Current status of the research project

This page will show the current status and main results of the research project

Continuation in experiments 


Figure 1: The experimental test-rig. A harmonically forced flexible non-linear impact oscillator with hard impacts and hardening spring stiffness. (1) Flexible impactor, (2) Hard impacts, (3) Platform, (4) Electromagnetic Shaker, (5) Laser displacement sensors, (6) Electromagnetic Actuators.

In the laboratory we have build the test-rig shown in figure 1. It consists of a mechanical system, sensors, actuators and a data acquisition- and control system. The mechanical system comprises a clamped flexible impactor (1) which, when vibrating with large enough amplitudes, impacts a mechanical stop (2) causing an increase of stiffness. This nonlinearity causes a change of natural frequency with oscillation amplitude, and the appearance of a hysteresis loop when varying the frequency of the external excitation, see figure 2. The impactor is mounted on a platform (3), which can be moved in the horizontal plane by means of an electromagnetic shaker (4). The displacement of the platform and the displacement of the pendulum is measured using two laser displacement sensors (5). An electromagnetic actuator (6) is mounted on each side of the impactor mass. Using an amplifier and a power supply, the strength and direction of the magnetic field can be varied using a control signal. Data acquisition and control is realized using a computer equipped with a dSPACE DS1104 board and MATLAB/Simulink.   


Figure 2: Experimental steady state response amplitudes recorded by sweeping the frequency while keeping fixed steps in amplitude.

Using this test-rig it has been possible successfully apply control-based continuation and hereby experimentally trace out bifurcation diagrams for the system. Examples of results from such tests are shown in figure 3. Note that when comparing with the conventional parameter-sweep method, it is possible to follow unstable states using control-based continuation. This is a novel feature for the method, which makes it possible to obtain information that is important for updating models and can help to  reveal dynamic features, that could otherwise easily have been overlooked.





Figure 3: Bifurcation diagrams (frequency response) for the driven impactor observed experimentally by using control-based continuation. (a) The whole diagram was traced in one continuous run. The sweep was made for a excitation signal with amplitude, A = 0.4. (b) shows how multiple continuation runs can be combined to obtain the full picture of the dynamics.

At the current state we are  working on improving the reliability and stability of the method, aiming at developing a control-based continuation software toolbox, Continex. This software will enable us to interface and apply the method to other already existing experiments already equipped with a closed control loop. Furthermore we try to develop methods for determining bifurcation points and detecting stability as well as testing the method on more advanced test rigs.