Nonlinear Natural Frequencies of Rotating Composite Thin-Walled Beam with Geometrical Nonlinear

2013 ◽  
Vol 683 ◽  
pp. 779-782 ◽  
Author(s):  
Yong Sheng Ren ◽  
Shuang Shuang Sun ◽  
Chun Jin Zhang
Keyword(s):  
Free Vibration ◽  
Nonlinear Eigenvalue Problem ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Laminated Composite ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Energy Principle ◽  
Rotating Speed ◽  
Thin Walled

The nonlinear governing equations of motion for the rotating composite thin-walled beam are derived using Hamilton’s energy principle and variational-asymptotical method (VAM) on the basis of von Karman’s assumption. The nonlinear vibration of the beam is studied using Galerkin method and harmonic balance method. The large amplitude free vibration of the beam can be expressed as a nonlinear eigenvalue problem and solved using an iterative solution procedure. Numerical results are obtained for Circumferentially Uniform Stiffness (CUS )laminated composite configuration thin-walled beam. The study exhibit the effect of the fiber orientation and rotating speed on nonlinear natural frequency vs. amplitude curves. The developed model can be capable of describing nonlinear free vibration behaviors of rotating composite thin-walled beam with large deformations.

Free Vibrations of Laminated Composite Noncircular Thin Cylindrical Shells

1994 ◽  
Vol 61 (4) ◽  
pp. 861-871 ◽  
Author(s):  
K. Suzuki ◽  
G. Shikanai ◽  
A. W. Leissa
Keyword(s):  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Power Series Expansion ◽  
Laminated Composite ◽  
Energy Functional ◽  
Solution Procedure ◽  
Free Vibrations ◽  
Layer Stacking ◽  
Kinetic Energy Functional ◽  
Energy Principles

An exact solution procedure is presented for solving free vibration problems for laminated composite noncircular cylindrical shells. Based on the classical lamination theory, strain energy and kinetic energy functional are first derived for shells having arbitrary layer stacking sequences. These functional are useful for a general analysis based upon energy principles. However, in the present work equations of motion and boundary conditions are obtained from the minimum conditions of the Lagrangian (Hamilton’s principle). The equations of motion are solved exactly by using a power series expansion for symmetrically laminated, cross-ply shells having both ends freely supported. Frequencies are presented for a set of elliptical cylindrical shells, and the effects of various parameters upon them are discussed.

On the Modeling of Coupled Vibration of Rotating Thin-Walled Closed-Section Composite Beams

2010 ◽  
Vol 26-28 ◽  
pp. 758-763
Author(s):  
Yong Sheng Ren ◽  
Xiang Hong Du ◽  
Wen Li Yao
Keyword(s):  
Equations Of Motion ◽  
Laminated Composite ◽  
Coupled Vibration ◽  
Cross Sectional ◽  
Box Beam ◽  
Vibration Model ◽  
Thin Walled ◽  
The Galerkin Method ◽  
Sectional Analysis ◽  
Asymptotical Method

The free vibration model of a rotating composite thin-walled closed-section beams is presented in this paper. The two-dimensional cross-sectional analysis based on the variational-asymptotical method(VAM) is combined with the Hamilton’s principle to derive the equations of motion and associated boundary conditions of the beams. The Galerkin method is employed in order to solve the coupled differential equations. The natural frequency results obtained for the present model are compared with those of the existing models. Numerical results are obtained for the laminated composite cantilevered box beam with Circumferentially Uniform Stiffness(CUS) configuration, the effects of the fiber orientation, pitch and precone on the natural frequencies associated with coupled vibration modes are investigated.

scholarly journals Dynamic Analysis of a Tapered Composite Thin-Walled Rotating Shaft Embedded with SMA Wires Using the Generalized Differential Quadrature Method

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Weiyan Zhong ◽  
Feng Gao ◽  
Yongsheng Ren ◽  
Xiaoxiao Wu ◽  
Hongcan Ma
Keyword(s):  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Governing Equations ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Generalized Differential Quadrature Method ◽  
Thin Walled ◽  
Generalized Differential

A dynamical model is developed for the tapered composite thin-walled rotating shaft with shape memory alloy (SMA) wires embedded in. The SMA wires are embedded at an interlayer of the shaft and arranged along the conical surface of the tapered composite shaft. Recovery stresses generated during the phase transformation are calculated based on one-dimensional Brinson’s model. The governing equations are obtained based on a refined variational asymptotic method (VAM) and Hamilton’s principle. The partial differential equations of motion are reduced to the ordinary differential governing equations by using the generalized differential quadrature method (GDQM). Numerical results of natural frequencies and critical speeds are obtained. The effects of the fraction of SMA wires, the initial strain of SMA wires, temperature, ply angle, taper ratio, boundary conditions, and rotating speed on the frequency characteristics are investigated.

scholarly journals Free Vibration and Damping of Rotating Composite Shaft with a Constrained Layer Damping

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Yongsheng Ren ◽  
Yuhuan Zhang
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Constrained Layer Damping ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Damping Characteristics ◽  
Reinforced Composite ◽  
Composite Shaft ◽  
Passive Constrained Layer Damping

The free vibration and damping characteristics of rotating shaft with passive constrained layer damping (CLD) are studied. The shaft is made of fiber reinforced composite materials. A composite beam theory taking into account transverse shear deformation is employed to model the composite shaft and constraining layer. The equations of motion of composite rotating shaft with CLD are derived by using Hamilton’s principle. The general Galerkin method is applied to obtain the approximate solution of the rotating CLD composite shaft. Numerical results for the rotating CLD composite shaft with simply supported boundary condition are presented; the effects of thickness of constraining layer and viscoelastic damping layers, lamination angle, and rotating speed on the natural frequencies and modal dampings are discussed.

