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Experimental cross verification of damping in three metals

The internal damping of aluminum, steel and brass in longitudinal vibration was measured using five techniques and theories to verify the easier technique

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Abstract

In order to ensure a valid damping measurement based on a proposed mathematical model, various laboratory techniques may be employed which require relatively simple instrumentation from which cross correlation of the data may be obtained.

Measurements were made (utilizing an accelerometer, strain gages, and a sound-level meter) under forced (3-dB frequency band or amplification factor Q) and free-vibration conditions at the fundamental and higher axial modes. Analysis (based on the viscous and complex-moduli theories) of the material damping of an aluminum alloy 2024-T4 in longitudinal vibrations shows good cross correlation between theories and experimental methods. These methods were extended to damping measurements of yellow brass and commercial steel. A multiple regression analysis was employed in the damping data reduction and was found to be useful in eliminating the data scatter. A sound-level meter was used as a noncontacting test method which proved useful even though its use does have drawbacks.

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Abbreviations

A :

cross-section area (m2)

B :

adiabatic bulk modulus (N/m2)

C :

wave velocity (m/s)

E :

elastic modulus (N/m2)

E * :

complex modulus (N/m2)

F o :

input force (N)

f :

frequency (Hz)

k 1 ,k d ,k s :

proportionality constant

l :

length of the specimen (m)

m :

attached mass (Kg)

P :

sound pressure (N/m2)

Q :

amplification factor

Q 1 :

strain-amplification factor

Q 2 :

displacement at the free end/displacement at the fixed end

S :

displacement of a particle of the transmitting medium (m)

t :

time (s)

u :

displacement in specimen (m)

U o :

peak amplitude of the displacement at the end point of a rod (m)

x :

distance from a reference point (m)

α:

damping coefficient due to surrounding fluid

δ:

logarithmic decrement

ε:

strain (m/m)

\(\tilde \varepsilon\) :

dynamic strain (m/m)

η:

damping loss factor

λ:

wavelength (m)

ρ:

density (Kg/m3)

σ:

stress (N/m2)

\(\tilde \sigma\) :

dynamic stress (N/m2)

\(\bar \tau\) :

viscosity coefficient

\(\phi _\eta\) :

phase angle (rad)

Ω:

fundamental angular natural frequency (rad/s)

\(\omega _n\) :

angular natural frequency (rad/s)

\(\omega _1 ,{\text{ }}\omega _2\) :

angular frequency at 3 dB (rad/s)

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Authors and Affiliations

  1. Iowa State University, 50010, Ames, IA

    J. M. Lee (Graduate Assistant) & K. G. McConnell (Associate Professor)

Authors
  1. J. M. Lee
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  2. K. G. McConnell
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Lee, J.M., McConnell, K.G. Experimental cross verification of damping in three metals. Experimental Mechanics 15, 347–353 (1975). https://doi.org/10.1007/BF02318875

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  • DOI: https://doi.org/10.1007/BF02318875

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