Singular Mode Characteristics of Fluid-Structure Interaction Modal Formulations

2012 ◽  
Author(s):  
Jeffrey L. Cipolla
Keyword(s):  
Low Frequency ◽  
Order Reduction ◽  
Coupled System ◽  
Forced Response ◽  
Coupled Modes ◽  
Model Order ◽  
Linear Elastic ◽  
Frequency Domains ◽  
Rigid Body Modes ◽  
Mode Characteristics

Modal formulations for linear acoustic and vibration problems are important for model order reduction as well as physical interpretation and insight. In the case of structural acoustic systems, a number of formulations exist for the computation of the modes of the coupled system: these may be referred to as ‘coupled modes’, ‘in-water modes’, etc. These modes have the desirable property that they diagonalize the undamped structural-acoustic problem, making forced-response computations in the time- and frequency-domains trivial. In this paper, we review a number of alternative formulations for the undamped FSI mode problem, and concentrate on a particular aspect: the existence and nature of the singular modes of the systems, i.e. the modes at zero frequency. Corresponding to rigid-body modes in linear elastic systems, these modes are essential for accurate low-frequency performance of reduced-order models. It is found that the original, nonsymmetric system of Zienkiewicz and Newton [53] maintains physically reasonable singular mode properties, while many other formulations do not.

Influence of Blade Flexibility on the Dynamic Response Simulation of a Turbomolecular Pump on Magnetic Bearings

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Alysson Bruno Barbosa Moreira ◽  
Fabrice Thouverez
Keyword(s):  
Mechanical Model ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Coupled System ◽  
Forced Response ◽  
Second Order ◽  
Magnetic Bearings ◽  
Flexible System ◽  
Turbomolecular Pump ◽  
Rigid Body Modes

Abstract This paper proposes the simulation of a complete mechanical model of a turbomolecular pump rotor, including rotor and blades flexibility, suspended by controlled active magnetic bearings. The mechanical model is composed of an eight stage blisk, attached to a shaft. Magnetic forces are linearized by the first-order Taylor expansion around a given point. Including blades and rotor flexibility makes the mechanical system asymmetric, so the equations of motion for the coupled system have periodic terms. A modal controller was designed to control rigid body modes, since the number of sensors is limited and no state observer is implemented. PID controllers are used for low frequency modes combined with the second order filters to damp high frequency modes. First of all, stability analysis was carried out for the axisymmetric case. Second, blades flexibility was included. Forced response of the whole system to an impulsive force was studied. Divergent responses for the system in rotation were obtained as a second order filter pole possibly interacting with blades modes. Taking the second order filters off the control loop allowed the system to be stable. These results show that the analysis method developed here is efficient to evaluate the performance of a controller in closed loop with the complete flexible system. This method may be used in industrial design processes as computation times for the complete system are very short.

Influence of Blade Flexibility on the Dynamic Response Simulation of a Turbomolecular Pump on Magnetic Bearings

2019 ◽  
Author(s):  
Alysson Bruno Barbosa Moreira ◽  
Fabrice Thouverez
Keyword(s):  
Mechanical Model ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Coupled System ◽  
Forced Response ◽  
Second Order ◽  
Magnetic Bearings ◽  
Flexible System ◽  
Turbomolecular Pump ◽  
Rigid Body Modes

Abstract This paper proposes the simulation of a complete mechanical model of a turbomolecular pump rotor, including rotor and blades flexibility, suspended by controlled active magnetic bearings. The mechanical model is composed of an eight stage blisk, attached to a shaft. Magnetic forces are linearized by first order Taylor expansion around a given point. Including blades and rotor flexibility makes the mechanical system asymmetric, so the equations of motion for the coupled system have periodic terms. A modal controller was designed to control rigid body modes, since the number of sensors is limited and no state observer is implemented. PID controllers are used for low frequency modes combined with second order filters to damp high frequency modes. First of all, stability analysis was carried out for the axisymmetric case. Secondly, blades flexibility was included. Forced response of the whole system to an impulsive force was studied. Divergent responses for the system in rotation were obtained as a second order filter pole possibly interacts with blades modes. Taking second order filters off the control loop allowed the system to be stable. These results show that the analysis method developed here is efficient to evaluate the performance of a controller in closed loop with the complete flexible system. This method may be used in industrial design processes as computation times for the complete system are very short.

Application of Model Order Reduction to Compressor Aeroelastic Models

2000 ◽  
Author(s):  
Karen Willcox ◽  
Jaime Peraire ◽  
James D. Paduano
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Forced Response ◽  
Single Frequency ◽  
Model Order ◽  
Transonic Compressor ◽  
Influence Coefficients ◽  
Aeroelastic Analysis ◽  
Blade Row ◽  
Low Order

A model order reduction technique that yields low-order models of blade row unsteady aerodyamics is introduced. The technique is applied to linearized unsteady Euler CFD solutions in such a way that the resulting blade row models can be linked to their surroundings through their boundary conditions. The technique is applied to a transonic compressor aeroelastic analysis, in which the high-fidelity CFD forced-response results are better captured than with models that use single-frequency influence coefficients. A low-speed compressor stage is also modeled to demonstrate the multistage capability of the method. These examples demonstrate how model order reduction can be used to systematically improve the versatility, fidelity, and range of applicability of the low-order aerodynamic models typically used for incorporation of CFD results into aeroelastic analyses.

Application of Model Order Reduction to Compressor Aeroelastic Models

2002 ◽  
Vol 124 (2) ◽  
pp. 332-339 ◽  
Author(s):  
K. Willcox ◽  
J. Peraire ◽  
J. D. Paduano
Keyword(s):  
Model Order Reduction ◽  
Unsteady Aerodynamics ◽  
Order Reduction ◽  
Forced Response ◽  
Single Frequency ◽  
Model Order ◽  
Transonic Compressor ◽  
Influence Coefficients ◽  
Blade Row ◽  
Low Order

A model order reduction technique that yields low-order models of blade row unsteady aerodynamics is introduced. The technique is applied to linearized unsteady Euler CFD solutions in such a way that the resulting blade row models can be linked to their surroundings through their boundary conditions. The technique is applied to a transonic compressor aeroelastic analysis, in which the high-fidelity CFD forced-response results are better captured than with models that use single-frequency influence coefficients. A low-speed compressor stage is also modeled to demonstrate the multistage capability of the method. These examples demonstrate how model order reduction can be used to systematically improve the versatility, fidelity, and range of applicability of the low-order aerodynamic models typically used for incorporation of CFD results into aeroelastic analyses.

Noniterative Integration Algorithms with Controllable Numerical Dissipations for Structural Dynamics

2019 ◽  
Vol 16 (07) ◽  
pp. 1850111 ◽  
Author(s):  
Jinze Li ◽  
Kaiping Yu
Keyword(s):  
Structural Dynamics ◽  
Low Frequency ◽  
Conditional Stability ◽  
Linear Elastic ◽  
New Family ◽  
Special Cases ◽  
Frequency Domains ◽  
Stability And Accuracy ◽  
Stiffness Softening ◽  
New Algorithms

A new family of noniterative algorithms with controllable numerical dissipations for structural dynamics is studied. Particularly, this paper provides nine members of the proposed algorithms and two existing methods are included as two special cases. The proposed algorithms achieve unconditional stability and are second-order accurate for linear elastic systems. The explicit expressions of stability conditions for nonlinear stiffness systems are completely presented, which shows that new algorithms possess unconditional and conditional stability for stiffness softening and hardening systems, respectively. A comprehensive stability and accuracy analysis, including numerical energy dissipations and dispersions, are studied in order to gain insight into spectral properties of new algorithms. Due to the existence of the nonzero spurious root, this paper also pays attention to the influence of the spurious root, which shows that the spurious root does not influence numerical accuracy at low-frequency domains. Although the proposed algorithms exhibit the unusual overshoot behaviors in either displacement or velocity, numerical damping ratios in new algorithms can significantly eliminate this overshoot at a few steps. The new dissipative algorithms are appropriate to solve numerical transient responses of the structure. Numerical examples are also presented to demonstrate the analytical results.

scholarly journals A Generic Control-Oriented Model Order Reduction Approach for High Step-Up DC/DC Converters Based on Voltage Multiplier

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1971
Author(s):  
Binxin Zhu ◽  
Qingdian Zeng ◽  
Mahinda Vilathgamuwa ◽  
Yang Li ◽  
Yao Chen
Keyword(s):  
Control System ◽  
System Design ◽  
Controller Design ◽  
Low Frequency ◽  
Order Reduction ◽  
Control System Design ◽  
Model Order ◽  
Modeling And Control ◽  
Simulation Results ◽  
And Control

The modeling and control system design of high step-up DC/DC converters based on voltage multipliers (VMs) are difficult, due to the various circuit topologies and the presence of large number of capacitors in VMs. This paper proposes a generic approach to reduce the model order of such converters by replacing the VM capacitors with voltage sources controlled by the output voltage of the converter. Theoretical analysis and simulation results show that the derived models can accurately represent the low frequency response of the converter which is valuable for obtaining a small-signal AC model for control system design. The detailed modeling and controller design process are demonstrated for the converter, and the obtained simulation results are verified experimentally on a 400 W prototype.

scholarly journals Design of Low Frequency Suitable Fractional Order Differintegrators

2019 ◽  
Vol 8 (2) ◽  
pp. 3251-3255
Keyword(s):  
Fractional Order ◽  
Model Order Reduction ◽  
Continued Fraction ◽  
Low Frequency ◽  
Order Reduction ◽  
The Novel ◽  
Continued Fraction Expansion ◽  
Reduction Procedure ◽  
Model Order ◽  
First Order

Design of low frequency applicable fractional order digital differentiators and integrators using direct discretization is the main objective of this paper. Model order reduction procedure is used to obtain the novel first order s-to-z transform. Continued fraction expansion (CFE) technique is used to discretize that transform. The design of one-half digital differintegrators based on proposed transforms will be compared with the well known existing first order transforms namely, Bilinear and Al-Alaoui transforms. The efficacy of the designed methods presented interms of normalized magnitude error (NME). The designed fractional order digital filter coefficients are tabulated and all simulation results are carried out by using MATLAB software.

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