Reference:

V.N. Chelomey, Vibration in technics, Handbook in six volumes; V.V. Bolotin, Volume 1, The vibrations of linear systems, Moscow, Mechanical Engineering, 1978, p. 207.

Problem description:

Determine the natural frequencies of the round plate clamped along the contour.

Problem sketch:

Type of created problem:

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

Geometric characteristics:

r = 0.5 m; t = 0.01 m.

Material properties:

Elastic modulus: E = 2.06·10¹¹ Pa;

Poisson’s ratio: μ = 0.3;

Density: γ = 7850 kg/m³.

Boundary conditions:

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

Loads:

Dead load.

Model description:

The system is modeled using 288 finite elements of thin plate with additional nodes (FE type is 19), splitting in the radial direction with a step of 0.0625 m and in the tangential with a step of 10°. To solve the problem, a modal analysis was performed.

Analytical solution:

J_n, I_n – Bessel functions.

Calculation results: