Multiparametric Analysis of Resonance Peak Vibrations for Nonlinear Jointed Structures

2011 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Frequency Domain Analysis ◽  
Resonance Peak ◽  
Test Cases ◽  
Finite Element Models ◽  
Contact Interface ◽  
Interface Elements ◽  
Practical Test ◽  
Nonlinear Contact

A methodology has been developed to analyse and to optimize the resonance peak amplitudes and frequencies for essentially nonlinear periodic vibrations of jointed structures. The frequency domain analysis of realistic finite element models of jointed structures which can contain millions of degrees of freedom is performed. The detailed description of friction, gap and other types of the nonlinear contact interfaces in jointed structures is provided by contact interface elements. The resonance peak characteristics are calculated directly as functions of several parameters of contact interfaces and excitation. The efficiency of the methodology is demonstrated on a representative set of practical test cases.

Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Discs With Scatter of Contact Interface Characteristics

2004 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Nonlinear Vibrations ◽  
Forced Response ◽  
Finite Element Models ◽  
Contact Interface ◽  
Linear Vibration ◽  
Interface Characteristics ◽  
Blade Frequency

An efficient method for analysis of nonlinear vibrations of mistuned bladed disc assemblies has been developed. As a result, this development has facilitated the use of large-scale finite element models for realistic bladed discs, as used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed discs. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interation forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed discs has been performed. For a practical high-pressure bladed turbine disc, several types of nonlinear forced response have been considered including: (i) mistuning by scatter of underplatform dampers; (ii) mistuning by shroud gap scatter; (iii) mistuning by blade frequency scatter in the presence of nonlinear shroud interactions.

A Parallel Solution Strategy for Finite Element Models

1996 ◽  
Author(s):  
Jordan J. Cox ◽  
Jeffrey A. Talbert ◽  
Eric Mulkay
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Decomposition Methods ◽  
Finite Element Models ◽  
Unique Contribution ◽  
Matrix Equations ◽  
Parallel Solution ◽  
The Finite Element Model ◽  
Parallel Fashion

Abstract This paper presents a method for naturally decomposing finite element models into sub-models which can be solved in a parallel fashion. The unique contribution of this paper is that the decomposition strategy comes from the geometric features used to construct the solid model that the finite element model represents. Domain composition and domain decomposition methods are used to insure global compatibility. These techniques reduce the N2 behavior of traditional matrix solving techniques, where N is the number of degrees of freedom in the global set of matrix equations, to a sum of m matrices with n2 behavior, where n represents the number of degrees of freedom in the smaller sub-model matrix equations.

Structural Abstraction in Snap-fit Analysis

2000 ◽  
Vol 122 (4) ◽  
pp. 395-402 ◽  
Author(s):  
Gaurav Suri ◽  
Anthony F. Luscher
Keyword(s):  
Finite Element ◽  
Accurate Estimation ◽  
Test Cases ◽  
Finite Element Models ◽  
Feature Models ◽  
Engineering Activity ◽  
End Conditions ◽  
Unrealistic Assumption ◽  
Fixed End ◽  
Plastic Parts

Snap-fit design has always been more of an art instead of an engineering activity. Research in this area focuses on generating finite element models for predicting the performance of snap-fit features. Such research typically uses fixed-end conditions at the base of the snap-fit feature. Often this is an unrealistic assumption, because snap-fits are usually molded on plastic parts with significant flexibility. The performance of snap-fits can be significantly influenced by this additional flexibility. To predict this performance of snap-fits it often becomes necessary to analyze the entire part, which can be a costly and time consuming process. There is no general methodology in the open literature to incorporate base-part flexibility into the design of snap-fit features. Existing work in this area is inaccurate and limited to certain base-part and snap-fit topologies. This paper proposes a new methodology called structural abstraction for incorporating base-part flexibility into snap-fit feature models. This methodology abstracts base-parts as spring elements with various stiffnesses. The underlying theory and the relevant relationships are developed and the approach is validated using several test cases. Independence of the approach to both base-part and snap-fit topologies is established and shown to be a major advantage of this technique. Use of this methodology will improve snap-fit analysis and give a more accurate estimation of retention strength. It is shown that in certain cases the improvement in accuracy over conventional finite element models of snap-fits can be as high as 70 percent. [S1050-0472(00)02504-6]

scholarly journals How to compute invariant manifolds and their reduced dynamics in high-dimensional finite element models

2021 ◽  
Author(s):  
Shobhit Jain ◽  
George Haller
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Invariant Manifolds ◽  
Mechanical Systems ◽  
Forced Response ◽  
High Dimensional ◽  
Nonlinear Phenomena ◽  
Finite Element Models ◽  
Engineering Structures ◽  
Backbone Curves

AbstractInvariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful tools for the computation of forced response curves, backbone curves, detached resonance curves (isolas) via exact reduced-order models. For conservative nonlinear mechanical systems, Lyapunov subcenter manifolds and their reduced dynamics provide a way to identify nonlinear amplitude–frequency relationships in the form of conservative backbone curves. Despite these powerful predictions offered by invariant manifolds, their use has largely been limited to low-dimensional academic examples. This is because several challenges render their computation unfeasible for realistic engineering structures described by finite element models. In this work, we address these computational challenges and develop methods for computing invariant manifolds and their reduced dynamics in very high-dimensional nonlinear systems arising from spatial discretization of the governing partial differential equations. We illustrate our computational algorithms on finite element models of mechanical structures that range from a simple beam containing tens of degrees of freedom to an aircraft wing containing more than a hundred–thousand degrees of freedom.

Improving Spot Weld Models in Structural Dynamics

2003 ◽  
Author(s):  
Matteo Palmonella ◽  
Michael I. Friswell ◽  
Cristinel Mares ◽  
John E. Mottershead
Keyword(s):  
Finite Element ◽  
Structural Dynamics ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Spot Weld ◽  
Physical Parameters ◽  
Finite Element Models ◽  
Spot Welds ◽  
Coarse Meshes

This paper gives an overview of the finite element modelling of spot welds for the analysis of the dynamic response of structures. In particular models for dynamic analysis that use coarse meshes and equivalent parameters are considered. A major requirement for these models is their accuracy in predicting the dynamic behaviour of spot welded structures despite the low number of degrees of freedom. Three different models of spot welds are investigated [1–3] and for each model physical parameters have to be assigned based on engineering insight. The aim of the present paper is to improve the accuracy of these three models by searching for the optimum values of the parameters characterising the spot weld models using experimental data. For this purpose a benchmark structure has been analysed, consisting of a thin walled hat section beam made of two plates welded together by twenty spot welds. The predicted natural frequencies and modes of the benchmark structure have been compared to the experimental modes. Updating of the finite element models has been performed and the accuracy of the three models has been significantly improved.

A Direct Two Response Approach for Updating Analytical Dynamic Models of Structures With Emphasis on Uniqueness

1990 ◽  
Vol 112 (1) ◽  
pp. 107-111 ◽  
Author(s):  
S. R. Ibrahim ◽  
C. Stavrinidis ◽  
E. Fissette ◽  
O. Brunner
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Normal Modes ◽  
Element Model ◽  
Finite Element Models ◽  
Complex Modes ◽  
Structural Responses ◽  
Stiffness And Damping ◽  
The Finite Element Model

An approach, based on utilizing only two sets of structural responses and the enforcement of the conditions for a unique solution, is presented for the updating of Finite Element Models. The responses required can be any two identified normal modes, any two identified complex modes, or two forced harmonic response vectors in the neighborhood of any two natural frequencies of the structure under test. The mass, stiffness, and damping matrices are interactively and simultaneously corrected in a direct noniterative procedure. A uniqueness factor is automatically computed in the procedure to indicate the correctability of the Finite Element Model under consideration. The number of measurement locations is assumed to be less than the number of degrees of freedom of the analytical model. Provisions for completing and smoothing the measured or identified responses are included to reduce the effects of measurement noise and identification error. Preliminary results on simple models are presented in support of the proposed technique.

