Search

The paper at hand shows how structural damping and stiffness parameters in shrunk joints can be determined by a generic joint experiment. With thin layer elements these parameters from the joint experiment are coupled to the structures Finite Element Model. Equivalent modal damping factors can be determined by performing a complex numerical modal analysis, by which the stability of the rotor can be tested. The two disc rotor is examined as an application sample. This rotor consists of a shaft with two shrunk-on discs. With the above mentioned approach, and by considering structural damping added to material damping, the modal damping of the first torsional eigenfrequency is calculated and then compared to the results of an experimental modal analysis. The paper shows that the presented approach leads to a reliable approximation of the examined structure’s dissipation properties. It serves as a prediction tool for the response behavior of a turbo-generator.

Local nonlinearities typically occur due to large deformation in certain parts of a structure or due to the presence of nonlinear coupling elements. Often the dynamic behavior of such elements is a priori unknown and has to be investigated experimentally before they can be included in numerical calculations. In this contribution an integrated method for estimation of linear as well as nonlinear system parameters based on the nonlinear normal modes (NNMs) of the structure is proposed. The characteristics of the nonlinear and linear parts of an assembly both contribute to its NNMs. Assuming that the functional form of the nonlinearity is known or can be estimated through non-parametric identification techniques, this feature can be exploited for the purpose of model updating. For the updating process the measured and calculated NNMs of a system are compared and their difference is minimized. In this context the numerical calculation of NNMs is performed using the Harmonic Balance Method (HBM). The properties of the proposed method are demonstrated on the numerical example of a 4DOF oscillator with a cubic nonlinearity. Furthermore, the effectiveness of the method is shown by updating the FE-model of a beam with cubic nonlinearity based on experimental data.

Rotor vibrations in electrical machines depend on structural damping and stiffness properties of the laminated cores. Structural damping determines torsional and transversal vibration amplitudes at resonances. Therefore, it is very important to know the structural damping and stiffness of the laminated cores to carry out structural dynamic simulations. In this paper, a measurement set-up is presented to determine the structural damping and direction-dependent stiffness for laminated cores and stacks. The dissipated damping energy is examined as a result of harmonic excitation of different excitation amplitudes, frequencies and axial pre-stressing conditions. Thereby, the measured structural damping factor is compared to the material damping factor from tables. To allow a conclusion for the reproducibility of the evaluated damping parameters, repeated measurements are carried out and the results are statistically analyzed using the Weibull distribution.

The damping properties of materials, joints, and assembled structures can be modeled efficiently using fractional derivatives in the respective constitutive equations. The respective models describe the damping behavior accurately over broad ranges of time or frequency where only few material parameters are needed. They assure causality and pure dissipative behavior. Due to the non-local character of fractional derivatives the whole deformation history of the structure under consideration has to be considered in time-domain computations. This leads to increasing storage requirements and high computational costs. A new concept for an effective numerical evaluation makes use of the equivalence between the Riemann–Liouville definition of fractional derivatives and the solution of a partial differential equation (PDE). The solution of the PDE is found by applying the method of weighted residuals where the domain is split into finite elements using appropriate shape functions. This approach leads to accurate results for the calculation of fractional derivatives where the numerical effort is significantly reduced compared with alternative approaches. Finally, this method is used in conjunction with a spatial discretization method and a simple structure is calculated. The results are compared to those obtained from alternative formulations by means of accuracy, storage requirements, and computational costs.

The paper at hand shows how structural damping and stiffness parameters in shrunk joints can be determined by a generic joint experiment. With thin-layer elements these parameters from the joint experiment are coupled to the structures finite element model. Equivalent modal damping factors can be determined by performing a complex numerical modal analysis, by which the stability of the rotor can be tested. The two-disc rotor is examined as an application sample. This rotor consists of a shaft with two shrunk-on discs. With the above mentioned approach, and by considering structural damping added to material damping, the modal damping of the first torsional eigenfrequency is calculated and then compared to the results of an experimental modal analysis. The paper shows that the presented approach leads to a reliable approximation of the examined structure’s dissipation properties. It serves as a prediction tool for the response behavior of a turbo-generator.

In this work, an efficient FE-modeling technique for assembled metallic structures is presented. Linear thin-layer elements containing damping and stiffness parameters are placed on the interfaces of bolted joints. The interface parameters are identified experimentally on an isolated lap joint and then used as an input for the FE-simulation. Since the presented modeling technique is linear, it delivers acceptable results only for small relative displacements in the joint interface, i.e. microslip. Therefore investigations on the transition from micro- to macroslip are conducted. A promising approach to detect macroslip is based on the significant increase of higher harmonic frequency generation. The application of this criterion results in a linear relation between the normal force and the maximum tolerable tangential force.

In many engineering applications vibro-impact systems play an important role for functionality like for example in percussion machines or cause undesirable effects like noise or fatigue. Also in assembled structures clearance in joints can lead to vibro-impact problems that affect the overall dynamics of the systems. Either way, the understanding and simulation of such systems is essential. Furthermore, combinations of impacts with other nonlinearities like friction or nonlinear springs are relevant in practice. This contribution examines similar methods for the investigation of springs with cubic stiffness and vibro-impact nonlinearities as well as their combination. The Harmonic Balance Method is used along with a continuation method to simulate Frequency Response Functions of the nonlinear systems. Additionally, the influence of higher harmonics and subharmonics is considered. In systems with impact or cubic spring also chaotic motions can occur depending on the parameters. The occurrence of these motions is estimated by the calculation of Lyapunov-Exponents. Their appearance is visualized in Poincare-Maps and phase portraits. Further investigations will be carried out on the calculation of backbone curves for vibro-impact systems and systems with combined nonlinearities to capture the frequency-energy dependency of these systems.

Wave-based SHM concepts are widely used for an efficient evaluation of the state of a structure. In order to localize defects in waveguides, an exact knowledge of the propagation properties of ultrasonic waves is required.