Modeling Infinitely Long Flexible Railroad Tracks Using Moving Modes and Krylov Subspaces Techniques

2013 ◽  
Author(s):  
Antonio M. Recuero ◽  
José L. Escalona
Keyword(s):  
Krylov Subspace ◽  
Complex Structure ◽  
Order Reduction ◽  
Element Model ◽  
Interesting Property ◽  
Krylov Subspaces ◽  
Flexible Body ◽  
Small Areas ◽  
Railroad Tracks ◽  
Flexible Track

This paper presents a method to model the flexibility of railroad tracks for the dynamic analysis of vehicle-track interaction. In addition to being a complex structure, the flexible track is infinitely long and shows small areas of deformation whose position moves with time. Due to these properties, the efficient modeling of the track as a flexible body in a multibody system formalism is a challenging problem. In this work the model is developed using the moving modes method in combination with Krylov subspaces techniques. The moving modes method that was previously presented by the authors defines the deformation modes in a trajectory frame whose position changes with respect to the flexible track. In this paper the moving modes are selected from a detailed finite element model of the track and a model order reduction technique based on Krylov subspaces. These modes of deformation are adequate to be selected as moving modes since they affect a small area of the flexible body and they are obtained by assuming the load distribution that actually takes place during the dynamic interaction. However, the most interesting property of the Krylov subspace modes is that they can be selected such that the frequency response function of the reduced order model matches that of the full model with the desired degree of accuracy. In this paper a multibody formulation of railroad vehicles and flexible tracks based on the trajectory frame is presented and applied to the numerical simulation of a full railroad car on a track with geometric irregularities.

Deterministic and Stochastic Model Order Reduction for Vibration Analyses of Structures With Uncertainties

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Ji Yang ◽  
Béatrice Faverjon ◽  
Herwig Peters ◽  
Steffen Marburg ◽  
Nicole Kessissoglou
Keyword(s):  
Finite Element ◽  
Stochastic Model ◽  
Dynamic Characteristics ◽  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Element Model ◽  
Uncertain Parameters ◽  
Model Order ◽  
Frequency Responses

To reduce the computational effort using polynomial chaos expansion to predict the dynamic characteristics of structures with several uncertain parameters, hybrid techniques combining stochastic finite element analysis with either deterministic or stochastic model order reduction (MOR) are developed. For the deterministic MOR, the Arnoldi-based Krylov subspace technique is implemented to reduce the system matrices of the finite element model. For the stochastic MOR, a stochastic reduced basis method is implemented in which the structural modal and frequency responses are approximated by a small number of basis vectors using stochastic Krylov subspace. To demonstrate the computational efficiency of each reduced stochastic finite element model, variability in the natural frequencies and frequency responses of a simply supported flexible plate randomized by uncertain geometrical and material parameters is examined. Results are compared with both Monte Carlo (MC) simulations and nonreduced stochastic models. Using the reduced models, the effects of the individual uncertain parameters as well as the combined uncertainties on the dynamic characteristics of the plate are examined.

scholarly journals Material Parameter Identification for Acoustic Simulation of Additively Manufactured Structures

Materials ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 168
Author(s):  
Sebastian Rothe ◽  
Christopher Blech ◽  
Hagen Watschke ◽  
Thomas Vietor ◽  
Sabine C. Langer
Keyword(s):  
Krylov Subspace ◽  
Mechanical Impedance ◽  
Element Model ◽  
Material Parameter Identification ◽  
Material Parameters ◽  
Material Deposition ◽  
Mechanical Models ◽  
Acoustic Black Holes ◽  
Full Design ◽  
Design Freedom

One possibility in order to manufacture products with very few restrictions in design freedom is additive manufacturing. For advanced acoustic design measures like Acoustic Black Holes (ABH), the layer-wise material deposition allows the continuous alignment of the mechanical impedance by different filling patterns and degrees of filling. In order to explore the full design potential, mechanical models are indispensable. In dependency on process parameters, the resulting homogenized material parameters vary. In previous investigations, especially for ABH structures, a dependency of the material parameters on the structure’s thickness can be observed. In this contribution, beams of different thicknesses are investigated experimentally and numerically in order to identify the material parameters in dependency on the frequency and the thickness. The focused material is polyactic acid (PLA). A parameter fitting is conducted by use of a 3D finite element model and it’s reduced version in a Krylov subspace. The results yield homogenized material parameters for the PLA stack as a function of frequency and thickness. An increasing Young’s modulus with increasing frequency and increasing thickness is observed. This observed effect has considerable influence and has not been considered so far. With the received parameters, more reliable results can be obtained.

scholarly journals Model reduction methods based on Krylov subspaces

Acta Numerica ◽  
2003 ◽  
Vol 12 ◽  
pp. 267-319 ◽  
Author(s):  
Roland W. Freund
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Circuit Simulation ◽  
Krylov Subspaces ◽  
Lanczos Algorithm ◽  
Linear Dynamical Systems ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Reduction Methods ◽  
Modelling Techniques

In recent years, reduced-order modelling techniques based on Krylov-subspace iterations, especially the Lanczos algorithm and the Arnoldi process, have become popular tools for tackling the large-scale time-invariant linear dynamical systems that arise in the simulation of electronic circuits. This paper reviews the main ideas of reduced-order modelling techniques based on Krylov subspaces and describes some applications of reduced-order modelling in circuit simulation.

