculation results: