Research Papers

Determination of System Damping From the Response Amplitude at Resonance

[+] Author and Article Information
Peter J. Torvik

Professor Emeritus
Fellow ASME
Department of Aeronautics and Astronautics,
Air Force Institute of Technology,
888 Timberlake Court,
Kettering, OH 45429
e-mail: torvikp@asme.org

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 18, 2015; final manuscript received September 10, 2015; published online October 26, 2015. Assoc. Editor: Ronald N. Miles.

J. Vib. Acoust 138(1), 011008 (Oct 26, 2015) (9 pages) Paper No: VIB-15-1172; doi: 10.1115/1.4031601 History: Received May 18, 2015; Revised September 10, 2015

A method for estimating the damping of a vibratory system from the frequency of resonance and the response amplitude at that resonant peak alone is reviewed and applied to the determination of the system loss or quality factors of uniform, rectangular cantilever bare titanium beams and beams with damping enhancing hard coatings. Using results from experiments with several different nonlinear coating systems vibrating in several modes and temperatures, comparisons are given for the damping measures obtained by this method with those obtained by the traditional method for determining system damping from the bandwidth (BW) of the frequency response functions (FRFs). These comparisons, made for strains of engineering interest (to strains over 1000 ppm), show that the BW method generally leads to inflated measures of system energy dissipation and that the inflation (10–70%) depends generally on the degree of nonlinearity, i.e., the extent to which the system loss factor varies with strain amplitude. While developed for the ideal uniform, rectangular, cantilever beam for which the mode shapes are well known, the method may be applied to more complex geometries through the use of a finite element analysis (FEA).

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Fig. 1

Test configuration for experiments: (a) specimen in fixture and (b) schematic of experiment

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Fig. 2

System loss factors of bare and coated beam (RT), two methods: (a) obtained from BWs and (b) obtained by ARs

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Fig. 3

Comparison of system quality factors (RT), two methods: (a) bare beam and (b) with Ti–Al/NiCrAlY coating

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Fig. 5

System loss factors before and after coating and infiltration, APS 700: (a) bare beams and (b) with Ti–Al/bond coat + APS 700

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Fig. 4

System damping with APS 600 infiltrate in TiAl/NiCrAlY coating: (a) system loss factors (AR) and (b) comparison of two methods

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Fig. 7

Damping measures for ASP 600 infiltrated titania–alumina on Ti6Al4V: (a) system loss factors and (b) comparison of two methods

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Fig. 6

Comparisons of system quality factors by two methods: (a) bare beams and (b) with Ti–Al/bond coat + APS 700

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Fig. 9

Damping measures for a magnetomechanical coating (EB-PVD): (a) system loss factors and (b) comparison of two methods

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Fig. 8

Damping measures for titania–alumina on Ti6Al4V with APS 700: (a) system loss factors and (b) comparison of two methods




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