scholarly journals Crosswind response analysis of structures with generalized Van der Pol-type aerodynamic damping by equivalent nonlinear equation method

2022 ◽  
Vol 221 ◽  
pp. 104887
Author(s):  
Kunpeng Guo ◽  
Qingshan Yang ◽  
Yukio Tamura
Keyword(s):  
Nonlinear Equation ◽  
Equation Method ◽  
Response Analysis ◽  
Van Der Pol ◽  
Aerodynamic Damping

Response Analysis of van der Pol Vibro-Impact System with Coulomb Friction Under Gaussian White Noise

2018 ◽  
Vol 28 (13) ◽  
pp. 1830043 ◽  
Author(s):  
Meng Su ◽  
Wei Xu ◽  
Guidong Yang
Keyword(s):  
White Noise ◽  
Coulomb Friction ◽  
Gaussian White Noise ◽  
Original System ◽  
Stochastic Averaging ◽  
Response Analysis ◽  
State Variables ◽  
Van Der Pol ◽  
Impact System ◽  
The Impact

In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Thomas Giersch ◽  
Jens Nipkau
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver

The forced response of the first rotor of an E3E-type high pressure compressor blisk is analyzed with regard to varying mistuning, varying engine order excitations and the consideration of aeroelastic effects. For that purpose, SNM-based reduced order models are used in which the disk remains unchanged while the Young’s modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient technique is employed to model aeroelastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades’ Young’s modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aeroelastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

Forced Response Analysis of a Transonic Fan

2012 ◽  
Author(s):  
Parthasarathy Vasanthakumar ◽  
Paul-Benjamin Ebel
Keyword(s):  
Finite Element ◽  
Flow Field ◽  
Forced Response ◽  
Navier Stokes ◽  
Response Analysis ◽  
Aerodynamic Damping ◽  
Forcing Function ◽  
Transonic Fan ◽  
Work Done ◽  
Highly Loaded

The forced response of turbomachinery blades is a primary source of high cycle fatigue (HCF) failure. This paper deals with the computational prediction of blade forced response of a transonic fan stage that consists of a highly loaded rotor along with a tandem stator. In the case of a transonic fan, the forced response of the rotor due to the downstream stator assumes significance because of the transonic flow field. The objective of the present work is to determine the forced response of the rotor induced as a result of the unsteady flow field due to the downstream stator vanes. Three dimensional, Navier-Stokes flow solver TRACE is used to numerically analyse the forced response of the fan. A total of 11 resonant crossings as identified in the Campbell diagram are examined and the corresponding modeshapes are obtained from finite element modal analysis. The interaction between fluid and structure is dealt with in a loosely coupled manner based on the assumption of linear aerodynamic damping. The aerodynamic forcing is obtained by a nonlinear unsteady Navier-Stokes computation and the aerodynamic damping is obtained by a time-linearized Navier-Stokes computation. The forced response solution is obtained by the energy method allowing calculations to be performed directly in physical space. Using the modal forcing and damping, the forced response amplitude can be directly computed at the resonance crossings. For forced response solution, the equilibrium amplitude is reached when the work done on the blade by the external forcing function is equal to the work done by the system damping (aerodynamic and structural) force. A comprehensive analysis of unsteady aerodynamic forces on the rotor blade surface as a result of forced response of a highly loaded transonic fan is carried out. In addition, the correspondence between the location of high stress zones identified from the finite element analysis and the regions of high modal force identified from the CFD analysis is also discussed.

Nonlinear Response of Marine Riser with Large Displacement Excited by Top-End Vessel Motion using Penalty Method

2020 ◽  
Vol 20 (04) ◽  
pp. 2050052 ◽  
Author(s):  
Karun Klaycham ◽  
Chainarong Athisakul ◽  
Somchai Chucheepsakul
Keyword(s):  
Nonlinear Equation ◽  
Nonlinear Dynamic ◽  
Oscillation Frequency ◽  
Penalty Method ◽  
Equation Of Motion ◽  
Ocean Current ◽  
Computational Time ◽  
Response Analysis ◽  
Marine Riser ◽  
Vessel Motion

