A Numerical Study on the Free Vibration of Symmetric Cross-Ply Laminated Cylindrical Helical Springs

1999 ◽  
Vol 66 (4) ◽  
pp. 1040-1043 ◽  
Author(s):  
V. Yildirm
Keyword(s):  
Free Vibration ◽  
Deformation Theory ◽  
Numerical Study ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Continuous System ◽  
First Order ◽  
Helical Springs ◽  
Helix Pitch ◽  
The Mathematical Model

The free-vibration problem of (0°/90°/90°/0°) laminated composite cylindrical helical springs is modeled theoretically as a continuous system. The first-order shear deformation theory is employed in the mathematical model. The free-vibration equations are solved by the transfer matrix method. A nondimensional parametric study is performed to investigate the effects of the number of active coils, the ratio of the diameter of the cylinder to the thickness of section, the helix pitch angle, and material types on the first six natural frequencies of helical springs with square section and fixed-fixed ends.

The influences of magnetostrictive layers on active vibration control of laminated composite rotating cylindrical shells based on first-order shear deformation theory

2019 ◽  
Vol 233 (13) ◽  
pp. 4606-4619 ◽  
Author(s):  
Shahin Mohammadrezazadeh ◽  
Ali Asghar Jafari
Keyword(s):  
Vibration Control ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Cylindrical Shells ◽  
Active Vibration Control ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
First Order ◽  
Vibration Responses ◽  
Active Vibration

In this paper for the first time, active vibration control of rotating laminated composite cylindrical shells embedded with magnetostrictive layers as actuators by means of first-order shear deformation theory is studied. Vibration equations of the rotating shell are extracted using Hamilton principle considering the effects of initial hoop tension, Coriolis, and centrifugal forces. The vibration differential equations are reduced to algebraic ones through Galerkin method. The validity of the study is proved by the comparison of some results with the literature results. Eventually, the influence of several parameters on damping characteristics and vibration responses are investigated in detail.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

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