Nonlinear Free Vibration of a Rotor Shaft System With Viscoelastically Supported Bearings

2003 ◽  
Author(s):  
N. Shabaneh ◽  
J. W. Zu
Keyword(s):  
Free Vibration ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Third Order ◽  
Rotor Shaft ◽  
Model Free ◽  
Damping Characteristics ◽  
Shaft System ◽  
Linear Damping ◽  
Nonlinear Elastic

This paper investigates the dynamic analysis of a single-rotor shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspension. A Timoshenko shaft model is utilized to incorporate the flexibility of the shaft; the rotor is considered to be rigid and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports are modeled using the Kelvin-Voigt model. Free vibration is investigated based on the direct multiple scales method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The results of the nonlinear analysis show that a limiting value of the internal damping coefficient of the shaft exists where the trend of the frequency-response curve switches.

Nonlinear Dynamic Analysis of a Rotor Shaft System With Viscoelastically Supported Bearings

2003 ◽  
Vol 125 (3) ◽  
pp. 290-298 ◽  
Author(s):  
Nabeel Shabaneh ◽  
Jean W. Zu
Keyword(s):  
Dynamic Analysis ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Nonlinear Dynamic Analysis ◽  
Primary Resonance ◽  
Rotor Shaft ◽  
Model Free ◽  
Shaft System ◽  
Nonlinear Elastic ◽  
Elastic Characteristics

This research investigates the dynamic analysis of a single-rotor shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspension. Timoshenko shaft model is utilized to incorporate the flexibility of the shaft; the rotor is considered to be rigid and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports are modeled using Kelvin-Voigt model. Free and forced vibration is investigated based on the direct multiple scales method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The results of the nonlinear analysis show that a limiting value of the internal damping coefficient of the shaft exists where the trend of the frequency-response curve switches. Also, the primary resonance peak shifts to higher frequencies with the increase of the bearing nonlinear elastic characteristics, but with a flattened curve and hence lower peak values. A jump phenomenon takes place for high values of the bearing nonlinear elastic characteristics.

On the Vibration of a Rotor-Shaft System With Viscoelastically Supported Bearings

2003 ◽  
Author(s):  
N. Shabaneh
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Vibration Analysis ◽  
Perturbation Expansion ◽  
Free Vibration Analysis ◽  
Rotating Shaft ◽  
Rotor Shaft ◽  
Model Free ◽  
Shaft System ◽  
Nonlinear Elastic

This paper investigates the dynamic behaviour of a single rotor-shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspensions. A Timoshenko shaft model is utilized to incororate the flexibility of the shaft; the rotor is considered to be rigig and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports of the bearings are modeled as Kelvin-Voigt model. Free vibration analysis is performed on the linear system including the damping of the bearings. Forced vibration analysis is performed on the nonlinear system. Equations of motion are derived for the nonlinear system based on the direct multiple scale method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The effects of stiffness and loss coefficients of the viscoelastic supports on the complex natural frequencies are identified for the linear system. The results show that optimum values of the viscoelastic stiffness and loss coefficient can be achieved for a specific rotating shaft system to reduce vibrations and increase the operating regions. In addition, the frequency response of the nonlinear system indicates that a jump phenomenon takes place for high values of the bearing nonlinear elastic coefficient.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

scholarly journals Heat transfer in the seabed boundary layer

2021 ◽  
Vol 928 ◽  
Author(s):  
S. Michele ◽  
R. Stuhlmeier ◽  
A.G.L. Borthwick
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Surface ◽  
Surface Waves ◽  
Multiple Scales ◽  
Perturbation Expansion ◽  
Phase Speed ◽  
Maximum Heat ◽  
Practical Applications ◽  
Free Surface Waves

We present a theoretical model of the temperature distribution in the boundary layer region close to the seabed. Using a perturbation expansion, multiple scales and similarity variables, we show how free-surface waves enhance heat transfer between seawater and a seabed with a solid, horizontal, smooth surface. Maximum heat exchange occurs at a fixed frequency depending on ocean depth, and does not increase monotonically with the length and phase speed of propagating free-surface waves. Close agreement is found between predictions by the analytical model and a finite-difference scheme. It is found that free-surface waves can substantially affect the spatial evolution of temperature in the seabed boundary layer. This suggests a need to extend existing models that neglect the effects of a wave field, especially in view of practical applications in engineering and oceanography.