A marine riser operated in a deep-water field could be substantially affected by large amounts of movement of the floating platform, which is more complicated and very challenging to analyze. This paper presents a mathematical model involving nonlinear dynamic response analysis of a marine riser caused by sways and heave motions at the top end, which are treated as the constraint conditions. The nonlinear equation of motion, arising from the nonlinearity of the ocean current and wave loadings, is derived and written in general matrix form using the finite element method. The excitation caused by platform movement is imposed on the riser system through the time-dependent constrained condition using the penalty method. The advantages of this method are that it is easily implemented on the nonlinear equation of motion and it requires no additional unknown variable, and thus consumes less computational time. By this method, the stiffness matrix and the force vector of the system are then modified, enforcing top-end vessel motion. The dynamic responses are evaluated by using numerical time integration based on Newmark’s method with direct iteration. The effects of the oscillation frequency of top-end vessel sway and heave motions on the nonlinear dynamic characteristics of the riser are investigated. The numerical results reveal that the riser responses to the top-end vessel excitation behave like a periodic motion, which is conformable to the characteristics of vessel movements. The increase in the oscillation frequency of the top-end vessel increases the maximum displacement amplitude for both the horizontal and vertical directions. The directional motion of the vessel also significantly influences the response amplitude of the riser.

Forced Response Analysis of a Mistuned Compressor Blisk

2013 ◽  
Author(s):  
Bernd Beirow ◽  
Arnold Kühhorn ◽  
Thomas Giersch ◽  
Jens Nipkau
Keyword(s):  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver ◽  
Displacement Based ◽  
Blade Frequency

The forced response of an E3E-type HPC-blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades namely stiffness and damping are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order and aerodynamic influences it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade alone frequencies as design variables are applied. The validity of the Whitehead-limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk’s stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Bernd Beirow ◽  
Thomas Giersch ◽  
Arnold Kühhorn ◽  
Jens Nipkau
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver

The forced response of the first rotor of an engine 3E (technology program) (E3E)-type high pressure compressor (HPC) blisk is analyzed with regard to varying mistuning, varying engine order (EO) excitations and the consideration of aero-elastic effects. For that purpose, subset of nominal system modes (SNM)-based reduced order models are used in which the disk remains unchanged while the Young's modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient (AIC) technique is employed to model aero-elastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades' Young's modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aero-elastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

A New Reduced Order Modeling for Stability and Forced Response Analysis of Aero-Coupled Blades Considering Various Mode Families

2010 ◽  
Author(s):  
Mari´a A. Mayorca ◽  
Damian M. Vogt ◽  
Hans Ma˚rtensson ◽  
Torsten H. Fransson
Keyword(s):  
Single Mode ◽  
Forced Response ◽  
Least Square ◽  
Response Analysis ◽  
Computational Domain ◽  
Unsteady Forces ◽  
Reduced Order ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Frequency Split

This paper presents the description and application of a new method for stability and forced response analyses of aerodynamically coupled blades considering the interaction of various mode families. The method, here referred as MLS (Multimode Least Square), considers the unsteady forces due to the blade motion at different modes shape families and calculates the aerodynamic matrixes by means of a least square (L2) approximations. This approach permits the prediction of mode families’ interaction with capabilities of structural, aerodynamic and force mistuning. A projection technique is implemented in order to reduce the computational domain. Application of the method on tuned and structural mistuned forced response and stability analyses is presented on a highly loaded transonic compressor blade. When considering structural mistuning the forced response amplitude magnification is highly affected by the change in aerodynamic damping due to mistuning. Analyses of structural mistuning without aerodynamic coupling might result in over-estimated or under-estimated response when the source of damping is mainly aerodynamic. The frequency split due to mistuning can cause that mode families’ interact due to reducing their frequencies separation. The advantage of the present method is that the effect of mode family interaction on aerodynamic damping and forced response is captured not being restricted to single mode families.

Improved Nonlinear Equation Method for Numerical Prediction of Jominy End-Quench Curves

2007 ◽  
Vol 14 (1) ◽  
pp. 37-41 ◽  
Author(s):  
Yue-peng Song ◽  
Guo-quan Liu ◽  
Sheng-xin Liu ◽  
Jian-tao Liu ◽  
Cheng-ming Feng
Keyword(s):  
Nonlinear Equation ◽  
Numerical Prediction ◽  
Equation Method

Forced Response Analysis of a Mistuned Compressor Blisk

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Bernd Beirow ◽  
Thomas Giersch ◽  
Arnold Kühhorn ◽  
Jens Nipkau
Keyword(s):  
Strong Dependence ◽  
Forced Response ◽  
Response Analysis ◽  
Influence Coefficient ◽  
Aerodynamic Damping ◽  
Design Variables ◽  
Engine Order ◽  
Main Driver ◽  
Displacement Based ◽  
Blade Frequency

The forced response of an E3E-type high pressure compressor (HPC) blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades, namely stiffness and damping, are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order, and aerodynamic influences, it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade-alone frequencies as design variables are applied. The validity of the Whitehead limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk's stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.

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