Multiharmonic Analysis of Nonlinear Whole Engine Dynamics With Bladed Disc-Casing Rubbing Contacts

2012 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Gas Turbine ◽  
Frequency Domain Analysis ◽  
Forced Response ◽  
Contact Forces ◽  
Turbine Engines ◽  
Test Cases ◽  
Gas Turbine Engines ◽  
Interface Elements ◽  
Friction Forces ◽  
Engine Components

A method has been developed for frequency domain analysis of steady state forced response in gas turbine engines in the presence of rubbing and snubbing contacts between bladed discs and casing and between other rotor and stator engine components. The multiharmonic contact interface elements have been derived for modelling the nonlinear contact interactions: (i) at bearings and (ii) bladed disc-casing rubbing contacts with using flexible models for rotor and stator structures. The elements allow for the asymmetry of the casing, the discrete blade contacts with casing, individual blade-casing gap values, nonlinear dependency of the contact forces on rotor-stator incursion and friction forces, intermittent contacts between blades and the casing. High accuracy and computational efficiency of the methods and models developed has been demonstrated on a set of test cases and on an example of analysis of a realistic gas turbine structure.

Dynamics of Large Scale Finite Element Models With Multiple Unilateral Constraints

2009 ◽  
Author(s):  
Christos Theodosiou ◽  
Anestis Iakovidis ◽  
Sotirios Natsiavas
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Complex Geometry ◽  
Finite Element Models ◽  
Unilateral Constraints ◽  
Nonlinear Properties ◽  
Unilateral Contact And Friction

Determination of the response of mechanical structures with complex geometry requires application of the finite element method. This leads frequently to models with a relatively large number of degrees of freedom, which may also possess nonlinear properties. Things become more complicated for systems involving unilateral contact and friction. In classical structural dynamics approaches, such constraints are usually modeled by special contact elements, with characteristics selected in a delicate manner. This study presents a systematic numerical methodology, which is suitable for determining dynamic response of large scale finite element models of mechanical systems involving multiple unilateral constraints. The method is based on a proper combination of results from two classes of direct integration methodologies. The first one includes standard methods employed in determining dynamic response of structural models with smooth nonlinearities, while the second class includes specialized methodologies that simulate response of dynamical systems with unilateral constraints. The validity and effectiveness of the methodology developed is illustrated by numerical results.

A Generalized Conforming Quadrilateral Membrane Element Less Sensitive to Geometric Distortion

1998 ◽  
Vol 1 (3) ◽  
pp. 185-191 ◽  
Author(s):  
Yin Xu ◽  
Zhifei Long ◽  
Yuqiu Long
Keyword(s):  
Finite Element ◽  
High Precision ◽  
Degrees Of Freedom ◽  
Geometric Distortion ◽  
Finite Element Models ◽  
Membrane Element ◽  
Mesh Distortion ◽  
Long Period ◽  
Rotational Degrees Of Freedom ◽  
General Method

Many finite element models have very acceptable performance when the computing meshes are regular. However, as the level of mesh distortion is increasing, the accuracy of the solutions deteriorates rapidly. Therefore, how to formulate an element that is less sensitive to geometric distortion is an important question for study for a long period. In this paper, a simple quadrilateral membrane element with rotational degrees-of-freedom is developed with the approach of the generalized conforming element proposed by Long Yuqiu (1989). The new element exhibits excellent feature, that is, less sensitive to geometric distortion. A general method to formulate high precision finite element less sensitive to geometric distortion is provided in this paper.

Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Disks With Scatter of Contact Interface Characteristics

2005 ◽  
Vol 127 (1) ◽  
pp. 128-136 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Forced Response ◽  
Finite Element Models ◽  
Linear Vibration ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Interface Characteristics ◽  
Blade Frequency

An efficient method for analysis of nonlinear vibrations of mistuned bladed disk assemblies has been developed. This development has facilitated the use of large-scale finite element models for realistic bladed disks, used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed disks. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interaction forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed disks has been performed. For a practical high-pressure bladed turbine disk, several types of nonlinear forced response have been considered, including mistuning by (i) scatter of underplatform dampers, (ii) shroud gap scatter, and (iii) blade frequency scatter in the presence of nonlinear shroud interactions.

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