TEST CASE 8.6 AMPLITUDE-FREQUENCY CHARACTERISTICS OF A SYSTEM WITH ONE DEGREE OF FREEDOM
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:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
u, m T = 0 Hz |
0.1 |
0.1 |
0.0 |
u, m; T = 1 Hz |
0.16716 |
0.16718 |
0.01 |
u, m; T = 1.57 Hz |
2.0 |
2.0005 |
0.025 |
Comparison chart: