Integrated Redesign of Large-Scale Structures by Large Admissible Perturbations

2003 ◽  
Vol 125 (4) ◽  
pp. 234-241 ◽  
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas ◽  
Denby Morrison
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Direct Method ◽  
Computational Effort ◽  
Forced Response ◽  
Response Amplitude ◽  
Computational Time ◽  
Performance Constraints ◽  
Large Admissible Perturbations ◽  
Design Selection

In structural redesign (inverse design), selection of the number and type of performance constraints is a major challenge. This issue is directly related to the computational effort and, most importantly, to the success of the optimization solver in finding a solution. These issues are the focus of this paper, which provides and discusses techniques that can help designers formulate a well-posed integrated complex redesign problem. LargE Admissible Perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, free vibration, static deformation, and forced response amplitude constraints. The existing algorithm, referred to as the Incremental Method is improved in this paper for problems with static and forced response amplitude constraints. This new algorithm, referred to as the Direct Method, offers comparable level of accuracy for less computational time and provides robustness in solving large-scale redesign problems in the presence of damping, nonstructural mass, and fluid-structure interaction effects. Common redesign problems include several natural frequency constraints and forced response amplitude constraints at various frequencies of excitation. Several locations on the structure and degrees of freedom can be constrained simultaneously. The designer must exercise judgment and physical intuition to limit the number of constraints and consequently the computational time. Strategies and guidelines are discussed. Such techniques are presented and applied to a 2,694 degree of freedom offshore tower.

Cognate Space Identification for Forced Response Structural Redesign

2003 ◽  
Vol 127 (3) ◽  
pp. 227-233
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas
Keyword(s):  
Direct Method ◽  
A Priori ◽  
Normal Modes ◽  
Forced Response ◽  
Response Amplitude ◽  
Computational Time ◽  
Practical Guidelines ◽  
Structural Redesign ◽  
Large Admissible Perturbations ◽  
Perturbation Equations

Large admissible perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, forced response amplitude constraints. In previous work, two LEAP algorithms, namely the incremental method (IM) and the direct method (DM), were developed. A powerful feature of LEAP is the general perturbation equations derived in terms of normal modes, the selection of which is a determinant factor for a successful redesign. The normal modes of a structure may be categorized as stretching, bending, torsional, and mixed modes and grouped into cognate spaces. In the context of redesign by LEAP, the physical interpretation of a mode-to-response cognate space lies in the fact that a mode from one space barely affects change in a mode from another space. Perturbation equations require computation of many perturbation terms corresponding to individual modes. Identifying modes with negligible contribution to the change in forced response amplitude eliminates a priori computation of numerous perturbation terms. Two methods of determining mode-to-response cognate spaces, one for IM and one for DM, are presented and compared. Trade-off between computational time and accuracy is assessed in order to provide practical guidelines to the designer. The developed LEAP redesign algorithms are applied to the redesign of a simple cantilever beam and a complex offshore tower.

Cognate Space Identification for Forced Response Structural Redesign

2002 ◽  
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas
Keyword(s):  
Direct Method ◽  
A Priori ◽  
Normal Modes ◽  
Forced Response ◽  
Response Amplitude ◽  
Computational Time ◽  
Incremental Method ◽  
Practical Guidelines ◽  
Structural Redesign ◽  
Perturbation Equations

LargE Admissibility Perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, forced response amplitude constraints. In previous work, two LEAP algorithms, namely the Incremental Method (IM) and the Direct Method (DM), were developed. A powerful feature of LEAP is the general perturbation equations derived in terms of normal modes, the selection of which is a determinant factor for a successful redesign. The normal modes of a structure may be categorized as stretching, bending, torsional, and mixed modes and grouped into cognate spaces. In the context of redesign by LEAP, the physical interpretation of a mode-to-response cognate space lies in the fact that a mode from one space barely affects change in a mode from another space. Perturbation equations require computation of many perturbation terms corresponding to individual modes. Identifying modes with negligible contribution to the change in forced response amplitude eliminates a priori computation of numerous perturbation terms. Two methods of determining mode-to-response cognate space, one for IM and one for DM, are presented and compared. Trade-off between computational time and accuracy is assessed in order to provide practical guidelines to the designer. The developed LEAP redesign algorithms are applied to the redesign of a simple cantilever beam and a complex offshore tower.

Vibration Analysis of Flexible Rotating Rings Using a Spectral Element Formulation

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Danilo Beli ◽  
Priscilla Brandão Silva ◽  
José R. de França Arruda
Keyword(s):  
Degrees Of Freedom ◽  
Beam Theory ◽  
Spectral Element ◽  
Forced Response ◽  
Computational Time ◽  
Applied Theory ◽  
Element Formulation ◽  
Arbitrary Boundary ◽  
Dynamics Problems ◽  
Euler Bernoulli Beam

In this work, the forced response of rotating rings exhibiting nonperiodic and periodic variations in material properties and geometry is assessed by means of the spectral element method (SEM). Based on the Euler–Bernoulli beam theory, a spectral element for a planar rotating ring is derived. This spectral element allows the investigation of the effects of structural damping, internal pressure and elastic foundations in the harmonic response of rotating rings. The dynamic response of rotating rings including periodic imperfections that lead to band gap effects is addressed. The spectral element formulation provides exact solutions within the range of validity of the applied theory using a reduced number of degrees-of-freedom. Thus, it contributes to reducing the computational time. It also provides a straightforward way to solve structural dynamics problems including arbitrary boundary conditions and discontinuities. The proposed formulation is validated by comparison with analytical solutions, which are available only for uniform homogenous rings.

Multiharmonic Response Analysis of Systems With Local Nonlinearities Based on Describing Functions and Linear Receptance

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
F. Wei ◽  
G. T. Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Time Integration ◽  
Computational Cost ◽  
Kinetic Equations ◽  
Computational Effort ◽  
Response Analysis ◽  
Algebraic Equations ◽  
Describing Functions ◽  
And Performance

Direct time integration methods are usually applied to determine the dynamic response of systems with local nonlinearities. Nevertheless, these methods are computationally expensive to predict the steady state response. To significantly reduce the computational effort, a new approach is proposed for the multiharmonic response analysis of dynamical systems with local nonlinearities. The approach is based on the describing function (DF) method and linear receptance data. With the DF method, the kinetic equations are converted into a set of complex algebraic equations. By using the linear receptance data, the dimension of the complex algebraic equations, which should be solved iteratively, are only related to nonlinear degrees of freedom (DOFs). A cantilever beam with a local nonlinear element is presented to show the procedure and performance of the proposed approach. The approach can greatly reduce the size and computational cost of the problem. Thus, it can be applicable to large-scale systems with local nonlinearities.

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.

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.

Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and its Application to Bladed Disks With Shroud Contact

2013 ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek ◽  
Christian Siewert ◽  
Andreas Hartung
Keyword(s):  
Modal Analysis ◽  
Limit Cycle ◽  
Large Scale ◽  
Computational Effort ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Modal Analysis

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the Multi-Harmonic Balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary e.g. for robust design optimization are often not possible in practice due to the resulting computational effort. In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using a Complex Nonlinear Modal Analysis technique based on the work of Laxalde and Thouverez [1]. The methodology in [1] was refined by an exact condensation approach as well as analytical calculation of gradients in order to efficiently study localized nonlinearities in large-scale systems. Moreover, a continuation method was employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the Single Nonlinear Resonant Mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for re-computation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system. The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. In contrast to [1], the contact constraints account for variable normal load and lift-off in addition to dry friction. Forced response functions, backbone curves for varying normal preload and excitation level as well as flutter-induced limit cycle oscillations are analysed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.

scholarly journals Development of an Efficient Thermal Electric Skipping Strategy for the Management of a Series/Parallel Hybrid Powertrain

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 889
Author(s):  
Vincenzo De Bellis ◽  
Enrica Malfi ◽  
Jean-Marc Zaccardi
Keyword(s):  
Control Strategy ◽  
Degrees Of Freedom ◽  
Control Strategies ◽  
Minimum Principle ◽  
Computational Effort ◽  
Pollutant Emissions ◽  
Computational Time ◽  
Pontryagin Minimum Principle ◽  
Optimal Control Strategy ◽  
Hybrid Powertrain

In recent years, the development of hybrid powertrain allowed to substantially reduce the CO2 and pollutant emissions of vehicles. The optimal management of such power units represents a challenging task since more degrees of freedom are available compared to a conventional pure-thermal engine powertrain. The a priori knowledge of the driving mission allows identifying the actual optimal control strategy at the expense of a quite relevant computational effort. This is realized by the off-line optimization strategies, such as Pontryagin minimum principle—PMP—or dynamic programming. On the other hand, for an on-vehicle application, the driving mission is unknown, and a certain performance degradation must be expected, depending on the degree of simplification and the computational burden of the adopted control strategy. This work is focused on the development of a simplified control strategy, labeled as efficient thermal electric skipping strategy—ETESS, which presents performance similar to off-line strategies, but with a much-reduced computational effort. This is based on the alternative vehicle driving by either thermal engine or electric unit (no power-split between the power units). The ETESS is tested in a “backward-facing” vehicle simulator referring to a segment C car, fitted with a hybrid series-parallel powertrain. The reliability of the method is verified along different driving cycles, sizing, and efficiency of the power unit components and assessed with conventional control strategies. The outcomes put into evidence that ETESS gives fuel consumption close to PMP strategy, with the advantage of a drastically reduced computational time. The ETESS is extended to an online implementation by introducing an adaptative factor, resulting in performance similar to the well-assessed equivalent consumption minimization strategy, preserving the computational effort.

Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and Its Application to Bladed Disks With Shroud Contact

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek ◽  
Christian Siewert ◽  
Andreas Hartung
Keyword(s):  
Limit Cycle ◽  
Large Scale ◽  
Computational Effort ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Reduced Order Model ◽  
Limit Cycle Oscillations ◽  
Order Model ◽  
Reduced Order ◽  
Modal Properties

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the multiharmonic balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary, e.g., for robust design optimization are often not possible in practice due to the resulting computational effort. In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using the generalized Fourier-Galerkin method. In order to efficiently study localized nonlinearities in large-scale systems, an exact condensation approach as well as analytically calculated gradients are employed. Moreover, a continuation method is employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the single nonlinear resonant mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for recomputation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system. The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. Forced response functions, backbone curves for varying normal preload, and excitation level as well as flutter-induced limit cycle oscillations are analyzed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.

Combustion Driven by Fragment-based Ab Initio Molecular Dynamics Simulation

2019 ◽  
Author(s):  
Liqun Cao ◽  
Jinzhe Zeng ◽  
Mingyuan Xu ◽  
Chih-Hao Chin ◽  
Tong Zhu ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Large Scale ◽  
Methane Combustion ◽  
Combustion Method ◽  
Dynamics Simulation ◽  
Ab Initio Molecular Dynamics ◽  
Computational Time ◽  
Combustion Mechanism ◽  
Daily Lives

Combustion is a kind of important reaction that affects people's daily lives and the development of aerospace. Exploring the reaction mechanism contributes to the understanding of combustion and the more efficient use of fuels. Ab initio quantum mechanical (QM) calculation is precise but limited by its computational time for large-scale systems. In order to carry out reactive molecular dynamics (MD) simulation for combustion accurately and quickly, we develop the MFCC-combustion method in this study, which calculates the interaction between atoms using QM method at the level of MN15/6-31G(d). Each molecule in systems is treated as a fragment, and when the distance between any two atoms in different molecules is greater than 3.5 Å, a new fragment involved two molecules is produced in order to consider the two-body interaction. The deviations of MFCC-combustion from full system calculations are within a few kcal/mol, and the result clearly shows that the calculated energies of the different systems using MFCC-combustion are close to converging after the distance thresholds are larger than 3.5 Å for the two-body QM interactions. The methane combustion was studied with the MFCC-combustion method to explore the combustion mechanism of the methane-oxygen system.

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