Das dynamische Verhalten von alternierend verstimmten Schaufelkränzen mit Reibelementkopplung

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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 of particle dampers for additive manufacturing

Damping mechanisms are a crucial factor for influencing the vibration behavior of dynamic systems. In many applications vibrations are undesirable and need to be reduced by appropriate measures. For instance, vibrations in vehicles can reduce driving comfort or in civil engineering resonance damage can occur in constructions. An interesting and cost-effective way of increasing damping is particle damping. In modern processes of additive manufacturing, like laser powder bed fusion (LPBF), unmelted powder can be left inside a structure on purpose after making and thus producing integrated particle dampers already. Additively manufactured particle damping has not yet reached the industrial level because there are no detailed specifications for the design process. This includes the modeling of (non-linear) dynamic properties, based on numerous design parameters. The state of the art reveals that the effect of particle damping has been convincingly demonstrated, but transferability of the obtained information is still limited. In this paper the effect of particle damping is investigated experimentally with LPBF manufactured beam structures made of AlSi10Mg. Particle damping is evaluated in terms of performance curves for different beam parameter sets. The aim is to help the designer, who needs to keep amplitudes in certain range to estimate the damping of the potential particle damper via the given performance curves. Damping is determined via experimental modal analysis by impulse excitation. The response is evaluated in the frequency domain using the Circle-Fit method with a focus on the beams first bending mode of vibration. Beyond that, a significantly increased damping could be verified up to the seventh bending mode covering a frequency range between 600 Hz and 18k Hz. Damping through particle-filled cavities shows up to 20 times higher damping compared to the same component with fused powder

High order sensitivity analysis of a mistuned blisk including intentional mistuning

Small deviations between turbine blades exist due to manufacturing tolerances or material inhomogeneities. This effect is called mistuning and usually causes increased vibration amplitudes and also a lower service life expectancy of bladed disks or so called blisks (bladed integrated disk). The major resulting problem is to estimate the maximum amplitude with respect to these deviations. Due to the probability distribution of these deviations, statistical methods are used to predict the maximum amplitude. State of the art is the Monte-Carlo simulation which is based on a high number of randomly re-arranged input parameters. The aim of this paper is to introduce a useful method to calculate the probability distribution of the maximum amplitude of a mistuned blisk with respect to the random input parameters. First, the applied reduction method is presented to initiate the sensitivity analysis. This reduction method enables the calculation of the frequency response function (FRF) of a Finite Element Model (FEM) in a reasonable calculation time. Based on the Taylor series approximation, the sensitivity of the vibration amplitude depending on normally distributed input parameters is calculated and therewith, it is possible to estimate the maximum amplitude. Calculating only a single frequency response function shows a good agreement with the results of over 1000 Monte-Carlo simulations

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

IMECE2011-63790 UNILATERAL IMPACT AND CONTACT OF ELASTIC STRUCTURES USING LAGRANGIAN MULTIPLIERS

ABSTRACT This paper deals with linear elastic structures exposed to impact and contact phenomena. Within a time stepping integration scheme contact forces are computed with a Lagrangian multiplier approach. The main focus is turned on a simplified solving method of the linear complementarity problem for the frictionless contact. Numerical effort is reduced by applying a CraigBampton transformation to the structural equations of motion

Limit cycle computation of self‐excited dynamic systems using nonlinear modes

A self-excited dynamic system is able to oscillate periodically by itself. Corresponding solutions of the autonomous differential equation are called limit cycles or periodic attractors. To find these solutions, a simple approach would be brute-force search for the corresponding basins of attraction. However, grid searching might become unfeasible with increasing number of degrees of freedom. Instead, solution path continuation techniques are often used to keep computational costs low. As the continuation of solution branches and their bifurcations provides only solutions which are connected to each other, isolas and detached branches are missed out. We present a method for fast limit cycle detection of self-excited systems with isolas based on nonlinear modes. A nonlinear mode, often referred to as nonlinear normal mode, is defined as a periodic motion of the undamped and unforced mechanical system. For nonconservative systems however, e.g. with friction nonlinearity, damping cannot be neglected as it is characteristic for the oscillators nonlinear dynamics. Therefore, the Extended Periodic Motion Concept (E-PMC) was proposed recently to find periodic solutions of nonconservative nonlinear systems. In this work, the E-PMC is applied to self-excited dynamic systems in order to find periodic attractors along its nonlinear modes. Zero crossings of the nonlinear damping curve indicate autonomous solutions which can be used as starting points for single parameter continuation. Thus, solutions corresponding to the main branch and detached curves in the solution space are connected by nonlinear modes. The proposed method is applied to a frictional oscillator with cubic stiffness and proves to be robust in the search for isolated periodic solutions that are already known from literature