Abstract
The governing equation of the flexural forced vibration of a cantilever sandwich beam excited by a sinusoidal displacement at the clamped end is developed by utilizing the conventional Hamilton's Principle. The effect of damping of the composite beam is incorporated into the elastic equation of motion by utilizing the Correspondence Principle of the linear viscoelastic theory. Several plots for different values of the composite damping factor are presented.
For comparison, an experimental setup was utilized to test different composite beams. The variation of the experimental results with those derived theoretically seem to be in agreement within the frequency range of the first few modes.
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Abbreviations
- A :
-
area of core
- A f :
-
area of face plates
- G :
-
shear modulus of core
- E :
-
elastic modulus of face plates
- E * :
-
complex elastic modulus
- E 1 :
-
storage modulus
- E 2 :
-
loss modulus
- L :
-
cantilever length of beam
- I :
-
moment of inertia of face plates about the neutral axis of the beam
- R a :
-
amplitude ratio
- R f :
-
frequency ratio
- U f :
-
strain energy of face plates
- U o :
-
strain energy of core
- U :
-
total strain energy
- V :
-
kinetic energy of vibrating beam
- Y o :
-
amplitude of forced exciting vibration
- h :
-
thickness of face plates
- c :
-
thickness of core
- b :
-
width of beam
- u :
-
extensional deformation of face plates
- y :
-
vertical deflection
- x :
-
coordinate in longitudinal direction
- t :
-
time
- m :
-
mass per unit length of beam
- p :
-
real part of amplitude-ratio function
- q :
-
imaginary part of amplitude-ratio function
- γ:
-
shear strain
- ω:
-
angular frequency
- ω r :
-
resonant frequency
- αL, βL :
-
complex Eigen mode functions
- λ:
-
complex ratio of αL to βL
- η:
-
specific energy loss per cycle
- η1 :
-
composite damping coefficient
- θ:
-
phase-lag angle
References
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Shoua, E.D. The composite damping capacity of sandwich cantilever beams. Experimental Mechanics 8, 300–308 (1968). https://doi.org/10.1007/BF02326020
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DOI: https://doi.org/10.1007/BF02326020