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.

Free Vibration Analysis of a Carbon Nanotube Reinforced Composite Beam

2014 ◽  
Vol 592-594 ◽  
pp. 2041-2045 ◽  
Author(s):  
B. Naresh ◽  
A. Ananda Babu ◽  
P. Edwin Sudhagar ◽  
A. Anisa Thaslim ◽  
R. Vasudevan
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Reinforced Composite ◽  
Vibration Responses

In this study, free vibration responses of a carbon nanotube reinforced composite beam are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced composite beam are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of aspect ratio and percentage of CNT content and boundary conditions on natural frequencies and mode shapes of a carbon nanotube reinforced composite beam. It is shown that the addition of carbon nanotube in fiber reinforced composite beam increases the stiffness of the structure and consequently increases the natural frequencies and alter the mode shapes.

Damping Characteristics of a Cantilever Plate Using Permanent Magnetic Constrained Layer Damping Strip Treatment

2012 ◽  
Vol 450-451 ◽  
pp. 466-471
Author(s):  
Ming Li ◽  
Hui Ming Zheng
Keyword(s):  
Ritz Method ◽  
Constrained Layer Damping ◽  
Structural Vibrations ◽  
Torsional Mode ◽  
Calculation Of Parameters ◽  
New Class ◽  
Damping Characteristics ◽  
Special Cases ◽  
Cantilever Rectangular Plate ◽  
Passive Constrained Layer Damping

Significant improvement of damping characteristics can be achieved by using the new class of magnetic constrained layer damping treatment (MCLD). This paper presents the damping properties of the first and second torsional mode for a five-layer cantilever rectangular plate treated with partial MCLD. The Rayleigh-Ritz method and Hamilton’s principle are employed in the analysis. We have chosen both single and segmented patches with different sizes. It can be observed that for the two modes single-patched MCLD treatment induces less improvement of damping characteristics especially for the short patch. The effects of calculation of parameters like placement strategies of discrete patches, the length of patches are analyzed and discussed. The results obtained from analytical show that the optimum location of the patch, for the torsional mode, is at edge of the plate. Favorable comparisons with the conventional passive constrained layer damping treatment (PCLD) on various special cases of the problem are obtained. The results demonstrate MCLD treatment still improvements over PCLD in damping structural vibrations.

Optimization of Nonlinear Unbalanced Flexible Rotating Shaft Passing Through Critical Speeds

2021 ◽  
Author(s):  
Sadegh Amirzadegan ◽  
Mohammad Rokn-Abadi ◽  
R. D. Firouz-Abadi
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Beam Theory ◽  
Rotor System ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Applied Torque

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler–Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations numerically, the finite element method (FEM) is used. Furthermore, for different bearing properties, rotor responses are examined and curves of passing through critical speeds with angular acceleration due to applied torque are plotted. Then the optimal values of bearing stiffness and damping are calculated to achieve the minimum vibration amplitude, which causes to pass easier through critical speeds. It is concluded that the value of damping and stiffness of bearing change the rotor critical speeds and also significantly affect the dynamic behavior of the rotor system. These effects are also presented graphically and discussed.

Free Vibration and Stability Analysis of Internally Damped Rotating Shafts With General Boundary Conditions

1998 ◽  
Vol 120 (3) ◽  
pp. 776-783 ◽  
Author(s):  
J. Melanson ◽  
J. W. Zu
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Beam Theory ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Rotating Shaft ◽  
Classical Boundary ◽  
Rotating Shafts ◽  
The Stability

Vibration analysis of an internally damped rotating shaft, modeled using Timoshenko beam theory, with general boundary conditions is performed analytically. The equations of motion including the effects of internal viscous and hysteretic damping are derived. Exact solutions for the complex natural frequencies and complex normal modes are provided for each of the six classical boundary conditions. Numerical simulations show the effect of the internal damping on the stability of the rotor system.

scholarly journals Performance Characteristics of Active Constrained Layer Damping

1995 ◽  
Vol 2 (1) ◽  
pp. 33-42 ◽  
Author(s):  
A. Baz ◽  
J. Ro
Keyword(s):  
Broad Band ◽  
Structural Response ◽  
Piezoelectric Sensor ◽  
Performance Characteristics ◽  
Constrained Layer Damping ◽  
New Class ◽  
Damping Characteristics ◽  
Active Constrained Layer Damping ◽  
Passive Constrained Layer Damping ◽  
Active Constrained Layer

