Measuring Operating Deflection Shapes (original) (raw)

Using FEA Modes to Scale Experimental Mode Shapes

2006

When Operating Modal Analysis (OMA) is used for finding the modal parameters of a structure, the excitation forces are not measured. Because the forces are not measured, the resulting mode shapes cannot be used in a modal model because they are not properly scaled to reflect the mass and stiffness properties of the structure. In a traditional multi-shaker modal survey using sinusoidal signals, the excitation forces are also not measured and the mode shapes are obtained from response only data. Again, these un-scaled shapes cannot be used in a modal model. Finally, even in an FRF-based impact or shaker where the excitation forces are measured, calibrated measurements must be made in order to properly scale the mode shapes. Also, a driving point measurement is usually required, which can often be difficult to make, resulting in error prone mode shape scaling. In this paper, we show how analytical mode shapes obtained from finite element analysis (FEA) can be used to scale experimental mode shapes. It is shown that analytical models having relatively few finite elements in them can yield mode shapes that correlate well with experimental shapes, and are therefore adequate for scaling the experimental shapes. A straightforward least squared error method is introduced for scaling the experimental shapes. Examples are included that illustrate how FEA models of various sizes will still yield accurate results.

A NEW FORMULATION FOR OPTIMUM MAGNITUDE OF ADDITIVE MASS IN SCALING OF MODE SHAPES

One of the most important necessities of structure designing is identification of its dynamic characteristics. In large structures such as bridges, buildings, towers, airplanes and etc. the measurement of the ambient forces is difficult or impossible. Therefore, only the response signals can be measured. The methods which identify the modal parameters of the structures by using output-only data are called Operational Modal Analysis (OMA) methods. As the structure is excited by unknown forces, the mode shapes cannot be scaled straightforward from the test. A major problem of OMA is that the mode shapes are un-scaled. So far, several approaches have been proposed for scaling the mode shapes. In this paper, the amount of optimum mass change has been obtained for one of the exact scaling formulas using sensitivity analysis of the FEM model of the structure. The error of scaling would be minimized by applying this amount of mass change. In order to consider the method numerically, an FE model of a cantilever beam was used. The beam has been excited by random forces and the responses have been measured. The SSI method was applied and the unscaled mode shapes have been achieved. The proposed relation was used to select the optimum mass change of the beam. Finally the mode shapes were scaled using Bernal formula and the accuracy of the obtained relation has been investigated.

Operational mode-shape normalisation with a structural modification for small and light structures

Mechanical Systems and Signal Processing, 2014

When dealing with small and light structures, difficulties occur when measuring the modal parameters. The resonant frequencies are usually relatively high and therefore a wide frequency range is needed for the measurement. Furthermore, the mass that is added to the structure by the sensors causes structural modifications. To overcome these difficulties, an improved method using an operational modal analysis instead of an experimental modal analysis is proposed in this study. It is derived from the sensitivity-based operational mode-shape normalisation with a consideration of the mode-shape variation. The measurement of the excitation force is not needed, because the operational modal analysis is used and only two simultaneous response measurements at an unknown excitation are required. The proposed method includes the cancellation of the added mass, resulting in mode shapes and

Model updating using operating deflection shapes

1998

Model updating using a structural model is based on the analysis of the discrepancies between analytical and experimental results. In order to compare these quantities, a matching process is necessary.

An optical-based technique to obtain operating deflection shapes of structures with complex geometries

Mechanical Systems and Signal Processing, 2019

The dynamic characteristics of structures are conventionally obtained by exciting the structure using an impulse hammer or a mechanical shaker and measuring the response using uniaxial or multi-axial accelerometers. However, contact-based sensors can mass-load the structure and do not provide full-field data. Hence, obtaining the true dynamics of the structure using conventional sensors can be challenging. That makes test engineers seek different non-contact techniques that can provide full-field data without mass-loading the structure. Recently, stereo-photogrammetry and three-dimensional digital image correlation (3D DIC) have been adopted to collect operating data for structural analysis. These non-contact optical techniques provide a wealth of distributed data over the entire structure. However, the stereo-camera system is limited by the field-of-view of the cameras; a single pair of DIC cameras may not be able to provide deformation data for the entire structure. Hence, it is challenging to obtain the vibration characteristics of the entire structure. In the current work, a multi-view 3D DIC approach is used and validated to predict the vibrational characteristics of an automotive muffler with a complex structure. A pair of DIC cameras travels over the entire structure to capture the deformation of each field of view. The measured data includes the geometry and displacement data, which is later mapped into a global coordinate system. The measured data in the time domain for each field-of-view is transformed to the frequency domain to extract the operational deflection shapes and resonant frequencies for each field of view. The obtained deflection shapes are stitched together in the frequency domain to extract the operating deflection shapes and resonant frequencies of the automotive body panel with a complex structure.

Scaling the Mode Shapes of a Building Model by Mass Changes

2004

NOMENCLATURE φ Mode shape vector scaled to unity ψ Mode shape vector scaled to normalize with mass matrix ω Natural frequency ω ∆ Natural frequency shift α Scaling factor M Mass matrix ∆M Mass change matrix m ∆ Scalar mass change D Diagonal matrix containing only unity values m ∆ Mass change vector σ

INTRODUCTION TO OPERATING DEFLECTION SHAPES By

Mode shapes and operating deflection shapes (ODS's) are related to one another. In fact, ODS's are always meas- ured in order to obtain mode shapes. Yet, they are quite different from one another in a number of ways. In this paper, we will discuss ODS measurements, and their rela- tionship to experimental modal parameters.

Relative scaling of mode shapes using transmissibility functions

Mechanical Systems and Signal Processing, 2013

Operational modal analysis (OMA) is the collective term for different techniques that estimate the modal parameters of a linear structure using only the structural responses to unknown excitations. Therefore, OMA is the preferred approach when operational forces are hard to measure, when operational conditions are hard to replicate in a controlled environment or when an experimental modal analysis (EMA) is too time-consuming. However, OMA does not allow us to determine the relative contribution of each mode, i.e. the mode shapes found with OMA are unscaled.