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.

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.

scholarly journals A reduced order approach for probabilistic inversions of 3-D magnetotelluric data I: general formulation

2020 ◽  
Vol 223 (3) ◽  
pp. 1837-1863
Author(s):  
M C Manassero ◽  
J C Afonso ◽  
F Zyserman ◽  
S Zlotnik ◽  
I Fomin
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Forward Problem ◽  
Parallel Structure ◽  
Data Sets ◽  
Magnetotelluric Data ◽  
Reduced Order ◽  
Mcmc Algorithms ◽  
Simulation Based ◽  
And Performance

SUMMARY Simulation-based probabilistic inversions of 3-D magnetotelluric (MT) data are arguably the best option to deal with the nonlinearity and non-uniqueness of the MT problem. However, the computational cost associated with the modelling of 3-D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT data sets. In this contribution, we present a novel and general inversion framework, driven by Markov Chain Monte Carlo (MCMC) algorithms, which combines (i) an efficient parallel-in-parallel structure to solve the 3-D forward problem, (ii) a reduced order technique to create fast and accurate surrogate models of the forward problem and (iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method. We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parametrizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3-D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth’s interior.

A fast method for statistical grammar induction

1998 ◽  
Vol 4 (3) ◽  
pp. 191-209 ◽  
Author(s):  
WIDE R. HOGENHOUT ◽  
YUJI MATSUMOTO
Keyword(s):  
Computational Complexity ◽  
Language Processing ◽  
Large Scale ◽  
Learning Algorithm ◽  
Computational Cost ◽  
Computational Effort ◽  
Fast Method ◽  
Statistical Induction ◽  
Stochastic Context Free Grammars ◽  
Context Free

The statistical induction of stochastic context free grammars from bracketed corpora with the Inside Outside Algorithm is an appealing method for grammar learning, but the computational complexity of this algorithm has made it impossible to generate a large scale grammar. Researchers from natural language processing and speech recognition have suggested various methods to reduce the computational complexity and, at the same time, guide the learning algorithm towards a solution by, for example, placing constraints on the grammar. We suggest a method that strongly reduces that computational cost of the algorithm without placing constraints on the grammar. This method can in principle be combined with any of the constraints on grammars that have been suggested in earlier studies. We show that it is feasible to achieve results equivalent to earlier research, but with much lower computational effort. After creating a small grammar, the grammar is incrementally increased while rules that have become obsolete are removed at the same time. We explain the modifications to the algorithm, give results of experiments and compare these to results reported in other publications.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Mode Superposition Analysis of Viscously Damped Nonlinear Structural Systems Using an Incremental Algorithm

1993 ◽  
Vol 115 (4) ◽  
pp. 397-402 ◽  
Author(s):  
Yang-Tai Lin ◽  
Te-Chang Sun
Keyword(s):  
Time Integration ◽  
Computational Cost ◽  
Computational Effort ◽  
Incremental Algorithm ◽  
Structural Systems ◽  
Superposition Method ◽  
Mode Superposition ◽  
Mode Superposition Method ◽  
Nonlinear Structural ◽  
Decomposition Procedure

A mode superposition method for approximately solving the dynamic response of viscously damped nonlinear structural systems is presented, which is characterized by high accuracy and low computational cost. The method is based on an incremental decomposition procedure to formulate the motion of the discrete system, which is established by finite element theory for spatial dependence and both geometric and material nonlinearities are considered. The accuracy and efficiency are studied through two practical problems. By comparing the results using the present method with those using the direct time integration, it is found that the error is negligible and the computational effort can be significantly reduced.

An efficient approach for dynamic analysis of a rotating beam using the discrete singular convolution

2016 ◽  
Vol 230 (20) ◽  
pp. 3642-3654 ◽  
Author(s):  
JunWei Chen ◽  
Ye Ding ◽  
Han Ding
Keyword(s):  
Dynamic Analysis ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Time Integration ◽  
Computational Effort ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
Efficient Approach ◽  
Discrete Singular Convolution ◽  
Dsc Method

This paper proposes an efficient approach for dynamic analysis of a rotating beam using the discrete singular convolution (DSC). By spatially discretizing the nonlinear equations of motion of the rotating beam using the DSC method, natural frequencies of the rotating beam are obtained. Numerical results show that the DSC method accurately captures not only the low-order but also the high-order frequencies of the beam rotating at a high angular velocity in very short time, compared with the classical finite element method. Moreover, by combining the DSC method and the differential quadrature method, the dynamic equations are reduced to a set of algebraic equations. Thus the dynamic response of the rotating beam is resolved accurately and efficiently with much less computational effort, and is able to be numerically stable for long-time integration.

A Hierarchical Method for Large-Scale Two-Dimensional Layout

1983 ◽  
Vol 105 (2) ◽  
pp. 242-248
Author(s):  
K. P. Lam
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Optimal Solution ◽  
Good Alternative ◽  
Computational Effort ◽  
Practical Consideration ◽  
Two Dimensional ◽  
Hierarchical Approach ◽  
Variable Window ◽  
Alternative Solutions

The optimal layout problem of allocating different types of rectangular shapes to a large rectangular sheet (also referred to as the two-dimensional knapsack problem) is tackled by a hierarchical approach using the concepts of quad-cut, guillotine-cut, and edge-cut with variable window sizes. The method can handle sheet defects and also allows for the specification of important pieces at a fixed or variable location. In addition, the hierarchical approach has the flexibility of generating different layout patterns with little computational effort once the knapsack function for the largest window has been obtained. Although the method is suboptimal in the sense that it may not achieve the best possible result with minimum waste, extensive simulation indicates that it always gives good alternative solutions at reasonable computational cost; this is in contrast with the optimal solution for large-scale problems which often requires excessive computational effort beyond practical consideration.