Stability analysis of rotor whirl under nonlinear internal friction by a general averaging approach

2016 ◽  
Vol 23 (5) ◽  
pp. 808-826 ◽  
Author(s):  
Francesco Sorge
Keyword(s):  
Internal Friction ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Stable Limit ◽  
Rotor Shaft ◽  
Shaft System ◽  
Flexible Supports ◽  
Asymmetric Rotor ◽  
Nonlinear Equations Of Motion ◽  
Shrink Fit

The two main sources of internal friction in a rotor-shaft system are the shaft structural hysteresis and the possible shrink-fit release of the assembly. The internal friction tends to destabilize the over-critical rotor running, but a remedy against this effect may be provided by a proper combination of some external damping in the supports and an anisotropic arrangement of the support stiffness, or at most by the support damping alone, depending on the system geometry. The present analysis reported here considers a general asymmetric rotor-shaft system, where the rotor is perfectly rigid and is constrained by viscous–flexible supports having different stiffnesses on two orthogonal planes. The internal friction is modelled by nonlinear Coulombian forces, which counteract the translational motion of the rotor relative to a frame rotating with the shaft ends. The nonlinear equations of motion are dealt with using an averaging approach based on the Krylov-Bogoliubov method with some adaptation to address the multi-degree-of-freedom nature of the problem. Stable limit cycles may be attained by the overcritical whirling motions, whose amplitudes are inversely proportional to the external dissipation applied by the supports. A noteworthy result is that the stiffness anisotropy of the supports is recognized as beneficial in reducing the natural whirl amplitudes, albeit mainly in the symmetric configuration of the rotor at the mid span and, to a rather lesser extent, in the asymmetric configuration, which then requires a stronger damping action in the supports.

Choice of configuration and parameters of the vibration protection system for gyroscopic angular velocity meters

2021 ◽  
Author(s):  
Keyword(s):  
Angular Velocity ◽  
Protection System ◽  
Technical Solution ◽  
Vibration Damper ◽  
Dynamic Vibration ◽  
Shock Absorbers ◽  
Damping Characteristics ◽  
Vibration Protection ◽  
High Elasticity ◽  
Nonlinear Elastic

The rationale for the choice of a technical solution to the issue of vibration protection of gyroscopic angular velocity meters, built on the basis of dynamically tuned gyroscopes (DTG) is presented. The proposed vibration protection system consists of shock absorbers with high elasticity and dynamic vibration dampers (DVD) with nonlinear elastic and damping characteristics. The main factors that determine the peculiarities of choosing a vibration protection system for precision gyroscopic devices are indicated. Keywords dynamically tuned gyroscope (DTG); dynamic vibration damper (DVD); vibration protection system; gyroscopic angular velocity meter

Oscillatory Third-Order Perturbation Solutions for Sums of Interacting Long-Crested Stokes Waves on Deep Water

1993 ◽  
Vol 37 (04) ◽  
pp. 354-383
Author(s):  
Willard J. Pierson
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Perturbation Expansion ◽  
The United States ◽  
Order Perturbation ◽  
Naval Academy ◽  
Third Order ◽  
First Order ◽  
Stokes Waves ◽  
Perturbation Solutions

Oscillatory third-order perturbation solutions for sums of interacting long-crested Stokes waves on deep water are obtained. A third-order perturbation expansion of the nonlinear free boundary value problem, defined by the coupled Bernoulli equation and kinematic boundary condition evaluated at the free surface, is solved by replacing the exponential term in the potential function by its series expansion and substituting the equation for the free surface into it. There are second-order changes in the frequencies of the first-order terms at third order. The waves have a Stokes-like form when they are high. The phase speeds are a function of the amplitudes and wave numbers of all of the first-order terms. The solutions are illustrated. A preliminary experiment at the United States Naval Academy is described. Some applications to sea keeping are bow submergence and slamming, capsizing in following seas and bending moments.

Sign in / Sign up

Export Citation Format

Share Document