Summary
The vibrations of a concentrated mass suspended from a coiled spring are studied when the material of the spring is capable of deforming both elastically and in consequence of creep. When the creep law is linear, the attenuation of the vibrations is independent of the amplitude. When the creep law is non-linear in the sense that the creep rate is a power function of the force transmitted by the spring, with the exponent greater than unity, the attenuation increases with increasing amplitude.
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Abbreviations
- g :
-
acceleration of gravity
- i :
-
= (-1)1/2
- k 1 :
-
spring constant
- k 2 :
-
dashpot constant
- m :
-
mass of particle
- n :
-
exponent in creep law
- p :
-
exponent
- r :
-
ratio defined in Eq. (81)
- t :
-
time
- ν :
-
velocity of motion of particle
- x :
-
displacement of particle
- A, B, C :
-
constants of integration
- C0, C1, C2:
-
coefficients of Fourier series
- C*1:
-
second approximation to value of C1
- D :
-
kinetic energy dissipated by creep
- D1, D2:
-
non-dimensional coefficients of Fourier series defined in Eq. (115)
- D*1:
-
second approximation to value of D1
- F :
-
force acting on spring
- G :
-
equivalent initial amplitude of displacement defined in Eq. (100)
- I :
-
integrand defined in Eq. (87)
- J :
-
definite integral defined in Eq. (86)
- R :
-
ratio of two consecutive maxima of velocity of oscillatory part of motion
- R*:
-
absolute value of ratio of amplitudes of velocity of oscillatory part of motion at t = π/ω and at t = 0
- T :
-
natural period of oscillation
- V :
-
increment in velocity at t = 0
- W cr :
-
energy absorbed by creep deformations
- α :
-
variable
- β :
-
damping constant defined in Eq. (16)
- δ :
-
correction to value of D1 defined in Eq. (128)
- ε :
-
increment in circular frequency
- ξ :
-
displacement of oscillatory part of motion defined in Eq. (7)
- ψ :
-
ratio of circular frequencies of damped and undamped systems
- ω :
-
circular frequency of damped system
- ω 0 :
-
circular frequency of undamped system
- Φ :
-
force in spring in absence of gravity defined in Eq. (7)
- Ω :
-
parameter defined in Eq. (69)
- cr :
-
creep
- cr st :
-
steady creep
- el :
-
elastic
- p :
-
particular
- st :
-
static
- T :
-
at end of period when t = T
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© 1962 Springer-Verlag OHG., Berlin/Göttingen/Heidelberg
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Hoff, N.J. (1962). Damping of the Vibrations of a Coiled Spring Due to Creep. In: Hoff, N.J. (eds) Creep in Structures. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86014-0_20
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DOI: https://doi.org/10.1007/978-3-642-86014-0_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-86016-4
Online ISBN: 978-3-642-86014-0
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