scholarly journals Behavior of Uniform Anisotropic Beams of Rectangular Section under Transverse Impact of a Mass

1997 ◽  
Vol 4 (2) ◽  
pp. 125-141 ◽  
Author(s):  
Lu Chun ◽  
K. Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Solution Procedure ◽  
Beam Deflection ◽  
Transverse Impact ◽  
Lagrange Principle ◽  
Arbitrary Boundary ◽  
Force Contact ◽  
Laminated Composite Beam

A numerical method is presented to investigate the dynamic response of uniform orthotropic beams subjected to an impact of a mass. Higher order shear deformation and rotary inertia are included in the analysis of the beams. The impactor and laminated composite beam are treated as a system. The nonlinear differential governing equations of motion are then derived based on the Lagrange principle and modified nonlinear contact law, and solved numerically. The solution procedure is applicable to arbitrary boundary conditions. Numerical results are compared with those available in the literature to demonstrate the validity of the method, and very good agreement is achieved. The effects of boundary conditions on the contact force, contact duration, stress distributions, and beam deflection are discussed.

COUPLED FREE VIBRATION ANALYSIS OF SHEAR-FLEXIBLE LAMINATED COMPOSITE I-BEAMS

2013 ◽  
Vol 21 (01) ◽  
pp. 1250024
Author(s):  
NAM-IL KIM
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Dynamic Stiffness Matrix ◽  
Analytical Technique

The coupled free vibration analysis of the thin-walled laminated composite I-beams with bisymmetric and monosymmetric cross sections considering shear effects is developed. The laminated composite beam takes into account the transverse shear and the restrained warping induced shear deformation based on the first-order shear deformation beam theory. The analytical technique is used to derive the constitutive equations and the equations of motion of the beam in a systematic manner considering all deformations and their mutual couplings. The explicit expressions for displacement parameters are presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the dynamic stiffness matrix is determined using the force–displacement relationships. In addition, for comparison, a finite beam element with two-nodes and fourteen-degrees-of-freedom is presented to solve the equations of motion. The performance of the dynamic stiffness matrix developed by study is tested through the solutions of numerical examples and the obtained results are compared with results available in literature and the detailed three-dimensional analysis results using the shell elements of ABAQUS. The vibrational behavior and the effect of shear deformation are investigated with respect to the modulus ratios and the fiber angle change.

Vibration Characteristics of Composite Thin-Wall Beams

2011 ◽  
Vol 250-253 ◽  
pp. 3993-4000
Author(s):  
Jing Min Ma ◽  
Yong Sheng Ren ◽  
Tao Tan
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Thin Wall ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Lagrange’S Equation ◽  
The Finite Element Analysis ◽  
Box Beams ◽  
Thin Walled

The equations of motion for the free vibration of composite thin-walled closed-section beams are derived based on Lagrange’s equation of the second kind. Two stiffness configuration box beams are considered and corresponding closed solutions formula of natural frequency presented. The finite element analysis software, ANSYS is used to calculate the natural frequency and vibration mode shape of composite thin-walled cantilever beams. And the results are compared with closed solutions. The influence of composite elastic coupling and ply angle to thin-walled beams’ free vibration is investigated.

scholarly journals Generalized Differential Quadrature Method for Free Vibration Analysis of a Rotating Composite Thin-Walled Shaft

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Weiyan Zhong ◽  
Feng Gao ◽  
Yongsheng Ren
Keyword(s):  
Free Vibration ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Rotating Speed ◽  
Generalized Differential Quadrature Method ◽  
Variational Asymptotic ◽  
Thin Walled ◽  
Generalized Differential

A refined variational asymptotic method (VAM) and Hamilton’s principle were used to establish the free vibration differential equations of a rotating composite thin-walled shaft with circumferential uniform stiffness (CUS) configuration. The generalized differential quadrature method (GDQM) was adopted to discretize and solve the governing equations. The accuracy and efficiency of the GDQM were validated in analyzing the frequency of a rotating composite shaft. Compared to the available results in literature, the computational results by the GDQM are accurate. In addition, effects of boundary conditions, rotating speed, ply angle, ratio of radius over thickness, and ratio of length over radius on the frequency characteristics were also investigated.

Free vibration analysis of multilayered composite and soft core sandwich plates resting on Winkler–Pasternak foundations

2016 ◽  
Vol 20 (2) ◽  
pp. 169-190 ◽  
Author(s):  
AM Zenkour ◽  
AF Radwan
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Plate Thickness ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Present Theory ◽  
Soft Core ◽  
Sandwich Plates

Free vibration of laminated composite and soft core sandwich plates resting on Winkler–Pasternak foundations using four-variable refined plate theory are presented. The theory accounts for the hyperbolic distribution of the transverse shear strains through the plate thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Equations of motion are derived from the dynamic version of the principle of virtual work. Navier technique is employed to obtain the closed-form solutions of antisymmetric cross-ply, angle-ply, and soft core laminates or soft core sandwich plates resting on elastic foundations. Numerical results obtained using present theory are compared with three-dimensional elasticity solutions and those computed using the first-order and the other higher-order theories. It can be concluded that the proposed theory is not only accurate, but also efficient in predicting the natural frequencies of laminated composite and soft core sandwich plates resting on Winkler–Pasternak foundations.

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