scholarly journals Vibration Characteristics of Rotating Mistuned Bladed Disks considering the Coriolis Force, Spin Softening, and Stress Stiffening Effects

2019 ◽  
Vol 2019 ◽  
pp. 1-22
Author(s):  
Shuai Wang ◽  
Chuanxing Bi ◽  
Bin Zi ◽  
Changjun Zheng
Keyword(s):  
Coriolis Force ◽  
High Speed ◽  
Equations Of Motion ◽  
Vibration Characteristics ◽  
Governing Equations ◽  
Bladed Disks ◽  
Reduced Order ◽  
Sector Model ◽  
Effective Component ◽  
Harsh Conditions

Bladed disks of engine rotors usually operate at harsh conditions of high rotating speeds, which may lead to nonnegligible rotordynamic effects, including Coriolis force, spin softening, and stress stiffening effects. These effects on the vibration of mistuned bladed disks are seldom discussed in available investigations. In this paper, the vibration characteristics of rotating mistuned bladed disks are addressed by considering these rotordynamic effects. First, finite element (FE) models of bladed disks are used to obtain the governing equations of motion, and an efficient method for getting the stress stiffening matrix of sector model is developed. Then, the effective component-mode mistuning method (CMM) is employed to create compact, yet accurate, reduced-order models (ROMs). Finally, the models are validated and used to study the influences of Coriolis force, spin softening, and stress stiffening effects on the vibration of bladed disks with frequency mistuning factors. Numerical results show that these rotordynamic effects could significantly affect the vibrations of mistuning bladed disks, especially in the ranges of high speed, and should be carefully considered during analysis.

The Motion Formalism for Flexible Multibody Systems

2021 ◽  
Author(s):  
Olivier Bauchau ◽  
Valentin Sonneville
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Solution Process ◽  
Flexible Multibody Systems ◽  
Structural Elements ◽  
Governing Equations ◽  
Euclidean Group ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Element Approach

Abstract This paper describes a finite element approach to the analysis of flexible multibody systems. It is based on the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) recognizes that these are members of the Special Euclidean group thereby coupling their displacement and rotation components, and (3) resolves all tensors components in local frames. The goal of this review paper is not to provide an in-depth derivation of all the elements found in typical multibody codes but rather to demonstrate how the motion formalism (1) provides a theoretical framework that unifies the formulation of all structural elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, and (4) prevents the occurrence of singularities.

Modelling vortex-induced fluid–structure interaction

2007 ◽  
Vol 366 (1868) ◽  
pp. 1231-1274 ◽  
Author(s):  
Haym Benaroya ◽  
Rene D Gabbai
Keyword(s):  
Variational Approach ◽  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Oscillator Model ◽  
List Type ◽  
Governing Equations ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Oscillator Models

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid–structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid–structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion. Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid–structure interaction models entails formulating generalized equations of motion, as a superset of the flow-oscillator models; and developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier–Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

Forced Wave Motion of Liquid Partially Filling a High-Speed Rotor

1985 ◽  
Vol 107 (4) ◽  
pp. 446-452
Author(s):  
J. Inoue ◽  
Y. Jinnouchi ◽  
Y. Araki
Keyword(s):  
High Speed ◽  
Wave Motion ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Rotor Vibration ◽  
Liquid Motion ◽  
Large Wave ◽  
Main Emphasis ◽  
Two Dimensional Flow ◽  
Theoretical Results

Wave motion of a liquid in a partially filled hollow cylindrical rotor, which rotates at a high speed and is forced to vibrate, is theoretically and experimentally investigated. Main emphasis is placed on the analysis of a large wave motion in the liquid which may cause self-excited vibrations of the rotor. Assuming a thin liquid layer, simplified equations of motion are derived by integration of the governing equations for a two-dimensional flow. Nonlinearity and viscosity are taken into account in the analysis. A large wave motion with a broken wavecrest is analyzed by applying a theory of hydraulic jump. Illustrating typical examples of the theoretical results together with the experimental ones, the dynamic behavior of the liquid motion and the basic relations between the liquid force and the rotor vibration are discussed.

scholarly journals Formulation of Shell Elements Based on the Motion Formalism

2021 ◽  
Vol 2 (4) ◽  
pp. 1009-1036
Author(s):  
Olivier Bauchau ◽  
Valentin Sonneville
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Solution Process ◽  
Flexible Multibody Systems ◽  
Governing Equations ◽  
Euclidean Group ◽  
Shell Elements ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Plates And Shells

This paper presents a finite element implementation of plates and shells for the analysis of flexible multibody systems. The developments are set within the framework of the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) couples their displacement and rotation components by recognizing that configuration and motion are members of the Special Euclidean group, and (3) resolves all tensors components in local frames. The formulation based on the motion formalism (1) provides a theoretical framework that streamlines the formulation of shell elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, (4) circumvents the shear locking phenomenon that plagues shell formulations based on classical kinematic descriptions, and (5) prevents the occurrence of singularities in the treatment of finite rotation. Numerical examples are presented to illustrate the advantageous features of the proposed formulation.

Collective Effect of Fluid's Coriolis Force and Nanoscale's Parameter on Instability Pattern and Vibration Characteristic of Fluid-Conveying Carbon Nanotubes

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Arman Ghasemi ◽  
Morteza Dardel ◽  
Mohammad Hassan Ghasemi
Keyword(s):  
Boundary Conditions ◽  
Coriolis Force ◽  
Equations Of Motion ◽  
Plug Flow ◽  
Vibration Characteristic ◽  
Governing Equations ◽  
Collective Effect ◽  
Aspect Ratios ◽  
Fluid Velocities ◽  
Nanoscale Effect

In the present work, the effects of nanoscale parameter and Coriolis force together are investigated on vibrating eigenvalues of fluid-conveying carbon nanotube (CNT). A nonlocal Timoshenko beam and a plug flow model are implemented to derive fluid–structure interaction (FSI) governing equations of motion. These equations solved by Galerkin to obtain instability pattern, critical fluid velocities (CFVs), frequency and damping at different nanoscale parameter, boundary conditions, and aspect ratios. The results demonstrate existence of multiple types of instabilities and bifurcations, which are deviated from classic FSI buckling and flutters' instabilities, and caused by damping from coalition of nanoscale effect and fluid's Coriolis force, this phenomena are more noticeable in the CNTs with asymmetrical boundary conditions and smaller size.

scholarly journals A Comparison between Two Reduction Strategies for Shrouded Bladed Disks

2018 ◽  
Vol 8 (10) ◽  
pp. 1736
Author(s):  
Alessandro Sommariva ◽  
Stefano Zucca
Keyword(s):  
Degrees Of Freedom ◽  
Computational Effort ◽  
Life Assessment ◽  
Test Cases ◽  
Cyclic Symmetry ◽  
Bladed Disks ◽  
Reduced Order ◽  
Sector Model ◽  
Bladed Disk ◽  
Reduction Strategies

Shrouded bladed disks exhibit a nonlinear dynamic behavior due to the contact interfaces at shrouds between neighboring blades. As a result, reduced order models (ROMs) are mandatory to compute the response levels during the design phase for high cycle fatigue (HCF) life assessment. In this paper, two reduction strategies for shrouded bladed disk reduction are presented. Both approaches rely on: (i) the cyclic symmetry of the linear bladed disk with open shrouds to perform only single sector calculations, (ii) the Craig–Bampton (CB) method to reduce the number of physical degrees of freedom (dofs). The two approaches are applied to a set of test cases in order to evaluate and compare their accuracy and the associated computational effort. Although both approaches allow for generating accurate ROMs, it is found that the numerical efficiency of the two methods depends on the ratio of the number of nodes at the inter-sector interfaces over the number of inner nodes of the elementary sector model.

Modeling Lubricated Revolute Clearance Joints in Multibody Mechanical Systems

2003 ◽  
Author(s):  
P. Flores ◽  
H. M. Lankarani ◽  
J. Ambro´sio ◽  
J. C. P. Claro
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Hydrodynamic Forces ◽  
Dynamic Loads ◽  
Governing Equations ◽  
Clearance Joints ◽  
Revolute Joints ◽  
System A

This work is concerned with the modeling of lubricated revolute clearance joints in multibody mechanical systems. The existence of the clearance at revolute joints is inevitable in all mechanical systems, and most of them are designed to operate with a lubricant fluid. It is known that the use of lubricant at revolute joints is demonstrated to be an effective way to ensuring better performance of the mechanical systems. The long journal-bearing theory for dynamic loads is used to evaluate the resulting hydrodynamic forces of the pressure distribution in the lubricated revolute joints. These hydrodynamic forces are included into the governing equations of motion of the system. A numerical example is presented in order to demonstrate the efficiency and accuracy of the methodology and procedures adopted. The results are close to those obtained with ideal joints even when simulated in a high-speed mechanism.

