Continuation methods for lab experiments of nonlinear vibrations

In this work, we will give an overview of our recent progress in experimental continuation. First, three different approaches are explained and compared which can be found in scientific papers on the topic. We then show S-Curve measurements of a Duffing oscillator experiment for which we derived optimal controller gains analytically. The derived formula for stabilizing PD-controller gains makes trial and error search for suitable values unnecessary. Since feedback control introduces higher harmonics in the driving signal, we consider a harmonization of the forcing signal. This harmonization is important to reduce shaker-structure interaction in the treatment of nonlinear frequency responses. Finally, the controlled nonlinear testing and harmonization is enhanced by a continuation algorithm adapted from numerical analysis and applied to a geometrically nonlinear beam test rig for which we measure the nonlinear forced response directly in the displacement-frequency plane

Nonlinear granular damping of structures with cavities from additive manufacturing

Additively manufactured parts are often created with cavities for weight reduction or other mechanical purposes. These cavities offer the optimal base for granular damping. Unfused raw material particles can be left inside the structure or another granular material can be filled in to increase structural damping. In this paper, a simple mechanical model is developed based on measurements of a basic experiment for granular damping with only a small amount of particles

Design Guidelines for Additive Manufactured Particle Dampers: A Review

Recently, additive manufacturing has been used to integrate particle dampers into structural components, particularly by means of laser powder bed fusion (LPBF), in order to significantly reduce component vibrations. The advantage over previous damping mechanisms is that these can be functionally integrated directly into the component during the additive manufacturing process by leaving unmelted powder in the component. This allows local damping effects to be adjusted and low-vibration lightweight structures to be developed and manufactured. In addition, the damping properties act over a wide frequency range and are insensitive to temperature. Despite the positive damping properties, the use of laser beam melted particle dampers is limited at the present time, since there are not yet sufficient design tools available due to the numerous non-linear influences. This is where the current contribution comes in, by developing design guidelines for laser beam melted particle dampers. The results were finally summarised in a design catalogue and support a suitable design of laser beam melted particle dampers

System identification of jointed structures: Nonlinear modal testing vs. State-space model identification

Two approaches for experimental identification of the nonlinear dynamical characteristics of jointed structures are investigated, (a) Nonlinear Modal Testing, (b) State-Space Model Identification. Both require only minimal a priori knowledge of the specimen. For method (a), the definition of nonlinear modes as periodic motions is used, in its generalized formulation recently proposed for nonconservative systems. The theoretically required negative damping compensating the frictional dissipation is experimentally realized by properly controlled excitation. This permits the extraction of modal frequencies, damping ratios and vibrational deflection shapes as a function of the vibration level. For method (b), a state-space model with multivariate polynomial nonlinear terms is identified from the vibration response to a properly designed excitation signal. Both methods are applied to a structure with bolted joints. The quality of the extracted modal and state-space models, respectively, is assessed by comparing model-based predictions of the forced vibration response to reference measurements