AutoFEM Harmonic Forced Oscillations Analysis

Analysis of forced oscillations is performed to predict the behaviour of a structure under external actions which change in accordance with the harmonic law. These actions include force and/or kinematic excitation. In addition to it, the impact of the system damping may be taken into account.

Forced Oscillations Analysis
Forced Harmonic Oscillations Analysis

The objective of the forced oscillation analysis is to obtain a dependence of the system’s response on frequency of compelling actions. As a result of calculations we get amplitudes of displacements, vibration acceleration, and vibration overload at the preset compelling frequency. According to these results, one can obtain, for a frequency range, the dependencies of amplitudes and vibration acceleration on frequency of compelling actions, which is important with the evaluation of vibration stability of the system in this preset frequency range.

Phase control of the result
Phase control of the result

The rotation of a shaft or spindle in the unbalanced state on elastic supports may serve an example of external harmonic force. Kinematic excitation is applied when values of compelling forces are not known, in contrast to amplitudes of oscillations of some structure elements which are known.

Graph of the amplitude-frequency response of the structure
Graph of the amplitude-frequency response of the structure

When considering forced oscillations, it is important to take into account the impact of damping forces. The process of energy dissipation of mechanic oscillations, leading to step-by-step attenuation of lump-sum produced oscillations of the system, is termed “damping”. Damping forces may have different origin, namely: friction between dry sliding surfaces, friction between lubricated surfaces, internal friction, air or liquid resistance, etc. It is usually presumed that the damping force is proportional to velocity (viscous damping). Resistance forces changing under the voluntary law are replaced for equivalent damping forces, proceeding from the condition that in one cycle, they dissipate the same amount of energy as real forces.

Dialog of Study's properties

The main results of calculation in the module of forced oscillations are the following values:

  • Amplitudes of displacement at finite element mesh nodes Um.
  • Vibro accelerations at finite element mesh nodes expressed via amplitudes Um as.
  • Vibro overloads, defined as the ratio of vibro acceleration to free fall acceleration.

Below you can find some examples of AutoFEM Forced Oscillations Analysis

Verification Examples of AutoFEM Forced Harmonic Oscillations Analysis

Forced oscillation of a spring-mass system

Vibrations of the spring-mass system because of oscillating foundation


Quick Start (Tutorial) on AutoFEM Forced Oscillations Analysis


This lesson will help you to perform the forced oscillation analysis by the AutoFEM Analysis package.

You will learn to : create a Forced Oscillation Analysis study;

create the finite element mesh;
specify a material;
specify loads and constraints;
obtain calculation results in the form of colour plots.

Download tutorial video of the AutoFEM Oscillation Analysis Module