Study of the coupled free vibration of helical springs

AIAA Journal ◽  
1992 ◽  
Vol 30 (5) ◽  
pp. 1443-1447 ◽  
Author(s):  
W. Jiang ◽  
T. L. Wang ◽  
W. K. Jones
Keyword(s):  
Free Vibration ◽  
Helical Springs

scholarly journals Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping

2012 ◽  
Vol 19 (6) ◽  
pp. 1167-1180 ◽  
Author(s):  
A.M. Yu ◽  
Y. Hao
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Cross Sectional ◽  
Helical Springs

Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.

Free Vibration of Helical Springs

1991 ◽  
Vol 58 (1) ◽  
pp. 222-228 ◽  
Author(s):  
W. Jiang ◽  
W. K. Jones ◽  
T. L. Wang ◽  
K. H. Wu
Keyword(s):  
Free Vibration ◽  
Theoretical Investigation ◽  
Torsional Vibration ◽  
Periodic Wave ◽  
The Other ◽  
Compressive Deformation ◽  
Torsional Deformation ◽  
Helical Springs ◽  
The Individual

This paper presents a theoretical investigation of the coupled extensional-torsional vibration of helical springs. The study shows that two types of periodic wave will propagate through the spring, one characterizing the extensional-compressive deformation and the other one, the torsional deformation. The shapes of the individual waves are simple, but the oscillation of the spring is complex due to the interaction and superposition of the component waves.

Fundamental Frequencies of Uniaxial Composite Barrel and Hyperboloidal Springs

1999 ◽  
Author(s):  
Vebil Yildirim ◽  
Erol Sancaktar ◽  
Erhan Kiral
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Shear Deformation Theory ◽  
Variable Coefficients ◽  
Axial Deformation ◽  
Circular Section ◽  
First Order ◽  
Helical Springs ◽  
Fundamental Frequencies ◽  
Constant Pitch

Abstract The fundamental natural frequencies of uniaxial composite non-cylindrical helical springs (barrel and hyperboloidal types) are determined theoretically based on the transfer matrix method. The rotary inertia, shear and axial deformation effects are considered with the first order shear deformation theory. The overall transfer matrix is obtained by integrating the twelve scalar ordinary differential equations with variable coefficients governing the free vibration behavior of non-cylindrical helical springs made of an anisotropic material. Numerical results are verified with the reported values for isotropic non-cylindrical helices. A parametric study is performed to investigate the effects of the number of active coils (n = 5–0), the helix pitch angle (α = 5° and 25°), the ratio of the minimum to maximum cylinder radii (Rmin/Rmax), and the ratio of the maximum cylinder diameter to the wire diameter (Dmax/d) on the fundamental free vibration frequencies of constant-pitch composite barrel and hyperboloidal helical springs with circular section and fixed-fixed ends.

Free Vibration of Helicoidal Beams of Arbitrary Shape and Variable Cross Section

2002 ◽  
Vol 124 (3) ◽  
pp. 397-409 ◽  
Author(s):  
Wisam Busool ◽  
Moshe Eisenberger
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Rotational Inertia ◽  
Variable Cross ◽  
Dynamic Stiffness Matrix ◽  
Helical Springs

In this study, the dynamic stiffness method is employed for the free vibration analysis of helical springs. This work gives the exact solutions for the natural frequencies of helical beams having arbitrary shapes, such as conical, hyperboloidal, and barrel. Both the cross-section dimensions and the shape of the beam can vary along the axis of the curved member as polynomial expressions. The problem is described by six differential equations. These are second order equations with variable coefficients, with six unknown displacements, three translations, and three rotations at every point along the member. The proposed solution is based on a new finite-element method for deriving the exact dynamic stiffness matrix for the member, including the effects of the axial and the shear deformations and the rotational inertia effects for any desired precision. The natural frequencies are found as the frequencies that cause the determinant of the dynamic stiffness matrix to become zero. Then the mode shape for every natural frequency is found. Examples are given for beams and helical springs with different shape, which can vary along the axis of the member. It is shown that the present numerical results agree well with previously published numerical and experimental results.

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