Brian Schwarz - Academia.edu (original) (raw)

Papers by Brian Schwarz

Topics in Modal Analysis & Testing, Volume 8, 2019

Structural Health Monitoring & Damage Detection, Volume 7, 2017

In two recent papers, we introduced the idea of numerically comparing currently acquired operatin... more In two recent papers, we introduced the idea of numerically comparing currently acquired operating data with archived data to identify faults in rotating machinery (Ganeriwala et al.: Using operating deflection shapes to detect unbalance in rotating equipment. In: IMAC XXVII. Orlando, FL (2009); Richardson et al.: Using operating data to locate and quantify unbalance in rotating machinery. In: IMAC XXXIV, January 25-28, 2016). We introduced a new metric for comparing two operating deflection shapes called the Shape Difference Indicator (SDI). In another previous paper (Richardson et al.: A new measure of shape difference. In: IMAC XXXII, February 3-6, 2014), we used SDI to measure the difference in modal frequencies from before and after a stiffness change was made to a mechanical structure. In this paper we provide more details of how experimental modal frequency and damping parameters can be used together with the SDI metric as a means of detecting and quantifying changes in the physical properties of a structure. Also, we have implemented SDI together with a search method for ranking the differences between currently acquired modal parameters and archived modal parameters. We call this new method Fault Correlation Tools (FaCTs™). FaCTs™ can be used in multiple applications, including structural health monitoring, production qualification testing, and recertification of machinery in field maintenance applications.

Topics in Modal Analysis I, Volume 7, 2014

Modes of vibration are defined as solutions to a set of linear differential equations which chara... more Modes of vibration are defined as solutions to a set of linear differential equations which characterize the resonant dynamic behavior of structures. One of the properties of these linear equation solutions is superposition. That is, the overall response of a structure can be represented as a summation of the responses of each of the modes. In this paper, it is shown how the superposition property of mode shapes can be used to; • Represent Operating Deflection Shapes (ODS's) as a summation of mode shape contributions. • Expand a set of shapes using a set of mode shapes with more DOFs in them. • Decompose a set of frequency or time domain waveforms into a summation of resonance curves. • Scale a set of EMA mode shapes, OMA mode shapes or ODS's using a modal model (a set of scaled mode shapes). • Derive the Modal Assurance Criterion (MAC) as a measure of the correlation between pairs of shapes. All of these applications lend more meaning to the term modal participation, which is commonly used to characterize structural vibration as a summation of resonant contributions. This new definition of modal participation is illustrated with several examples.

Conventional broad-band modal testing is done by acquiring a single-reference or multiple-referen... more Conventional broad-band modal testing is done by acquiring a single-reference or multiple-reference set of FRFs and curvefitting them to obtain modal parameters. Since a (fixed) reference sensor is required throughout the data acquisition process, testing a large structure requires that a (potentially) long wire be used to connect the reference sensor to the acquisition system. In a previous paper [1], a new modal testing method was introduced which does not require the use of a fixed reference sensor. This method is based on the calculation of a series of Transmissibility's, called a TRN chain. This method has several important advantages, 1. Excitation forces need not be acquired 2. Only two response sensors are required for data acquisition 3. The two sensors can be physically close to one another throughout data acquisition Since the excitation forces need not measured, data for calculating a TRN chain can be acquired from an operating machine, or during any test where excit...

A set of scaled mode shapes is a complete representation of the linear dynamic properties of a st... more A set of scaled mode shapes is a complete representation of the linear dynamic properties of a structure. They can be used for a variety of different analyses, including structural modifications, forced response simulations, excitation force calculations from measured responses, and FRF synthesis for comparison with experimental data. When mode shapes are obtained experimentally from operating data, they are not properly scaled to preserve the mass & elastic properties of the structure. By operating data, we mean that only structural responses were measured. Excitation forces were not measured. In this paper, we review the traditional methods for scaling experimental mode shapes using FRFs, and also introduce two new methods that don’t require FRF measurement. The new methods combine a search algorithm with the SDM (Structural Dynamics Modification or eigenvalue modification) algorithm to perform a series of structural modifications until proper scaling of the mode shapes is achieve...

