Abstract
Experimental eigenvalues of both square and rectangular clamped flat plates were measured using digital spectrum analysis. Individual mode shapes were recorded experimentally using holographic interferometry. Plate spectra showing the first 35 modes of vibration for each of the square and rectangular piates were recorded, allowing the experimentally determined eigenvalues to be compared with published theoretical predictions. Over 25 modes for a square plate and 16 modes for a rectangular plate with aspect ratio of 2/3 were recorded holographically. Selected recorded mode shapes are compared with beam mode shapes as well as with modified Bolotin mode shapes, both of which are popular assumed mode shapes in current numerical techniques. It was found that both of these assumed mode shapes agree favorably with the experimental results. The beam mode shapes agree better in some modes; the modified Bolotin mode shapes agree more favorably in others.
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Abbreviations
- a, b :
-
linear dimensions of plate in X and Y directions, respectively
- D :
-
flexural rigidity,Eh 3 / 12(1 - v2)
- D :
-
Young's modulus
- f :
-
frequency, Hz
- h :
-
thickness of plate
- m, n :
-
number of half waves in mode shape in X and Y directions, respectively, i.e., the number of nodal lines in the X and Y directions where each clamped boundary is considered as half a nodal line
- X, Y, Z:
-
Cartesian coordinate axes
- ν:
-
Poisson's ratio
- ϱ:
-
density of plate material per unit plate area
- ω:
-
circular frequency, radians/second
- λ:
-
dimensionless frequency parameter, ωa 2√ϱh/D
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Hazell, C.R., Mitchell, A.K. Experimental eigenvalues and mode shapes for flat clamped plates. Experimental Mechanics 26, 209–216 (1986). https://doi.org/10.1007/BF02320044
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DOI: https://doi.org/10.1007/BF02320044