Theoretical and experimental performance characteristics of the new class of actively controlled constrained layer damping (ACLD) are presented. The ACLD consists of a viscoelastic damping layer sandwiched between two layers of piezoelectric sensor and actuator. The composite ACLD when bonded to a vibrating structure acts as a “smart” treatment whose shear deformation can be controlled and tuned to the structural response in order to enhance the energy dissipation mechanism and improve the vibration damping characteristics. Particular emphasis is placed on studying the performance of ACLD treatments that are provided with sensing layers of different spatial distributions. The effect of the modal weighting characteristics of these sensing layers on the broad band attenuation of the vibration of beams fully treated with the ACLD is presented theoretically and experimentally. The effect of varying the gains of a proportional and derivative controller and the operating temperature on the ACLD performance is determined for uniform and linearly varying sensors. Comparisons with the performance of conventional passive constrained layer damping are presented also. The results obtained emphasize the importance of modally shaping the sensor and demonstrate the excellent capabilities of the ACLD.

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.

An Improved Transfer Matrix Method for Steady-State Analysis of Nonlinear Rotor-Bearing Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 303-310 ◽  
Author(s):  
J. W. Zu ◽  
Z. Ji
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Roller Bearing ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Rotating Shaft ◽  
Damping Characteristics ◽  
Rotor Bearing

An improved transfer matrix method is developed to analyze nonlinear rotor-bearing systems. The rotating shaft is described by the Timoshenko beam theory which considers the effect of the rotary inertia and shear deformation. A typical roller bearing model is assumed which has cubic nonlinear spring and linear damping characteristics. Transfer matrices for the Timoshenko shaft element, disk element, and nonlinear bearing element are derived and the global transfer matrix is formed. The steady-state response of synchronous, subharmonic, and superharmonic whirls is determined using the harmonic balance method. Two numerical examples are presented to demonstrate the effectiveness of this approach.

Nonlinear Free Vibration of Hybrid Composite Moving Beams Embedded with Shape Memory Alloy Fibers

2016 ◽  
Vol 16 (07) ◽  
pp. 1550032 ◽  
Author(s):  
M. R. Ebrahimi ◽  
A. Moeinfar ◽  
M. Shakeri
Keyword(s):  
Shape Memory Alloy ◽  
Free Vibration ◽  
Shape Memory ◽  
Hybrid Composite ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parametric Studies ◽  
The One ◽  
Nonlinear Equations Of Motion

The aim of this paper is to investigate the free vibration of hybrid composite moving beams embedded with shape memory alloy (SMA) fibers. The nonlinear equations of motion are derived based on the Euler–Bernoulli beam theory in conjunction with the von Karman type of nonlinearity in strain–displacement relations via the extended Hamilton principle. Also, the recovery stress induced by the SMA fibers is computed by applying the one-dimensional Brinson model and Reuss scheme. Then, an analytical approach in used to solve the nonlinear equation of motion for the simply supported shape memory alloy hybrid composite (SMAHC) moving beams. Based on the analytical solution, several parametric studies are presented to show the effects of various parameters such as volume fraction, pre-strain in the SMA fibers, temperature rise and velocity on the fundamental frequency of the SMAHC moving beams. Due to the lack of similar results in the specialized literature on the subject of interest, this paper is likely to fill a gap in the state of the art of the related research.

Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads

1992 ◽  
Vol 114 (2) ◽  
pp. 249-259 ◽  
Author(s):  
S. H. Choi ◽  
C. Pierre ◽  
A. G. Ulsoy
Keyword(s):  
Torsional Vibration ◽  
Axial Load ◽  
Finite Strain ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Rotating Shaft ◽  
Principal Moments Of Inertia ◽  
Mass Eccentricity

The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.

Nonlinear Free Vibration of a Beam With Off-Axis Attached Mass

2013 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Free Vibration ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Beam Theory ◽  
Governing Equations ◽  
Attached Mass ◽  
Lumped Mass ◽  
Nonlinear Free Vibration ◽  
Euler Bernoulli Beam

A model of a clamped-clamped beam with an attached lumped mass is presented in this paper. The system is modeled using the Euler-Bernoulli beam theory. In the models presented in literature, it is assumed that the center of mass of the attached mass is located on the neutral axis of the beam. In this paper, this assumption is relaxed. The governing equations of motion are derived. It has been shown that the off-axis center of mass of the attached mass generates an amplitude-dependent transverse force in the beam, which introduces a quadratic nonlinearity. The nonlinear governing equations of motion are solved using the Multiple Scales method. The nonlinear free vibration frequencies are determined.

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