The Structural Dynamics Modification (SDM) method is very useful for solving the so-called forwar... more The Structural Dynamics Modification (SDM) method is very useful for solving the so-called forward variational problem for structures. That is, given changes in a structure's mass, stiffness, or damping properties, SDM efficiently calculates the corresponding changes in its modal properties. Although this method is very useful for exploring potential modifications to real structures using experimentally derived modal data, its practical use has been limited to date, because only simple linear spring, damper, and point mass modification elements have been available in commercial software. In this paper, we show how all of the most commonly used elements of finite element analysis (FEA) can also be used to model structural modifications. These include rods, bars, triangular and quadrilateral plate and shell elements, and tetrahedron, prism, and brick solid elements. An example flat plate structure with a rib stiffener attached to its centerline was tested and modeled using SDM, wi...

Special Topics in Structural Dynamics, Volume 5, 2018

In a recent paper (Richardson et al. (2014) A new measure of shape difference, In: IMAC XXXII, Fe... more In a recent paper (Richardson et al. (2014) A new measure of shape difference, In: IMAC XXXII, February 3–6), we introduced a new metric for comparing two operating .deflection shapes called the Shape Difference Indicator (SDI). In another previous paper (Richardson et al. (2017) Using modal parameters for structural health monitoring, In: IMAC XXXV, January 30–February 2), we used SDI to measure the difference in modal frequencies resulting from a joint stiffness change in a mechanical structure.

In this paper, post-processing methods were applied to three different sets of multiple channel t... more In this paper, post-processing methods were applied to three different sets of multiple channel time domain vibration response data taken from the Z24 highway bridge in Switzerland. The objective of this exercise was to compare the mode shapes resulting from each of these data sets with one another. Ideally, all of the tests should yield the same mode shapes, although perhaps not all modes would be excited in each case. The three different test cases were; Case 1: Two shaker response data, including the simultaneously measured excitation forces. The shakers were driven by uncorrelated random signals. Case 2: Impact response data, including three reference responses but no measured forces. The impact force was provided by a 100 kg. drop weight impactor. Case 3: Ambient response data, including three reference (fixed) responses. Excitation was provided by automobile traffic on an adjoining bridge. Excitation forces were measured in Case 1, so multiple reference Frequency Response Func...

Vibration, 1999

Technical Reports are published for timely dissemination of research results and scientific work ... more Technical Reports are published for timely dissemination of research results and scientific work carried out at the Department of Civil Engineering (DCE) at Aalborg University. This medium allows publication of more detailed explanations and results than typically allowed in scientific journals. Technical Memoranda are produced to enable the preliminary dissemination of scientific work by the personnel of the DCE where such release is deemed to be appropriate. Documents of this kind may be incomplete or temporary versions of papers-or part of continuing work. This should be kept in mind when references are given to publications of this kind. Contract Reports are produced to report scientific work carried out under contract. Publications of this kind contain confidential matter and are reserved for the sponsors and the DCE. Therefore, Contract Reports are generally not available for public circulation. Lecture Notes contain material produced by the lecturers at the DCE for educational purposes. This may be scientific notes, lecture books, example problems or manuals for laboratory work, or computer programs developed at the DCE. Theses are monograms or collections of papers published to report the scientific work carried out at the DCE to obtain a degree as either PhD or Doctor of Technology. The thesis is publicly available after the defence of the degree. Latest News is published to enable rapid communication of information about scientific work carried out at the DCE. This includes the status of research projects, developments in the laboratories, information about collaborative work and recent research results.

Topics in Modal Analysis & Testing, Volume 8, 2019

This paper expands on the ideas presented in two previous papers [1] & [2]. Here, we again show w... more This paper expands on the ideas presented in two previous papers [1] & [2]. Here, we again show with examples how all vibration, whether it is represented in the form of time waveforms, frequency spectra, or ODS's, can be represented as a summation of mode shapes. The title of this paper is actually a universal law which is used for all modal analysis, Fundamental Law of Modal Analysis (FLMA): All vibration is a summation of mode shapes. The modal parameters of a structure can be obtained in two ways, 1. Experimental Modal Analysis (EMA): EMA mode shapes are obtained by curve fitting a set of experimentally derived time waveforms or frequency spectra that characterize the structural dynamics 2. Finite Element Analysis (FEA): FEA mode shapes are obtained as the eigensolution of a set of differential equations that characterize the structural dynamics In this paper, it will be shown how the benefits of analytical FEA mode shapes can be combined with experimental data to yield more robust dynamic models [5], [7]. FEA mode shapes will be used to "decompose" and then "expand" experimental data to include DOFs that cannot or were not determined experimentally [4]. A unique advantage of this approach is that only mode shapes themselves are required. Modal frequency & damping are not used. Another unique advantage is that mode shapes from an FEA model with free-free boundary conditions and no damping can be used. It usually requires a great deal of skill and effort to modify an FEA model and its boundary conditions so that its modal frequencies and mode shapes accurately match EMA modal frequencies and mode shapes. In addition, adding accurate damping to an FEA model is usually so difficult that damping is left out of the model altogether. The approach presented here circumvents both of these difficulties. KEY WORDS Auto power spectrum (APS) Cross power spectrum (XPS) Frequency Response Function (FRF) Operating Deflection Shape (ODS) Experimental Modal Analysis mode shape (EMA mode shape) Finite Element Analysis mode shape (FEA mode shape) Modal Assurance Criterion (MAC) Shape Difference Indicator (SDI)\ Multi-Input Multi-Output (MIMO) Modeling & Simulation

Special Topics in Structural Dynamics, Volume 5, 2018

Tooling used in machining of safety critical components are seldom used without highly frequent i... more Tooling used in machining of safety critical components are seldom used without highly frequent inspection. Worn or damaged tools produce undesirable surface finishes leading often to early failure of the part due to fatigue crack growth. In the development stages of polycrystalline boron nitride tools, an off-line run-to-failure method of tool wear inspection is undertaken which interrupts the cutting process intermittently to measure the tool wear using optical and scanning microscopy. The time consumption of this method leads to expensive tests and bottlenecks in the workshop. The overall aim in industry is to develop an on-line, automated system which is capable of informing the operator of the tool ′ s imminent failure. This paper focuses on treating this process as a preventative maintenance problem by studying whether acoustic emission can be used as an indirect measurement of tool wear at any given time. Acoustic emission measurements taken from the machining process of face turning are investigated here. Basic analysis in the frequency domain using principle component analysis reveals a number of interesting insights into the process. Relationships between the sharpness of the tool and the magnitude of the frequencies suggests promising link between acoustic emission and tool wear.

Conference Proceedings of the Society for Experimental Mechanics Series, 2013

Damping forces are typically ignored during the Finite Element Analysis (FEA) of mechanical struc... more Damping forces are typically ignored during the Finite Element Analysis (FEA) of mechanical structures. In most real structures, it can be assumed that there are several damping mechanisms at work, but they may be difficult to identify, and even more difficult to model. Since both mass & stiffness matrices are available during an FEA, a common method of modeling viscous damping is with a proportional damping matrix. That is, the viscous damping matrix is assumed to be a linear combination of the mass & stiffness matrices. Therefore, in order to model viscous damping with a proportional damping matrix, the two constants of proportionality must be determined. In this paper, a least-squared-error relationship between experimental modal frequency & damping and the proportional damping constants of proportionality is developed. An example is included in which experimental modal parameters are used to calculate the constants of proportionality. The modal parameters of an FEA model with proportional damping are then compared with the original experimental modal parameters.

Proceedings of Spie the International Society For Optical Engineering, 1996

The Structural Dynamics Modification (SDM) algorithm is very useful for solving the so-called for... more The Structural Dynamics Modification (SDM) algorithm is very useful for solving the so-called forward variational problem for structures. That is, given changes in a structure's mass, stiffness, or damping properties, SDM efficiently yields the corresponding changes in its modal properties.

Proceedings of Spie the International Society For Optical Engineering, 2001

In this paper, a new curve fitting technique is introduced for estimating modal parameters from a... more In this paper, a new curve fitting technique is introduced for estimating modal parameters from ambient response data. The curve fitting method is applied to a set of ODS FRFs that were calculated from impact response and ambient response data taken from a concrete bridge. These estimates are then compared with estimates obtained by curve fitting a set of FRFs taken from the same bridge. This paper uses the results of another IMAC paper [1], where post-processing methods were applied to three different sets of multiple channel time domain vibration response data taken from the Z24 highway bridge in Switzerland. The three different test cases were; Case 1: Two shaker test, provided simultaneously acquired acceleration response and excitation force time waveforms. The shakers were driven by uncorrelated random signals. Case 2: Impact test, provided simultaneously acquired acceleration response time waveforms, including three reference (fixed) responses. The impact force was provided by a 100 kg. drop weight impactor, and was not measured. Case 3: Ambient test, provided simultaneously acquired acceleration response time waveforms, including three reference (fixed) responses. Excitation was provided by traffic on an adjoining bridge.

Proceedings of Spie the International Society For Optical Engineering, 1997

Topics in Modal Analysis & Testing, Volume 10, 2016

In this paper, we employ the fact that all experimental vibration data, whether in the form of a ... more In this paper, we employ the fact that all experimental vibration data, whether in the form of a set of FRFs or a set of output-only spectra, is a summation of resonance curves, each curve due to a mode of vibration. We also use this superposition property of modes to calculate a modal participation matrix, a measure of the participation of each mode in the experimental vibration data First we show how this superposition property can be used to curve fit a set of FEA mode shapes to EMA mode shapes or ODS's. The modal participation matrix is calculated as a leastsquared-error solution, so any number of FEA mode shapes can be curve fit to any number of EMA mode shapes or ODS's. Next we show how an expanded and enhanced set of FRFs, Cross spectra or ODS FRFs is obtained by curve fitting FEA mode shapes to experimental data. This approach in an alternative to FEA Model Updating, where an FEA model is modified so that its modes more closely correlate with experimental data. By curve fitting FEA shapes to experimental data, an extending and enhanced dynamic model is obtained which is more suitable for machinery & structural health monitoring, and for troubleshooting noise & vibration problems using SDM and MIMO methods.

Operating Modal Analysis (OMA) has been applied in a number of cases recently for finding the exp... more Operating Modal Analysis (OMA) has been applied in a number of cases recently for finding the experimental modal parameters from structures when their excitation forces cannot be measured. Without force measurement, a classical Experimental Modal Analysis (EMA), which relies on the application of modal parameter estimation, or curve fitting methods to a set of Frequency Response Function (FRF) measurements, cannot be performed. In this paper, we show that the application of a de-convolution window to cross power spectrum data yields the effective recovery of the FRFs involving each vibration response signal. A set of recovered FRFs can then be curve fit using classical FRF-based curve fitting methods to identify the experimental modal parameters of the structure. Use of the de-convolution window is illustrated in an example that uses a FRF matrix model to calculate structural responses to simulate a multireference OMA.

Spie Proceedings Series, 2002

The Complex Mode Indicator Function (CMIF) was originally proposed as a method for improving moda... more The Complex Mode Indicator Function (CMIF) was originally proposed as a method for improving modal parameter estimation. CMIF utilizes singular value decomposition (SVD) on a set of FRFs as a mechanism for extracting parameters. The Multivariate Mode Indicator Function (MMIF) was originally proposed as a method for force appropriation to excite normal modes. MMIF utilizes an eigenvalue solution method on a set of FRFs to isolate modes. Both CMIF & MMIF also have the ability to indicate the presence of closely coupled modes or repeated roots in a structure. Both methods can be used as tools for identifying a minimum set of reference DOFs for performing a modal test. Using a small set of potential reference FRFs and their cross measurements, either CMIF or MMIF can be used to determine the minimum number of references required to adequately excite all the desired modes in a frequency band. This technique has previously been demonstrated to provide reasonable results on several test structures. In this paper, the previous work is extended to provide a testing strategy for determining the number and locations of optimum references for modal testing. Examples are provided to demonstrate its use.

When Operating Modal Analysis (OMA) is used for finding the modal parameters of a structure, the ... more 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.

S V Sound and Vibration, 2003

Topics in Modal Analysis & Testing, Volume 8, 2019

Structural Health Monitoring & Damage Detection, Volume 7, 2017

Topics in Modal Analysis I, Volume 7, 2014

Special Topics in Structural Dynamics, Volume 5, 2018

Vibration, 1999

Topics in Modal Analysis & Testing, Volume 8, 2019

Special Topics in Structural Dynamics, Volume 5, 2018

Conference Proceedings of the Society for Experimental Mechanics Series, 2013

Proceedings of Spie the International Society For Optical Engineering, 1996

Proceedings of Spie the International Society For Optical Engineering, 2001

Proceedings of Spie the International Society For Optical Engineering, 1997

Topics in Modal Analysis & Testing, Volume 10, 2016

Spie Proceedings Series, 2002

S V Sound and Vibration, 2003