Reference:

Panovko J.G. Introduction to the theory of mechanical oscillations — M.: Nauka, 1980.

Problem description:

The behavior of a single-mass elastic system under excitation by a force that varies in time according to a harmonic law with different excitation frequencies is analyzed.

Problem sketch:

Type of created problem:

Spatial design (X, Y, Z, UX, UY, UZ).

Geometric characteristics:

Bar: L = 1 m.

Material properties:

Spring stiffness: K = EA/L = 100 kN/m.

Boundary conditions:

Node 1: X = Y = Z = UX = UY = UZ = 0.

Loads:

Concentrated mass: m = 10 kN;

The amplitude value of the force: F = 10 kN;

Damping parameter: ξ = 0.025.

Model description:

The system is modeled by 10 bar elements (FE 10 type).

Analytical solution:

where ω — natural frequency of the undamped system.

Calculation results:

Comparison chart: