FOCUS: Dr. Allen is the principal investigator on over $3.3M of funded research ($5.5M if funds expended by others are included). Our research group is focused on experimentally probing and analytically predicting the dynamic motion of structures, especially:

- Nonlinear dynamics of geometrically nonlinear structures, extensions to substructuring for these structures and test and model updating methods
- Nonlinear normal modes and their utility in design and response prediction for nonlinear dynamic systems
- Methods to experimentally characterize and predict damping and nonlinearity in structures due to friction at bolted/riveted/press-fit interfaces
- Test strategies and data analysis procedures to characterize linear, nonlinear and time-varying dynamic systems
- Experimental/analytical substructuring methods and applications to noise and response prediction during product development

Some current projects are described below. (Note that this page is not updated frequently. See the Publications page for papers on our most recent projects.)

CURRENT PROJECTS:

**“New Method for System Identification of Nonlinear Geometry,”
**

In industry, constructing useful models is an important aspect of analysis. Many models, no matter how detailed, require additional measurements of the system in order to bring them into alignment with reality, and so that further analysis can be conducted.

Kwarta starts with a discussion of methods to estimate nonlinear normal modes, such as SNRM (Single Nonlinear Resonant Mode Algorithm). With measurements of a nonlinear resonance point and a near-resonance point, a nonlinear normal mode can be estimated by rearranging linear theory. As a result, phase and damping can be expressed in the frequency domain.

A discussion is made about NIFO (Nonlinear Identification through Feedback of the Output) that handles complex and frequency dependent inputs and outputs. The outputs are small linear systems. Kwarta extends this method to create a large linear system of frequency independent parameters to create an undetermined system, which is solved by taking additional data points. This new method is called NIXO (Nonlinear Identification through eXtended Output).

In case studies, it is found that NIXO effectiveness at identifying system parameters is independent of input signal (unlike NIFO) and is computationally 1.31-1.34 times faster. In case studies, NIXO shows agreement with NIFO. In addition, if NIXO and SNRM results agree, then there is a good chance that NIXO’s results are accurate.

**“Substructure Reduction Techniques to Capture Joint Nonlinearity,”**

When designing components in structural dynamics, the industry standard process is to begin with a design, followed by modeling, then testing to make sure the model is valid, followed by making design changes. Repeat until all modeling and testing suggest that the design is ready to be implemented.

However, additional complications arise when the design in question also includes joints such as screws or nuts (virtually everything). Modeling joints is computationally intensive, making it difficult to model joints, which may lead to failure if modeling or testing does not reveal where a joint will fail. Failing to predict when a joint will fail dangerous, especially in the aerospace industry where the environments tend to be especially intense. Joint failure is responsible for many crashes and accidents in aircraft.

Another issue with current models is that they tend to trade accuracy in measuring damping for inaccuracy in measuring frequency behavior, or vice versa.

In “Substructure Reduction Techniques to Capture Joint Nonlinearity,” Singh expands upon existing methods to model joint nonlinearities with a novel technique called “S-CC reduction.” If successful, it may be possible to capture both the frequency and damping behavior of nonlinear joint problems with greater accuracy, while also using less computational resources.

**PAST PROJECTS:**

*“Testing And Model Updating For Geometrically Nonlinear Hypersonic **Vehicle Assemblies Using Nonlinear Normal Modes,” **P**I, Air Force Office **of Scientific Research, Structural Mechanics & Prognosis Program under **Jaime Tiley, 2017-2020, $455,793. *

Read the news release at: https://sd.engr.wisc.edu/nonlinear-designs/

“Modeling and Identification of Damping due to Bolted Interfaces,” PI, Sandia National Laboratories, Program Manager: Matthew R.W. Brake, 2016-2018, $108k

The presentation below provides an overview to our work in this area.

Also, a tutorial on this topic is available here.

“Noninvasive Assessment of in Vivo Tissue Loads to Enhance the Treatment of Gait Disorders,” Collaborative Research with the UW-Madison Neuromuscular Biomechanics Group, “Gauging force by tapping tendons,”. For athletes and weekend warriors alike, returning from a tendon injury too soon often ensures a trip right back to physical therapy. However, a new technology developed by University of Wisconsin-Madison engineers could one day help tell whether your tendons are ready for action…. (Click here to read the full article)

SELECTED PAST PROJECTS:

“Method for Experimental Identification of Nonlinear Dynamic Systems of Unknown Form and Order with Application to Human Gait,” PI, National Science Foundation, Program Manager: Eduardo Misawa, 2010-2014, $279,982

- Click here for a summary of this project.
- News post on this project:

Allen & Sracic recently showed that newly developed system identification methods can be used to increase the spatial resolution of laser vibrometer measurements by at least two orders of magnitude. The new method produces high-resolution measurements of the deflection shape of the structure, in the time that traditional methods require for a single point. Further advances have allowed this method to be used to find the vibration modes of a wind turbine blade as it vibrated due to ambient wind. This information can be used to modify the design of a turbine to avoid failure, or to monitor the health of the turbine in the field. Click on the picture below for more information.

For a video showing how continuous-scan laser vibrometry (CSLDV) works, follow this link to see a video of a CSLDV test on a downhill ski: (Low Resolution 18 MB), (High Resolution 68 MB)

“Substructuring with Nonlinear Subcomponent Models Based on Nonlinear Normal Modes with Application to Hypersonic Vehicle Design,” PI, Young Investigator Program, Air Force Office Of Scientific Research, Program Manager: David Stargel, 2011-2014, $364,180

Read the news release at https://sd.engr.wisc.edu/sr71/.

“Experimental/Analytical Substructuring under Uncertainty,”co-PI, Sandia National Laboratories, 2007-2015*, $239,604* (*total of ongoing grants through 2012).

The natural frequencies of a system depend on the dynamic properties of all of its parts. For example, this means that one cannot say whether the crankshaft of an engine will fail due to resonant vibration without knowing the dynamic properties of the transmission, axles, tires, etc… This is a challenge since each of these parts may be built by a different supplier. This work is developing new methods of predicting the dynamics of assemblies such as these. One can avoid having to create a simulation model for a certain subcomponent (which may be difficult to model) by performing a dynamic test and coupling the test model to the model for the rest of the system. Experimental models contain different types of uncertainties than analytical models, and these issues must be considered to obtain meaningful predictions.

Other Past Projects

The Atomic Force Microscope is a versatile new tool that allows one to image, manipulate and probe structures ranging in size from hundreds of microns (the size of common cells) down to individual atoms in a lattice. The AFM has already contributed to revolutionary advancements in surface science, biology, chemistry, electronics and medicine. The AFM must be calibrated to determine the force that one is exerting on a sample. This project evaluates the effect of assumptions that are made when calibrating AFM probes, some of which may reduce the accuracy of, or even invalidate, the calibration. Click here to see a presentation describing some of our work in this area.

Image above shows Histograms of the contact velocity of a high-speed switch after optimization, considering the uncertainty in the manufacturing process. If uncertainty is not considered, one obtains worse performance than if no optimization had been performed at all. (click on the image above to see a presentation summarizing this work)

Some of Dr. Allen’s Research Prior to Joining UW-Madison: