# Browsing by Subject "Modal analysis"

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Item Efficient frequency response computation for structures with structural damping(2015-04-03) Palmer, Jeremiah Fletcher; Bennighof, Jeffrey Kent, 1960-; Bui, Tan T; Fahrenthold, Eric P; van de Geijn, Robert; Sirohi, JayantShow more The modern procedure for analyzing the dynamics of a large, complex structure, such as an automobile, is to use the finite element method to discretize the structure with millions of degrees of freedom. For the steady-state response to a harmonic excitation, a frequency response problem (FRP) is derived for the finite element discretization. To ease computational cost, modal analysis is performed, creating a corresponding FRP in an approximating modal subspace with a substantial reduction in dimension. Typically, more than one level of structural damping is present in a complex structure. This results in a fully populated modal damping matrix, so that the frequency-dependent coefficient matrix of the modal FRP is full. This problem is traditionally solved using a brute-force approach, which can be prohibitively expensive since it requires O(n³) operations for each of the hundreds of frequencies. This dissertation presents two new approaches for solving modal FRPs of automobile structures that have any composition of structural damping. Each approach requires a single frequency-independent O(n³) operation which changes the full coefficient matrix of the modal FRP into one with a simpler form. The first approach presents a new method which creates a low rank approximation of the modal structural damping matrix. The second approach is used when the modal structural damping matrix has high rank and relies on a new method for determining an accurate eigenvalue decomposition of a complex symmetric matrix. Computing responses using these two approaches then only requires O(n²) operations for every frequency. Automobile companies perform analyses on computers with multi-core CPU processors and graphics processing units which can perform dense linear algebra operations with high efficiency. This dissertation shows how the two approaches are implemented to take advantage of these parallel technologies. The accuracy and performance of the two new approaches are presented and compared with the brute-force approachShow more Item Frequency response computation for complex structures with damping and acoustic fluid(2004-12) Kim, Chang-wan, 1969-; Bennighof, Jeffrey Kent, 1960-Show more Modal frequency response analysis is a very economical approach for large and complex structural systems since there is an enormous reduction in dimension from the original finite element frequency response problem to the number of modes participating in the response. When damping does not exist, the modal frequency response problem is inexpensive to solve because it becomes uncoupled. However, when damping exists, the modal damping matrices can become fully populated, making the modal frequency response problem expensive to solve at many frequencies. The conventional approach to solve the modal frequency response problem with damping is to use either direct methods with O(n 3 ) operations at each frequency, or iterative methods with O(n 2 ) operations per iteration and numerous iterations at each frequency, where n is the number of modes used to represent the response. Another approach is to use a state space formulation and an eigensolution to uncouple the damped modal frequency response problem, but this doubles the dimension of the problem. All of the existing traditional methods are very expensive for systems with many modes. In this dissertation, a new algorithm to solve the modal frequency response problem for large and complex structural systems with structural and viscous damping is presented. The newly developed algorithm, fast frequency response analysis (FFRA), solves the damped modal frequency response problem with O(n 2 ) operations at each frequency. The FFRA algorithm considers both structural damping and viscous damping for structural systems. When only structural damping exists, the modal frequency response problem is uncoupled by applying the eigensolution of the complex symmetric modal stiffness matrix. A complex symmetric matrix eigensolver (CSYMM) has been developed to solve the complex symmetric matrix eigenvalue problem efficiently. If a viscous damping matrix is also present, the algorithm handles viscous damping by noting that the rank of the viscous damping matrix is typically very low for the problems of interest in the automobile industry because of the small number of viscous damping elements such as shock absorbers and engine mounts. This algorithm has also been applied to the coupled response of systems consisting of a light acoustic fluid and structure, and systems with enforced motion. Also, the algorithm is implemented in parallel on shared memory multiprocessor machines for performance improvement. The FFRA algorithm is evaluated for several industry finite element models which have millions of degrees of freedom. The FFRA algorithm produces outstanding performance compared to the methods available in the commercial finite element software MSC.Nastran or NX.Nastran in terms of analysis time, since the new algorithm is many times faster while obtaining almost the same accuracy as MSC.Nastran. Therefore, the new FFRA algorithm makes inexpensive high frequency analysis possible and extends the capability of solving modal frequency response analysis to higher frequencies.Show more Item Modal analysis of long wave equations(2002) Socha, Katherine Sue; Vishik, Mikhail; Bona, J. L.Show more This work studies the use of modal expansion approximations of solutions of model long wave equations. Such model equations are of interest to oceanographers and engineers because they describe the propagation of surface water waves, used in near-shore models of sandbar formation. General theoretical results are derived for standard long wave models in the form of dispersive, nonlinear partial differential equations. Particular numerical results are computed for such model equations, including the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the Benjamin-Ono equation, among others.Show more Item Operational modal analysis of a rotating cantilever beam using high-speed digital image correlation(2015-12) Rizo-Patron, Sergio Sebastian; Sirohi, Jayant; Ravi-Chandar, KrishnaswamyShow more A novel procedure to perform an operational modal analysis on a rotating cantilever beam is described. This procedure uses Digital Image Correlation (DIC) to measure the deformation of a beam from images captured with a pair of high-speed digital cameras. Modal parameters including natural frequencies and mode shapes are determined from the deformation data through application of the Ibrahim Time Domain method. The procedure was validated on a 2 m diameter, Mach-scale helicopter rotor, excited by a jet of compressed air. Images of the rotor blade were captured at a sampling rate of 1000 Hz at rotational speeds up to 900 RPM. The out-of-plane deformation of the rotor was measured with a spatial resolution of 7.2 mm and an accuracy of 60 μm, or 0.006% of the rotor radius. The first three flap bending modes were identified at each rotational speed and compared to an analytical model of the system. It was found that the analytical model over-predicted the natural frequencies due to differing boundary conditions between the model and the experiment, and so the analytical frequencies were scaled to the results of a rap test using traditional frequency domain analysis. The scaled analytical and experimental natural frequencies agreed to within 0.2% in the best case and 10.0% in the worst case. The experimental mode shapes were also found to closely match the analytical model. The results of this test demonstrate the ability of this procedure to determine the modal parameters of rotating cantilever beams.Show more Item Screening procedure to identify power system events of the Texas Synchrophasor Network(2012-05) Sant, Aprajita; Grady, W. M.; Santoso, SuryaShow more This work presents a method for screening synchrophasor data to search for power system events of interest. The method employs prony algorithm to perform modal analysis and estimate mode amplitude, frequency, and damping ratio on the data obtained from the Texas Synchrophasor Network. The procedure uses seven different Linear Prediction Model (LPM) orders, plus a 10 second window width that slides in steps of 1 second, to minimize the possibility of overlooking events of interest. Further, the algorithm is extended to include user defined modal characteristics thresholds, window length and step size to capture specific power system events.Show more Item Seismic analysis of a retrofitted reinforced concrete building in Mexico City(2019-08-16) Ruiz Barba, Ulises; Murcia-Delso, JuanShow more This thesis presents a study on the dynamic characteristics and seismic performance of a retrofitted concrete building located in the soft soil area of Mexico City. The original structure consisted of reinforced concrete frames in two orthogonal directions. Damaged during an earthquake in 1979, the building was retrofitted by installing external steel braces in its transverse direction and reinforced concrete infill walls in its longitudinal direction. The retrofitted structure presented minor damage after the 1985 and 2017 earthquakes. The structural response of the building and the effectiveness of the retrofit has been assessed using an analytical model of the structure, in combination with data from post-earthquake damage inspections and ambient vibration tests. A three-dimensional linear elastic model of the building has been developed to study the modal characteristics of the building and its seismic response during the 1985 and 2017 events. The results of the analyses have been used to discuss the effects of the retrofit intervention, as well as the influence of the soil-structure interaction and other modeling assumptions in the response of the building.Show more