In the work based on the stiffness method reported in this paper, considering the rotary inertia, the axial and shear deformation terms, the natural frequencies of conical, barrel and hyperboloidal-type helical springs fixed at both ends are calculated. The results are presented in dimensionless graphical forms for the six lowest natural frequencies of all types of noncylindrical helices for a wide range of vibrational parameters which influence the natural frequencies. A discussion about the effects of vibrational parameters on the natural frequencies is also presented.
Issue Section:
Technical Papers
1.
Bathe, K. J., and Wilson, E. L., 1976, Numerical Methods in Finite Element Analysis, Prentice-Hall Englewood Cliffs, NJ.
2.
Craig, R. R., 1981, Structural Dynamics—An Introduction to Computer Methods, John Wiley and Sons, New York.
3.
Epstein
I.
1947
, “The Motion of A Conical Coil Spring
,” Journal of Applied Physics
, Vol. 18
, pp. 368
–374
.4.
Haktanir
V.
Kiral
E.
1993
, “Statical Analysis of Elastically and Continuously Supported Helicoidal Structures by the Transfer and Stiffness Matrix Methods
,” Comput. Struct.
, Vol. 49
, pp. 663
–677
.5.
Nagaya
K.
Takeda
S.
Nakata
Y.
1986
, “Free Vibration of Coil Spring of Arbitrary Shape
,” Int. J. Numer. Meth. Engng.
, Vol. 23
, pp. 1081
–1099
.6.
Nguyen
D. T.
Arora
J. S.
1986
, “An Algorithm for Solution of Large Eigenvalue Problems
,” Comput. Struct.
, Vol. 24
, No. 4
, pp. 645
–650
.7.
Mottershead
J. E.
1980
, “Finite Elements for Dynamical Analysis of Helical Rods
,” Int. J. Mech. Sci.
, Vol. 22
, pp. 267
–283
.8.
Omid
B. N.
Parlett
B. N.
Taylor
R. L.
1983
, “Lanczos versus Subspace Iteration for Solution of Eigenvalue Problems
,” Int. J. Numer. Meth. Engng.
, Vol. 19
, pp. 859
–871
.9.
Pestel, E. C., and Leckie, F. A., 1963, Matrix Methods in Elastomechanics, McGraw-Hill, New York.
10.
Weingarten
V. I.
Ramanathan
R. K.
Chen
C. N.
1983
, “Lanczos Eigenvalue Algorithm for Large Structures on a Minicomputer
,” Comput. Struct.
, Vol. 16
, pp. 253
–257
.11.
Wilson
E. L.
Itoh
T.
1983
, “An Eigen Solution Strategy for Large Systems
,” Comput. Struct.
, Vol. 16
, pp. 259
–265
.12.
Yıldırım
V.
1995
, “Investigation of Free Vibration of Helical Springs by the Stiffness Matrix Method
,” Turkish Journal of Engineering and Environmental Sciences
, Vol. 19
, No. 4
, pp. 343
–356
(in Turkish).13.
Yıldırım
V.
1996
a, “The Myklestad’s Method for the Free Vibration of Non-Cylindrical Helical Springs
,” Turkish Journal of Engineering and Environmental Sciences
, Vol. 20
, No. 2
, pp. 121
–128
(in Turkish).14.
Yıldırım
V.
1996
b, “Investigation of Parameters Affecting Free Vibration Frequency of Helical Springs
,” Int. J. Numer. Methods Eng.
, Vol. 39
, No. 1
, pp. 99
–114
.15.
Yıldırım
V.
1997
a, “A Computer Program for the Free Vibration Analysis of Elastic Arcs
,” Comput. Struct.
, Vol. 62
, No. 3
, pp. 475
–485
.16.
Yıldırım
V.
Ince
N.
1997
b, “Natural Frequencies of Helical Springs of Arbitrary Shape
,” Journal of Sound and Vibration
, Vol. 204
, No. 2
, pp. 311
–329
.17.
Yıldırım
V.
1997
c, “Free Vibration Analysis of Non-Cylindrical Coil Springs by Combined Use of the Transfer Matrix and the Complementary Functions Methods
,” Communications in Numerical Methods in Engineering
, Vol. 13
, pp. 487
–494
.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.