Periodic steady state response of large scale mechanical models with local nonlinearities

Theodosiou, Christos; Sikelis, K.; Natsiavas, S.

doi:10.1016/j.ijsolstr.2009.06.007

Cited by 8 publications

(15 citation statements)

References 22 publications

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“…For the long-term response to be steady state, the mass flow in must be greater than the mass flow out, that is, m a . m b in equations (1)- (3). For the response to be zero, mass flow out must exceed mass flow in, m b .…”

Section: Two-parameter Continuation Resultsmentioning

confidence: 99%

“…A variety of approaches to complement conventional time history simulations of nonlinear dynamic models have been presented in engine literature: recurrence plots and recurrence quantification analysis have been used to investigate the relation between injection impulse with engine speed 1 and the dynamics associated with cycle-to-cycle variations in a diesel engine 2 ; multi-level substructuring procedures were used to study periodic responses of large engine models in Theodosiou et al 3 ; 0-1 testing was applied to classify chaotic behaviour within the combustion process. 4 Understanding the steady-state response of engine models is also highlighted as a challenge in the literature: in Beno et al, 5 the authors studied the calibration of a turbocharged diesel engine by representing the highly nonlinear system as a mean value model.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical continuation applied to internal combustion engine models

Smith

Knowles

Mason

2020

Proceedings of the Institution of Mechanical Engineers, Part D:

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This paper proposes tools from bifurcation theory, specifically numerical continuation, as a complementary method for efficiently mapping the state-parameter space of an internal combustion engine model. Numerical continuation allows a steady-state engine response to be traced directly through the state-parameter space, under the simultaneous variation of one or more model parameters. By applying this approach to two nonlinear engine models (a physics-based model and a data-driven model), this work determines how input parameters ‘throttle position’ and ‘desired load torque’ affect the engine’s dynamics. Performing a bifurcation analysis allows the model’s parameter space to be divided into regions of different qualitative types of the dynamic behaviour, with the identified bifurcations shown to correspond to key physical properties of the system in the physics-based model: minimum throttle angles required for steady-state operation of the engine are indicated by fold bifurcations; regions containing self-sustaining oscillations are bounded by supercritical Hopf bifurcations. The bifurcation analysis of a data-driven engine model shows how numerical continuation could be used to evaluate the efficacy of data-driven models.

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Section: Two-parameter Continuation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical continuation applied to internal combustion engine models

Smith

Knowles

Mason

2020

Proceedings of the Institution of Mechanical Engineers, Part D:

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“…Consequently, the ultimate objective of this work is to present a complete and systematic methodology, which will be useful for performing fatigue studies of complex mechanical models, by appropriately employing and combining effective numerical techniques developed in earlier studies for the first time. 4,17 In fact, this is the novelty of the present work.…”

Section: Introductionmentioning

confidence: 89%

“…In particular, a method developed recently for obtaining periodic steady-state response of a periodically excited nonlinear system is applied, leading to an additional reduction in the calculations needed in predicting the fatigue life of a structure. 17 The validity and effectiveness of the new methodology is illustrated by presenting numerical results for an involved finite element model of a city bus, subjected to excitation resulting from typical urban road irregularities. Determination of the response leads to information, which is then utilized for predicting fatigue failure.…”

Section: Introductionmentioning

confidence: 99%

Stochastic dynamics and fatigue analysis of large-scale mechanical models using multilevel substructuring

Georgios

Sikelis

Natsiavas

2012

Proceedings of the Institution of Mechanical Engineers, Part K:

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An efficient methodology is presented for predicting dynamic response and fatigue life of large-scale nonlinear mechanical models, subjected to random excitation. The methodology developed is based on a combination of techniques leading to a fast and accurate determination of the dynamic response with a method related to an efficient prediction of fatigue life. Specifically, the first step involves application of an appropriate coordinate transformation, causing a drastic reduction in the degrees of freedom. This opens the way to the application of another numerical method, leading to direct determination of periodic steady-state response of nonlinear systems under periodic forcing. This approach provides a solid foundation for the subsequent application of a rainflow stress cycle counting method, leading to prediction of fatigue failure. The computational accuracy and effectiveness of the methodology is illustrated by a quite involved example model, representing a city bus subjected to road excitation. Typical results are presented for both the stochastic response and the fatigue life by considering excitation arising from selected road profiles with known statistical properties. Special attention is paid to assessing the effect of the nonlinearity, by considering profiles of different quality. Moreover, a critical comparison is performed on results referring to the expected fatigue lifetime, obtained by applying methods in both the frequency and the time domain. In this way, the applicability of classical spectral methods in nonlinear models is also investigated.

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“…motions [1]. In fact, the method applied here is an extension of a similar method applied to systems with smooth nonlinearities, subjected to periodic external excitation [23]. In particular, a shooting method has been applied for the purposes of the present study, adjusted to fit the class of dynamical systems examined [4].…”

Section: Periodic Steady State Response and Stabilitymentioning

confidence: 99%

On periodic steady state response and stability of Filippov-type mechanical models

2011

Self Cite

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In the first part of this study, the basic steps of a methodology are presented, leading to a long time response of a class of periodically excited mechanical models with contact and dry friction. In particular, the models examined belong to the special class of Filippov-type dynamical systems, which possess continuous displacements and velocities, but exhibit discontinuities in their accelerations. The direct determination of periodic steady state response of this class of models is achieved by combining suitable numerical integration of the equations of motion with an appropriate technique yielding the corresponding monodromy matrix. This matrix, which arises from a linearization of the motion around a located periodic solution, involves saltations (jumps) and is also useful in predicting its stability properties. The analytical part is complemented by a suitable continuation procedure, enabling evaluation of complete branches of periodic motions. In the second part of the study, the effectiveness of the methodology developed is confirmed by presenting representative sets of numerical results obtained for selected examples. The first two of them are single degree of freedom oscillators. Besides investigating some interesting aspects of regular periodic response, some cases involving rich dynamics of the C. Theodosiou · A. Pournaras · S. Natsiavas ( ) class of the system examined are also studied in a systematic way. The last example is a more involved and challenging model, related to the function of an engine valve and characterized by large numerical stiffness.

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Periodic steady state response of large scale mechanical models with local nonlinearities

Cited by 8 publications

References 22 publications

Numerical continuation applied to internal combustion engine models

Numerical continuation applied to internal combustion engine models

Stochastic dynamics and fatigue analysis of large-scale mechanical models using multilevel substructuring

On periodic steady state response and stability of Filippov-type mechanical models

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