Unbalance Response of Flexible Rotors Coupled With Torsion

1989 ◽  
Vol 111 (2) ◽  
pp. 179-186 ◽  
Author(s):  
H. Diken ◽  
I. G. Tadjbakhsh
Keyword(s):  
Shear Deformation ◽  
Equations Of Motion ◽  
Continuous System ◽  
Internal Damping ◽  
Governing Equations ◽  
Disk System ◽  
Torsional Oscillations ◽  
Unbalance Response ◽  
Flexible Rotors ◽  
Mass Eccentricity

The effect of coupling with torsion on the unbalance response of flexible rotors, supported by isotropic flexible and damped bearings is investigated. Flexural vibrations of the shaft-disk system are coupled with torsional oscillations through mass eccentricity. The governing equations of motion of the continuous system are solved numerically with a modified Myklestad-Prohl method without the necessity of considering an equivalent lumped system. The cases of constant or harmonic torque applied to the disk are considered. Gyroscopic, rotary inertia, shear deformation, external and internal damping effects are taken into account.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

Ritz Series Analysis of Rotating Shaft System: Validation, Convergence, Mode Functions, and Unbalance Response

2002 ◽  
Vol 124 (4) ◽  
pp. 492-501 ◽  
Author(s):  
Nicole L. Zirkelback ◽  
Jerry H. Ginsberg
Keyword(s):  
Equations Of Motion ◽  
Ritz Method ◽  
Natural Mode ◽  
Rotating Shaft ◽  
Disk System ◽  
Element Analysis ◽  
Cross Sectional ◽  
Energy Functionals ◽  
Unbalance Response ◽  
Gyroscopic Coupling

A shaft with attached rigid disks is modeled as a rotating Timoshenko beam supported by nonconservative, flexible bearing supports. The continuous shaft-disk system is described with kinetic and potential energy functionals that fully account for transverse shear, translational and rotatory inertia, and gyroscopic coupling. Ritz series expansions are used to describe the flexural displacements and cross-sectional rotations about orthogonal fixed axes. The equations of motion are derived from Lagrange’s equations and placed in a state-space form that preserves the skew-symmetric gyroscopic matrix as well as the full effects of the bearings. Both the general and adjoint eigenproblems for the nonsymmetric equations are solved. Bi-orthogonality conditions lead to the ability to evaluate dynamic response via modal analysis. Whirl speeds and logarithmic decrements calculated with the present model are verified with a finite element analysis. The present work provides two ways of evaluating the convergence of results to demonstrate an advantage of the Ritz method over other discretization methods. Natural mode functions and unbalance response are calculated for an example system.

Experimental Identification of Nonlinear Continuous Vibratory Systems Using Nonlinear Principal Component Analysis: Application to Structural Modification

2007 ◽  
Author(s):  
Keisuke Kamiya ◽  
Yuichi Mizuno
Keyword(s):  
Principal Component Analysis ◽  
Structural Modification ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Principal Component ◽  
Continuous System ◽  
Nonlinear Normal Modes ◽  
Nonlinear Functions ◽  
Governing Equations ◽  
Nonlinear Normal

In identifying machines and structures, one sometimes encounters cases in which the system should be regarded as a nonlinear continuous system. The governing equations of motion of a nonlinear continuous system are described by a set of nonlinear partial differential equations and boundary conditions. Determining both of them simultaneously is a quite difficult task. Thus, one has to discretize the governing equations of motion, and reduce the order of the equations as much as possible. In analysis of nonlinear vibratory systems, it is known that one can reduce the order of the system by using the nonlinear normal modes while preserving the effect of the nonlinearity accurately. The nonlinear normal modes are description of motion by nonlinear functions of the coordinates for analysis. In identification it is expected that an accurate mathematical model with minimum degree of freedom can be determined if one can express the response as nonlinear functions of the coordinates for identification. Based on this idea, in a previous report the authors proposed an identification technique which uses nonlinear principal component analysis by a neural network. In this report, procedure to apply the identified result to structural modification is presented. It is shown via numerical example that when the structural modification is not so large, response prediction of the modified system with enough accuracy is possible.

Experimental Identification of Nonlinear Continuous Vibratory Systems Using Nonlinear Principal Component Analysis

2006 ◽  
Author(s):  
Keisuke Kamiya ◽  
Yuichi Mizuno ◽  
Kimihiko Yasuda
Keyword(s):  
Principal Component Analysis ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Principal Component ◽  
Continuous System ◽  
Nonlinear Normal Modes ◽  
Component Analysis ◽  
Nonlinear Functions ◽  
Governing Equations ◽  
Nonlinear Normal

In identifying machines and structures, one sometimes encounters cases in which the system should be regarded as a nonlinear continuous system. The governing equations of motion of a nonlinear continuous system are described by a set of nonlinear partial differential equations and boundary conditions. Determining both of them simultaneously is a quite difficult task. Thus, one has to discretize the governing equations of motion, and reduce the order of the equations as much as possible. In analysis of nonlinear vibratory systems, it is known that one can reduce the order of the system by using the nonlinear normal modes preserving the effect of the nonlinearity accurately. The nonlinear normal modes are description of motion by nonlinear functions of the coordinates for analysis. In identification it is expected that an accurate mathematical model with minimum degree of freedom can be determined if one can express the response as nonlinear functions of the coordinates for identification. Based on this idea, this paper proposes an identification technique which uses nonlinear principal component analysis by a neural network. Applicability of the proposed technique is confirmed by numerical simulation.

Well-posed two-phase nonlocal integral models for free vibration of nanobeams in context with higher-order refined shear deformation theory

2021 ◽  
pp. 107754632110399
Author(s):  
Pei Zhang ◽  
Hai Qing
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Well Posedness ◽  
Governing Equations ◽  
Two Phase

In this article, the well-posedness of several common nonlocal models for higher-order refined shear deformation beams is studied. Unlike the case of classic beams models, both strain-driven and stress-driven purely nonlocal theories lead to an ill-posed issue (i.e., there are excessive mandatory boundary conditions) when considering higher-order shear deformation assumption. As an effective remedy, the well-posedness of strain-driven and stress-driven two-phase nonlocal (StrainDTPN and StressDTPN) models is pertinently evidenced by studying the free vibration problem of nanobeams. The governing equations of motion and standard boundary conditions are derived from Hamilton’s principle. The integral constitutive relation is transformed equivalently to a differential form equipped with two constitutive boundary conditions. Using the generalized differential quadrature method (GDQM), the governing equations in terms of displacements are solved numerically. Numerical results show that both the StrainDTPN and StressDTPN models can predict consistent size-effects of beams with different boundary conditions.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

Reduction of Noise Inside a Cavity by Piezoelectric Actuators

2003 ◽  
Vol 125 (1) ◽  
pp. 12-17 ◽  
Author(s):  
I. Hagiwara ◽  
D. W. Wang ◽  
Q. Z. Shi ◽  
R. S. Rao
Keyword(s):  
Sound Pressure ◽  
Control Mechanism ◽  
Equations Of Motion ◽  
Piezoelectric Actuators ◽  
Governing Equations ◽  
Control Laws ◽  
Modal Coupling ◽  
Modal Amplitude ◽  
Global And Local ◽  
Fully Coupled

A new analytical model is developed for the reduction of noise inside a cavity using distributed piezoelectric actuators. A modal coupling method is used to establish the governing equations of motion of the fully coupled acoustics-structure-piezoelectric patch system. Two performance functions relating “global” and “local” optimal control of sound pressure levels (SPL) respectively are applied to obtain the control laws. The discussions on associated control mechanism show that both the mechanisms of modal amplitude suppression and modal rearrangement may sometimes coexist in the implementation of optimal noise control.

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