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The dynamic response of thin membranes by the moiré method

Specimen preparation, test apparatus and test results are reported by the author for a circular and a rectangular membrane

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Abstract

This investigation considers the suitability of the moiré method as a technique for determining the dynamic response of thin membranes. Specimen preparation, test apparatus and test results are reported for a circular and a rectangular membrane. The applicability of the method for measuring transient as well as periodic behavior is discussed. Theoretical and experimental values are compared for the case of periodic response.

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Abbreviations

N :

tensile force in membrane (lb/in.)

η:

deflection

ρ:

mass density per unit area of membrane (lb sec2/in.2)

t :

time (sec)

Z :

total impedance of membrane and surrounding air

Z m :

mechanical impedance of membrane

Z a :

mechanical impedance of surrounding air

A :

viscous or damping portion of air impedance

B :

stiffness and mass portion of air impedance

i :

square root of −1

ω:

circular frequency (rad/sec)

a :

length of rectangular specimen (alongx)

b :

width of rectangular specimen (alongy)

c :

outer radius of circular specimen

x andy :

coordinates associated with rectangular specimen

r and θ:

coordinates associated with circular specimen

m :

number of nodal diameters in circular

n :

number of nodal circles in circular specimen

J n :

denotes Bessel function of first kind and orderm

μ:

number of half wavelengths inx direction on rectangular membrane

v :

number of half wavelengths iny direction on rectangular membrane

α:

\(\sqrt {N/\rho } \)

References

  1. Miles, D. O., “Direct Mechanical Determination of the Dynamic Response of Diaphragms,” Jnl. ASA,36 (8), (1964).

  2. Chobotov, V. A., and Binder, R. C., “Nonlinear Response of a Circular Membrane to Sinusoidal Excitation,” Ibid. Jnl. ASA, (1), (1964).

  3. Rule, E., Suellentrop, F.J., and Perls, T. A., “Second-Order Instrumentation Systems With Frequency-Dependent Stiffness and Damping,” Ibid. Jnl. ASA,31 (11), (1959).

  4. Brüel and Kjaer Technical Review, “Pressure Equalization of Condenser Microphones,” No. 1 (1960).

  5. Ligtenberg, F. K., “The Moiré Method,”Proc. SESA, XII (2),83–98 (1955).

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  6. Morse, P. M., “Vibration and Sound,” McGraw-Hill Book Co. 1948.

  7. Handbook of Experimental Stress Analysis, Ed. M. Hetényi, John Wiley & Sons, 1950.

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Authors and Affiliations

  1. IBM Systems Development Division, Endicott, N. Y.

    Wayne E. Nickola (Staff Engineer)

Authors
  1. Wayne E. Nickola
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Nickola, W.E. The dynamic response of thin membranes by the moiré method. Experimental Mechanics 6, 593–601 (1966). https://doi.org/10.1007/BF02326827

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  • DOI: https://doi.org/10.1007/BF02326827

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