Investigation of Coriolis Effect on Vibration Characteristics of a Realistic Mistuned Bladed Disk

2011 ◽  
Author(s):  
Jianqiang Xin ◽  
Jianjun Wang
Keyword(s):  
Coriolis Force ◽  
Vibration Characteristics ◽  
Bladed Disks ◽  
Disk Model ◽  
Coriolis Forces ◽  
Response Characteristics ◽  
Bladed Disk ◽  
Damping Matrix ◽  
Disk Rotation ◽  
Speed Effect

Mistuning, which refers to inevitable variations in blades properties, will change the vibration of bladed disks dramatically. Bladed disks are exposed to effects of forces caused by bladed disk rotation, such as centrifugal and Coriolis forces. However, there is little research on the vibration behavior of a realistic bladed disk with Coriolis force. An investigation of the speed effect, i.e., the effects of centrifugal and Coriolis forces, on the vibration characteristics of a realistic mistuned bladed disk model is presented in this paper. Finite element method (FEM) is used to obtain the system mass, stiffness and damping matrix. The effects of Coriolis force and centrifugal force on the modal frequency and harmonic response characteristics of tuned bladed disk are investigated first, then the modal localization and response characteristics of mistuned bladed disk are researched. This investigation indicates that: Coriolis force has efficient influences on the modal and response characteristics of a realistic mistuned bladed disk: it can both increase and decrease the localization of the mistuned bladed disk for different situations.

A Reduced-Order Model for an Oscillating Hydrofoil Near the Free Surface

2015 ◽  
Author(s):  
Rory C. Kennedy ◽  
Dillon Helfers ◽  
Yin Lu Young
Keyword(s):  
Free Surface ◽  
High Speed ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
Reduced Order Model ◽  
Order Model ◽  
Disturbing Force ◽  
Reduced Order ◽  
Resonance Frequencies ◽  
Force Components

The first objective of this work is to numerically investigate how the proximity to the free surface influences the hydrodynamic response and susceptibility to cavitation of a hydrofoil undergoing controlled pitching oscillations, for high-speed full-scale operating conditions. A second objective is to develop a time-domain Reduced Order Model (ROM) to predict the unsteady hydrodynamic loads (for rapid exploration of the design space and for real-time active/passive actuation/control). The ROM delineates the fluid-structure interaction (FSI) forces into fluid inertial, damping, and disturbing force components, and only predicts the primary oscillation frequency. In addition to predicting the unsteady loads, when coupled with the solid equations of motion, the ROM can also be used to calculate the natural resonance frequencies and damping characteristics with consideration for viscous and free surface effects. This will allow designers to better predict and control the dynamic response of lifting surfaces operating near the free surface.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
O. G. McGee ◽  
C. Fang ◽  
Y. El-Aini
Keyword(s):  
Finite Element ◽  
Predictive Accuracy ◽  
Equations Of Motion ◽  
Response Prediction ◽  
Companion Paper ◽  
Energy Model ◽  
Forced Response ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk

In this paper, a reduced order model for the vibrations of bladed disk assemblies was achieved. The system studied was a 3D annulus of shroudless, “custom-tailored,” mistuned blades attached to a flexible disk. Specifically, the annulus was modeled as a spectral-based “meshless” continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3D displacement field of mathematically complete, orthonormal “blade-disk” polynomials multiplied by generalized coefficients. The coefficients were determined by constraining the polynomial series to satisfy the extended Ritz stationary equations and essential boundary conditions of the bladed disk. From this, the governing equations of motion were generated into their usual dynamical forms to calculate upper-bounds on the actual free and forced responses of bladed disks. No conventional finite elements and element connectivity or component substructuring data were needed. This paper, Part I, outlines the theoretical foundation of the present model, and through extensive Monte Carlo simulations, establishes the analytical basis, predictive accuracy, and re-analysis efficiency of the present technology in the prediction of 3D maximum response amplitude of mistuned bladed disks having increasing numbers of nodal diameter excitations. Further applications validating the 3D approach against conventional finite element procedures of free and forced response prediction of a mistuned Integrally-Bladed Rotor used in practice is presented in a companion paper, Part II (Fang, McGee, and El-Aini, 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., to be published.

Sign in / Sign up

Export Citation Format

Share Document