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Designing the vibroacoustic properties of thin-walled structures is of particularly high practical relevance in the design of vehicle structures. The vibroacoustic properties of thin-walled structures, e.g., vehicle bodies, are usually designed using finite element models. Additional development effort, e.g., experimental tests, arises if the quality of the model predictions are limited due to inherent model uncertainty. Model uncertainty of finite element models usually occurs in the modeling process due to simplifications of the geometry or boundary conditions. The latter highly affect the vibroacoustic properties of a thin-walled structure. The stiffness of the boundary condition is often assumed to be infinite or zero in the finite element model, which can lead to a discrepancy between the measured and the calculated vibroacoustic behavior. This paper compares two different boundary condition assumptions for the finite element (FE) model of a simply supported rectangular plate in their capability to predict the vibroacoustic behavior. The two different boundary conditions are of increasing complexity in assuming the stiffness. In a first step, a probabilistic model parameter calibration via Bayesian inference for the boundary conditions related parameters for the two FE models is performed. For this purpose, a test stand for simply supported rectangular plates is set up and the experimental data is obtained by measuring the vibrations of the test specimen by means of scanning laser Doppler vibrometry. In a second step, the model uncertainty of the two finite element models is identified. For this purpose, the prediction error of the vibroacoustic behavior is calculated. The prediction error describes the discrepancy between the experimental and the numerical data. Based on the distribution of the prediction error, which is determined from the results of the probabilistic model calibration, the model uncertainty is assessed and the model, which most adequately predicts the vibroacoustic behavior, is identified. more...

Scaling laws are used to scale-up calculation or measurement results from a prototype structure to those of an original structure or vice versa. The scaling laws of mechanical structures are usually obtained from their equations of motion or from a dimensional analysis. This paper proposes scaling laws that are represented by a power law. The power law is directly deduced from the Π -theorem of similitude theory and the coefficients of the power law are obtained from first order sensitivities (sensitivity-based scaling laws). Among existing similitude analysis methods such as dimensional analysis the sensitivity-based scaling laws can be directly obtained from a model without a priori knowledge of its scaling behavior, e.g., from a finite element (FE) model. The applicability of the sensitivity-based scaling laws is demonstrated in three case studies. A simply supported rectangular plate subject to mechanical vibrations is modeled by an analytical approach based on the Kirchhoff plate theory and by an FE model based on the Mindlin-Reissner theory. The plate’s dimensions are considered as design parameters for the sensitivity-based scaling laws. It is found in the first case study that the sensitivity-based scaling laws exactly predict the natural frequencies and the mean squared transfer admittances of scaled models from those of the original plate. This is in agreement with current literature and, thus, the method proposed in this paper can be considered verified. In the second case study the sensitivity-based scaling laws are directly obtained from the FE model. A good accuracy of the predicted vibration responses of the scaled models is found since (1) the scaled model and the original one are in similitude, i.e., the mode shape order and the damping are kept, and (2) the scaled plate can still be considered thin. The latter is assessed by the length (or width) to thickness ratios of the investigated plates and a lower bound is proposed. The third case study comprises a simplified car undercarriage to demonstrate the applicability of the method in practical design engineering. Besides the geometry parameters the material properties are incorporated in the sensitivity-based scaling laws as well. It is found that the natural frequencies as well as the vibration velocities at an arbitrarily chosen receiver point of the scaled models can be accurately predicted from those of the original one for complete similitude conditions. more...

Engineers often use similitude analyses to design small scale models for experimental tests or to design size ranges of mechanical structures such as drive technology systems. This paper is concerned with similitude analysis methods for vibration analyses of rectangular plates. If their geometry is scaled by different factors (distorted similitude), the scaling laws approximate the actual vibration responses with a certain accuracy only. This paper introduces a performance measure that reliably assesses how well the scaling laws approximate the actual vibration responses of rectangular plates. This measure, the so-called Mahalanobis distance, applies in a-posteriori analyses, where the vibration responses obtained from the scaling laws are compared to the actual ones. Numerical and experimental investigations on vibrating rectangular plates validate that the Mahalanobis distance is suitable to assess the performance of similitude analyses. The Mahalanobis distance can be linked to the geometrical properties of the rectangular plates in order to define a maximum permissible distortion of the geometry. Scaling laws approximate the vibration responses of the rectangular plates sufficiently well up to this maximum permissible distortion. Furthermore, the performance of two different state-of-the-art similitude analysis methods is compared. Both similitude analysis methods are found to perform well up to the maximum permissible amount of geometrical distortion. more...

In structures, high vibration levels can destroy components; therefore, the reduction of the vibration levels represents a fundamental target in the industrial field. The structural intensity (STI) field provides information about the energy flow that propagates within a structure. It shows the position of dampers in structures, thus, it can be used for solving structure-borne noise problems. The analysis of the energy distribution on a structure allows to understand where to implement locally concentrated modifications introducing damping patches in order to reduce structure-borne noise. The aim of this paper is to investigate the structural intensity in composite structures and to evaluate the influence of some modeling parameters, such as mesh density, structural damping, etc., on the accuracy of the results. In this paper, numerical investigations on the STI in a fiber composite plate are carried out. Two different numerical models are considered: the first one with solid elements, the second one with shell elements. The two-dimensional model does not allow to analyze and study the composite plate on micro level. The first law of thermodynamics allows to define the accuracy of the STI evaluations. The investigation on two-dimensional and three-dimensional composite structure modeling presents the limits and the advantages of the two different types of approach. The different characteristics of the STI fields provided by these models are analyzed in order to understand the difference between local and global approach. more...

The bearing of a strain wave gearing and the covering thin-walled cup, i.e., the so-called flexspline, are elliptically deformed. This leads to a characteristic excitation of vibration. In this paper, a model for describing the vibration of elliptically deformed bearings is presented. First, the flexspline stiffness is calculated using an a priori finite element (FE) analysis that is validated with measured data. Second, the deformation of the bearing and the flexspline is calculated by superimposing single loads. A numerical study shows that vibrations are mainly caused by the rotation of the ellipse. Furthermore, two types of impulses, i.e., negative impulses and positive impulses, lead to vibration excitation. The negative impulses are caused by the balls passing the angular position of the contact force maxima, while the positive impulses are caused by the balls impacting the surfaces of the races due to the radial tolerance of the bearing. Both negative and positive impulses coincide with characteristic frequencies of the nondeformed bearing. If the surfaces of the bearing are considered to be rough, the characteristic frequencies are not affected. Therefore, characteristic frequencies of nondeformed bearings can be utilized to describe vibrations of elliptically shaped bearings as well. more...