Damping in a micro-cantilever beam was measured for a very broad range of air pressures from atmosphere (10 5 Pa) down to 0.2 Pa. The beam was in open space free from squeeze films. The damping ratio, due mainly to air drag, varied by a factor of 10 4 within this pressure range. The damping due to air drag was separated from other sources of energy dissipation so that air damping could be measured at 10 -6 of critical damping factor. The linearity of the damping was confirmed over a wide range of beam vibration levels. Lastly, the measured damping was compared with several existing theories for air-drag damping for both rarified and viscous flow gas theories. The measured data indicate that, in the rarefied regime the air damping is proportional to pressure, independent of viscosity, and in the viscous regime the damping is determined by viscosity.
The focus of this paper is on the development of validated models for wind turbine blades. Validation of these models is a comprehensive undertaking which requires carefully designing and executing experiments, proposing appropriate physics-based models, and applying correlation techniques to improve these models based on the test data. This paper will cover each of these three aspects of model validation, although the focus is on the third - model calibration. The result of the validation process is an understanding of the credibility of the model when used to make analytical predictions. These general ideas will be applied to a wind turbine blade designed, tested, and modeled at Sandia National Laboratories. The key points of the paper include discussions of the tests which are needed, the required level of detail in these tests to validate models of varying detail, and mathematical techniques for improving blade models. Results from investigations into calibrating simplified blade models are presented.
A series of modal tests were performed in order to validate a finite element model of a complex aerospace structure. Data was measured using various excitation methods in order to extract clean modes and damping values for a lightly damped system. Model validation was performed for one subassembly as well as for the full assembly in order to pinpoint the areas of the model that required updating and to better ascertain the quality of the joint models connecting the various components and subassemblies. After model updates were completed, using the measured modal data, the model was validated using frequency response functions (FRFs) as the independent validation metric. Test and model FRFs were compared to determine the validity of the finite element model.
A series of modal tests were performed to validate a finite-element model of a complex aerospace structure. Data were measured using various excitation methods to extract clean modes and damping values for a lightly damped system. Model validation was performed for one subassembly as well as for the full assembly to pinpoint the areas of the model that required updating and to better ascertain the quality of the joint models connecting the various components and subassemblies. After model updates were completed using the measured modal data, the model was validated using frequency response functions (FRFs) as the independent validation metric. Test and model FRFs were compared to determine the validity of the finite-element model.
When measuring the structural dynamic response of test objects, the desired data is sometimes combined with some type of undesired periodic data. This can occur due to N-per-revolution excitation in systems with rotating components or when dither excitation is used. The response due to these (typically unmeasured) periodic excitations causes spikes in system frequency response functions (FRFs) and poor coherence. This paper describes a technique to remove these periodic components from the measured data. The data must be measured as a continuous time history which is initially processed as a single, long record. Given an initial guess for the periodic signal's fundamental frequency, an automated search will identify the actual fundamental frequency to very high accuracy. Then the fundamental and a user-specified number of harmonics are removed from the acquired data to create new time histories. These resulting time histories can then be processed using standard signal processing techniques. An example of this technique will be presented from a test where a vehicle is dithered with a fixed-frequency, sinusoidal force to linearize the behavior of the shock absorbers, while measuring the acceleration responses due to a random force applied elsewhere on the vehicle.
In this paper we present the results of a study to quantify uncertainty in experimental modal parameters due to test set-up uncertainty, measurement uncertainty, and data analysis uncertainty. Uncertainty quantification is required to accomplish a number of tasks including model updating, model validation, and assessment of unit-tounit variation. We consider uncertainty in the modal parameters due to a number of sources including force input location/direction, force amplitude, instrumentation bias, support conditions, and the analysis method (algorithmic variation). We compute the total uncertainty due to all of these sources, and discuss the importance of proper characterization of bias errors on the total uncertainty. This uncertainty quantification was applied to modal tests designed to assess modeling capabilities for emerging designs of wind turbine blades. In an example, we show that unit-to-unit variation of the modal parameters of two nominally identical wind turbine blades is successfully assessed by performing uncertainty quantification. This study aims to demonstrate the importance of the proper pre-test design and analysis for understanding the uncertainty in modal parameters, in particular uncertainty due to bias error.
In order to create an analytical model of a material or structure, two sets of experiments must be performed-calibration and validation. Calibration experiments provide the analyst with the parameters from which to build a model that encompasses the behavior of the material. Once the model is calibrated, the new analytical results must be compared with a different, independent set of experiments, referred to as the validation experiments. This modeling procedure was performed for a crushable honeycomb material, with the validation experiments presented here. This paper covers the design of the validation experiments, the analysis of the resulting data, and the metric used for model validation.
Structural dynamic systems are often attached to a support structure to simulate proper boundary conditions during testing. In some cases, the support structure is fairly simple and can be modeled by discrete springs and dampers. In other cases, the desired test conditions necessitate the use of a support structure which introduces dynamics of its own. For such cases, a more complex structural dynamic model is required to simulate the response of the full combined system. In this paper, experimental frequency response functions, admittance function modeling concepts, and least squares reductions are used to develop a support structure model including both translational and rotational degrees of freedom at an attachment location. Subsequently, the modes of the support structure are estimated, and a NASTRAN model is created for attachment to the tested system.
When a modal test is to be performed for purposes of correlation with a finite element model, one needs to design the test so that the resulting measurements will provide the data needed for the correlation. There are numerous issues to consider in the design of a modal test; two important ones are the number and location of response sensors, and the number, location, and orientation of input excitation. From a model correlation perspective, one would like to select the response locations to allow a definitive, one-to-one correspondence between the measured modes and the predicted modes. Further, the excitation must be designed to excite all the modes of interest at a sufficiently high level so that the modal estimation algorithms can accurately extract the modal parameters. In this paper these two issues are examined in the context of model correlation with methodologies presented for obtaining an experiment design.
Force reconstruction is a procedure in which the externally applied force is inferred from measured structural response rather than directly measured. In a recently developed technique, the response acceleration time-histories are multiplied by scalar weights and summed to produce the reconstructed force. This reconstruction is called the Sum of Weighted Accelerations Technique (SWAT). One step in the application of this technique is the calculation of the appropriate scalar weights. In this paper a new method of estimating the weights, using measured frequency response function data, is developed and contrasted with the traditional SWAT method of inverting the mode-shape matrix. The technique uses frequency response function data, but is not based on deconvolution. An application that will be discussed as part of this paper is the impact into a rigid barrier of a weapon system with an energy-absorbing nose. The nose had been designed to absorb the energy of impact and to mitigate the shock to the interior components.
The Jet Propulsion Laboratory is developing a large space-truss to support a micro-precision interferometer. A finite element model will be used to design and place passive and active elements in the truss to suppress vibration. To improve the model`s predictive capability, it is desirable to identify uncertain structural parameters in the model by utilizing experimental modal data. Testing of both the components and the system was performed to obtain the data necessary to identify the structural parameters. Extracting a modal model, absent of bias errors, from measured data requires great care in test design and implementation. Testing procedures that are discussed include: verification of non-constraining shaker attachment, quantification of the non-linear structural response, and the design and effects of suspension systems used to simulate a free structure. In addition to these procedures, the accuracy of the measured frequency response functions are evaluated by comparing functions measured with random excitation, using various frequency resolutions, and with step sine excitation.