Boundary Conditions and Craig-Bampton Substructuring Technique With Free-Free Modes

2017 ◽  
Author(s):  
Grzegorz Orzechowski ◽  
Aki M. Mikkola
Keyword(s):  
Boundary Conditions ◽  
Reference Frame ◽  
Deformable Body ◽  
Order Reduction ◽  
The Body ◽  
Model Order ◽  
Practical Applications ◽  
Static Correction ◽  
Local Reference ◽  
Deformation Modes

The floating frame of reference formulation allows for description of the kinematics of a deformable body using generalized coordinates that define the body local reference frame and deformations with respect to that frame. In practical applications, the formulation need to be used in conjunction with of a model order reduction approach. The paper investigates the usage of the model reduction through the Craig-Bampton method with the mean-axis reference frame conditions. Analysis involves static numerical examples of the beam structures, modeled using commercial packages with different boundary conditions and loads. It is shown that commonly employed orthonormalization technique dissolves the influence of the static correction modes in many assumed deformation modes of a deformable body. Consequently, a care should be taken in model validation when this popular approach for modeling flexible bodies is used.

scholarly journals Model order reduction of thermo-mechanical models with parametric convective boundary conditions: focus on machine tools

2020 ◽  
Author(s):  
Pablo Hernández-Becerro ◽  
Daniel Spescha ◽  
Konrad Wegener
Keyword(s):  
Boundary Conditions ◽  
Machine Tools ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Convective Boundary Conditions ◽  
Frequency Range ◽  
Order Model ◽  
Convective Boundary ◽  
Model Order ◽  
Reduced Order

Abstract Thermo-mechanical finite element (FE) models predict the thermal behavior of machine tools and the associated mechanical deviations. However, one disadvantage is their high computational expense, linked to the evaluation of the large systems of differential equations. Therefore, projection-based model order reduction (MOR) methods are required in order to create efficient surrogate models. This paper presents a parametric MOR method for weakly coupled thermo-mechanical FE models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal Subspace (KMS), and a theoretical bound of the reduction error. The developed method addresses the parametric dependency of the convective boundary conditions using the concept of system bilinearization. The reduced-order model reproduces the thermal response of the original FE model in the frequency range of interest for any value of the parameters describing the convective boundary conditions. Additionally, this paper investigates the coupling between the reduced-order thermal system and the mechanical response. A numerical example shows that the reduced-order model captures the response of the original system in the frequency range of interest.

Dynamic Surface Solutions in Linear Elasticity and Viscoelasticity With Frictional Boundary Conditions

1995 ◽  
Vol 117 (4) ◽  
pp. 445-451 ◽  
Author(s):  
J. A. C. Martins ◽  
J. Guimara˜es ◽  
L. O. Faria
Keyword(s):  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Deformable Body ◽  
The Body ◽  
Dynamic Surface ◽  
Linear Elastic ◽  
Finite Dimensional ◽  
Rigid Plane ◽  
Short Time ◽  
Plane Oscillations

This paper presents a study on the dynamic stability of the steady frictional sliding of a linear elastic or viscoelastic half-space compressed against a rigid plane which moves with a prescribed nonvanishing tangential speed. The system of differential equations and boundary conditions that govern the small plane oscillations of the body about the steady-sliding state of deformation is established. It is shown that for large coefficient of friction and large Poisson’s ratio the steady-sliding of the elastic body is dynamically unstable. This instability manifests itself by growing surface oscillations which necessarily propagate from front to rear and which in a short time lead to situations of loss of contact or stick. Similarly to what has been found with various finite dimensional frictional systems, these flutter type surface instabilities result from the intrinsic nonsymmetry of dry friction contact laws. The effect of viscous dissipation within the deformable body is also assessed: when viscous dissipation is present larger coefficients of friction are required for the occurrence of surface solutions propagating and growing from front to rear.

scholarly journals Model reduction of unstable systems based on balanced truncation algorithm

2021 ◽  
Vol 11 (3) ◽  
pp. 2045
Author(s):  
Ngoc Kien Vu ◽  
Hong Quang Nguyen
Keyword(s):  
Model Reduction ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Order System ◽  
Balanced Truncation ◽  
Model Order ◽  
Unstable Systems ◽  
Practical Applications ◽  
Simulation Results ◽  
Lower Order System

Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms.

Identification of temperature-dependent boundary conditions using MOR

2019 ◽  
Vol 30 (2) ◽  
pp. 1009-1022
Author(s):  
Tobias Frank ◽  
Steffen Wieting ◽  
Mark Wielitzka ◽  
Steffen Bosselmann ◽  
Tobias Ortmaier
Keyword(s):  
Boundary Conditions ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Complex Geometries ◽  
Temperature Dependent ◽  
Model Order ◽  
Content Type ◽  
Model Based Control ◽  
Model Based ◽  
Film Coefficient

Purpose A mathematical description of temperature-dependent boundary conditions is crucial in manifold model-based control or prototyping applications, where accurate thermal simulation results are required. Estimation of boundary condition coefficients for complex geometries in complicated or unknown environments is a challenging task and often does not fulfill given accuracy limits without multiple manual adaptions and experiments. This paper aims to describe an efficient method to identify thermal boundary conditions from measurement data using model order reduction. Design/methodology/approach An optimization problem is formulated to minimize temperature deviation over time between simulation data and available temperature sensors. Convection and radiation effects are expressed as a combined heat flux per surface, resulting in multiple temperature-dependent film coefficient functions. These functions are approximated by a polynomial function or splines, to generate identifiable parameters. A formulated reduced order system description preserves these parameters to perform an identification. Experiments are conducted with a test-bench to verify identification results with radiation, natural and forced convection. Findings The generated model can approximate a nonlinear transient finite element analysis (FEA) simulation with a maximum deviation of 0.3 K. For the simulation of a 500 min cyclic cooling and heating process, FEA takes a computation time of up to 13 h whereas the reduced model takes only 7-11 s, using time steps of 2 s. These low computation times allow for an identification, which is verified with an error below 3 K. When film coefficient estimation from literature is difficult due to complex geometries or turbulent air flows, identification is a promising approach to still achieve accurate results. Originality/value A well parametrized model can be further used for model-based control approaches or in observer structures. To the knowledge of the authors, no other methodology enables model-based identification of thermal parameters by physically preserving them through model order reduction and therefore derive it from a FEA description. This method can be applied to much more complex geometries and has been used in an industrial environment to increase product quality, due to accurate monitoring of cooling processes.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

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