Development Of Large-Scale Three-Dimensional Seismic Ground Strain Response Analysis Method and Its Application to Tokyo using Full K Computer

2016 ◽  
Vol 10 (05) ◽  
pp. 1640017 ◽  
Author(s):  
Kohei Fujita ◽  
Tsuyoshi Ichimura
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Three Dimensional ◽  
Time History ◽  
Response Analysis ◽  
Target Area ◽  
Strain Response ◽  
Analysis Method ◽  
Ground Structure ◽  
Modeling And Analysis

We developed a large-scale three-dimensional ground analysis method aimed at improving the estimation of dynamic ground strain during earthquakes. Using the developed ground modeling and analysis method, a 40 billion degrees-of-freedom unstructured finite element ground model of a 3.25[Formula: see text]km × 3.25[Formula: see text]km area of Tokyo was generated with 0.66[Formula: see text]m sized elements, and its strain time history for ground motion of the 1995 Kobe wave was computed using the full K computer system with 82,944 compute nodes. The obtained strain response showed a complex distribution reflecting the input wave characteristics, surface topography, and underlying ground structure. We also showed the seismic response of 41,675 buildings in the target area computed using the wave at surface as an input. Such a method is expected to be useful for the improvement of seismic design and mitigation of pipelines against anticipated earthquakes.

Forced Response Analysis of a Radial Turbine With Different Modelling Methods

2019 ◽  
Author(s):  
Yang Gao ◽  
Mauricio Gutierrez Salas ◽  
Paul Petrie-Repar ◽  
Tobias Gezork
Keyword(s):  
Periodic Boundary ◽  
Computational Cost ◽  
Computational Effort ◽  
Forced Response ◽  
Response Analysis ◽  
Phase Lag ◽  
Blade Vibration ◽  
Radial Turbine ◽  
High Level ◽  
Key Aspects

Abstract Forced response analysis is a critical part in the radial turbine design process. It estimates the vibration mode and level due to aerodynamic excitations and then enables the analysis of high-cycle fatigue (HCF) to determine the life span of the turbine stage. Two key aspects of the forced response analysis are the determination of the aerodynamic forcing and damping which can be calculated from unsteady 3D computational fluid dynamics (CFD) simulations. These simulations are problematic due to the high level of complexity in the simulations (multi-row, full annular, tip gap, etc.) and the consequent high-computational cost. The aim of this paper is to investigate and compare different CFD methods applied to the forced response analysis of a radial turbine. Full annular simulations are performed for the prediction of the excitation force. This method is taken as the baseline and is usually the most time-consuming one. One method of reducing the computational effort is to use Phase-lag periodic boundary conditions. A further reduction can be obtained by using a frequency-based method called nonlinear harmonic. For the prediction of aero-damping, the Phase -lag periodic boundary condition method is also available. Moreover, a frequency-based method called harmonic balance can further accelerate the aero-damping calculation. In this paper, these CFD methods will be applied to the simulations of an open-geometry radial turbine with a vaned volute. A comparison of unsteady results from different methods will be presented. These unsteady results will also be implemented to a tuned forced response analysis in order to directly compare the corresponding maximum blade vibration amplitudes.

scholarly journals A New Precursor Integral Method for Solving Space-Dependent Kinetic Equations in Neutronic and Thermal-Hydraulic Coupling System

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yingjie Wu ◽  
Baokun Liu ◽  
Han Zhang ◽  
Jiong Guo ◽  
Fu Li ◽  
...  
Keyword(s):  
Integral Method ◽  
Large Scale ◽  
Computational Cost ◽  
Kinetic Equations ◽  
Control Technique ◽  
Exponential Approximation ◽  
Taylor Approximation ◽  
Coupling System ◽  
Flux Approximation ◽  
Hydraulic Coupling

The accurate prediction of the neutronic and thermal-hydraulic coupling system transient behavior is important in nuclear reactor safety analysis, where a large-scale nonlinear coupling system with strong stiffness should be solved efficiently. In order to reduce the stiffness and huge computational cost in the coupling system, the high-performance numerical techniques for solving delayed neutron precursor equation are a key issue. In this work, a new precursor integral method with an exponential approximation is proposed and compared with widely used Taylor approximation-based precursor integral methods. The truncation errors of exponential approximation and Taylor approximation are analyzed and compared. Moreover, a time control technique is put forward which is based on flux exponential approximation. The procedure is tested in a 2D neutron kinetic benchmark and a simplified high-temperature gas-cooled reactor-pebble bed module (HTR-PM) multiphysics problem utilizing the efficient Jacobian-free Newton–Krylov method. Results show that selecting appropriate flux approximation in the precursor integral method can improve the efficiency and precision compared with the traditional method. The computation time is reduced to one-ninth in the HTR-PM model under the same accuracy when applying the exponential integral method with the time adaptive technique.

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