(Generalized) Bloch mode synthesis for the fast dispersion curve calculation of 3D periodic metamaterials

2021 ◽  
Vol 263 (4) ◽  
pp. 2102-2113
Author(s):  
Vanessa Cool ◽  
Lucas Van Belle ◽  
Claus Claeys ◽  
Elke Deckers ◽  
Wim Desmet
Keyword(s):  
Dispersion Curve ◽  
Periodic Structures ◽  
Cell Model ◽  
Stop Band ◽  
Computational Cost ◽  
Order Reduction ◽  
Element Model ◽  
Unit Cell ◽  
Reduction Techniques ◽  
Bloch Mode

Metamaterials, i.e. artificial structures with unconventional properties, have shown to be highly potential lightweight and compact solutions for the attenuation of noise and vibrations in targeted frequency ranges, called stop bands. In order to analyze the performance of these metamaterials, their stop band behavior is typically predicted by means of dispersion curves, which describe the wave propagation in the corresponding infinite periodic structure. The input for these calculations is usually a finite element model of the corresponding unit cell. Most common in literature are 2D plane metamaterials, which often consist of a plate host structure with periodically added masses or resonators. In recent literature, however, full 3D metamaterials are encountered which are periodic in all three directions and which enable complete, omnidirectional stop bands. Although these 3D metamaterials have favorable vibro-acoustic characteristics, the computational cost to analyze them quickly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this problem. In this work, the Bloch Mode Synthesis (BMS) and generalized BMS (GBMS) reduction techniques are extended from 2D to 3D periodic structures. Through several verifications, it is demonstrated that dispersion curve calculation times can be strongly reduced, while accurate stop band predictions are maintained.

Stiffness Model of the Armature Assembly in a Jet Pipe Pressure Servo Valve

2020 ◽  
Author(s):  
Yaobao Yin ◽  
Chengpeng He ◽  
Jing Li
Keyword(s):  
Finite Element ◽  
Complex Structure ◽  
Small Deformation ◽  
Element Model ◽  
Continuity Condition ◽  
The Finite Element Method ◽  
Servo Valve ◽  
Linear Elastic ◽  
Stiffness Model ◽  
Static Performance

Abstract The armature assembly of the jet pipe pressure servo valve plays an important role in connecting the torque motor and the jet pipe amplifier. A stiffness model of its complex structure is very necessary for analyzing the dynamic/static performance of the jet pipe pressure servo valve. At the present work, the component parts in the armature assembly are simplified into linear elastic beams. The simplified armature assembly is a fourfold statically indeterminate structure under the premise of small deformation. The unknown forces and moments are solved by using the section continuity condition as the additional supplement equation, and the functional relationship between the electromagnetic torque produced from the torque motor and the armature rotation angle /the nozzle displacement is derived based on the Castigliano's Theorem. The finite element model of the armature assembly is also established to calculate the deformation under different loads and different spring tube lengths. The simulated displacements with the finite element method are consistent with the theoretical results. The experimental results of the recovery pressure of the jet pipe valve verified the theoretical model. The proposed stiffness calculation method can be used as a reference for designing and optimizing the armature assembly in the jet pipe pressure servo valve.

Structural Analysis of Riveted Structures Using a New FE Modelling Technique

2010 ◽  
Author(s):  
Michele Ferracci ◽  
Francesco Vivio ◽  
Vincenzo Vullo
Keyword(s):  
Degrees Of Freedom ◽  
Complex Structure ◽  
Element Model ◽  
3D Models ◽  
Fatigue Behaviour ◽  
Fe Analysis ◽  
Structural Behaviour ◽  
Fe Modelling ◽  
Closed Form Solutions ◽  
Riveted Joints

A theoretical approach, in order to define the structural behaviour of riveted joints, is presented. The closed form solutions lead to the definition of a Rivet Element useful to FE models of multi-riveted structures. The objective is an accurate evaluation of the local stiffness of riveted joints in FE analysis, which is fundamental to perform a reliable simulation of multi-joint structures and, consequently, a good estimate of loads acting on connections; this makes it possible to introduce new general criteria allowing, for example, to predict fatigue behaviour. On the other hand, a low number of degrees of freedom is needed when several connections are present in a complex structure. The goal is to reach a reliable model of the rivet region which can be used as the basis to develop a Rivet Element in FE analysis. The proposed Rivet Element combines the precision in the simulation with a very limited number degrees of freedom in the finite element model of a complex structure having several rivets. In the present paper the structural behavior of two simple riveted specimens is investigated experimentally and numerically using a new Rivet Element. A comparison with a joint model performed with very refined non-linear 3D models of rivet and with experimental data is performed and a good agreement is shown.

Research on Sound Insulation Performance of Poroelastic Material in Complex Structure

2018 ◽  
Vol 911 ◽  
pp. 56-60
Author(s):  
Jun Zhang ◽  
Yi Hang Yu ◽  
Wen Zhong Zhao
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Transmission Loss ◽  
Complex Structure ◽  
Element Model ◽  
Acoustic Vibration ◽  
Acoustic Power ◽  
Sound Insulation ◽  
Poroelastic Materials ◽  
Flow Resistivity

A finite element model of the double-wall acoustic insulation structure with a air layer and an acoustic absorbent layer made of the poroelastic materials is set up, the responses of this acoustic-vibration system are calculated by using of the direct finite element method when having a diffuse incident acoustic field acting on the incident surface, the radiant acoustic power from the another surface are achieved, then the Transmission Loss(TL) are formulated using the incident acoustic power and the radiant acoustic power. The effects of the thicknesses, elastic modulus, flow resistivity and viscous lengths of the poroelastic materials on TL are analyzed. The results show that the thicknesses and elastic modulus have a significant effects on TL, TL are enhanced with the thicknesses increasing of the poroelastic materials layers, a 4.9dB addition of TL is achieved when thickness is added from 2cm to 3cm; TL are enhanced with the reduction of the elastic modulus in considered frequency range, and TL are reduced with the declining of viscous lengths and with the addition of the flow resistivity when the frequencies are higher than 600Hz.

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