Nonlinear dynamics and control in macro/micro-mechanics: some computational issues

Computational issues in the global dynamics of two systems in micro- and macro-mechanics, with different dimensionality, are addressed. Attention is focused on calculation of integrity measures, determination of saddle manifolds undergoing global bifurcations, implementation of a control procedure for delaying basins erosion, selection of 2D cross-sections of multidimensional basins of attraction for understanding the role of transient dynamics in the global scenario of coupled steady responses

Response robustness and safety against jump to contact in AFMs controlled via different techniques

The role of a global dynamics analysis to assess a system robustness and actual safety in operating conditions is investigated by studying the effect of different local and global control techniques on the nonlinear behavior of a noncontact AFM via dynamical integrity concepts and tools

Space-time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables

This paper presents space-time numerical simulation and validation of analytical predictions for the finite-amplitude forced dynamics of suspended cables. The main goal is to complement analytical and numerical solutions, accomplishing overall quantitative/qualitative comparisons of nonlinear response characteristics. By relying on an approximate, kinematically non-condensed, planar modeling, a simply supported horizontal cable subject to a primary external resonance and a 1:1, or 1:1 vs. 2:1, internal resonance is analyzed. To obtain analytical solution, a second-order multiple scales approach is applied to a complete eigenfunction-based series of nonlinear ordinary-differential equations of cable damped forced motion. Accounting for both quadratic/cubic geometric nonlinearities and multiple modal contributions, local scenarios of cable uncoupled/coupled responses and associated stability are predicted, based on chosen reduced-order models. As a cross-checking tool, numerical simulation of the associated nonlinear partial-differential equations describing the dynamics of the actual infinite-dimensional system is carried out using a finite difference technique employing a hybrid explicit-implicit integration scheme. Based on system control parameters and initial conditions, cable amplitude, displacement and tension responses are numerically assessed, thoroughly validating the analytically predicted solutions as regards the actual existence, the meaningful role and the predominating internal resonance of coexisting/competing dynamics. Some methodological aspects are noticed, along with a discussion on the kinematically approximate versus exact, as well as planar versus non-planar, cable modeling

Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables

Recent research literature mostly deals with nonlinear resonant dynamics of low-extensible cables involving transversal modes. Herein, we aim to investigate geometrically nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables, whose material properties are assumed to be linearly elastic. Depending on cable elasto-geometric properties, the spectrum of low-order planar frequencies manifests primary and secondary frequency crossover phenomena of transversal/transversal and longitudinal/transversal modes, respectively. By focusing on 1:1 internal resonances, nonlinear equations of finite-amplitude, harmonically forced and damped, cable motion are considered, fully accounting for overall inertia and displacement coupling effects. Meaningful quadratic nonlinear contributions of non-resonant, higher-order, longitudinal modes are highlighted via a multimode-based, second-order multiple scales solution. Overall coupled/uncoupled dynamic responses, bifurcations, stability and space-time-varying displacements due to longitudinal/transversal (vs. transversal/transversal) modal interactions at secondary (vs. primary) crossovers are analytically and numerically evaluated, along with the resonant longitudinal mode-induced dynamic forces

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part II : internal resonance activation, reduced-order models and nonlinear normal modes

Resonant multi-modal dynamics due to planar 2:1 internal resonances in the nonlinear, finite-amplitude, free vibrations of horizontal/inclined cables are parametrically investigated based on the second-order multiple scales solution in Part I [1]. The already validated kinematically non-condensed cable model accounts for the effects of both non-linear dynamic extensibility and system asymmetry due to inclined sagged configurations. Actual activation of 2:1 resonances is discussed, enlightening on a remarkable qualitative difference of horizontal/inclined cables as regards non-linear orthogonality properties of normal modes. Based on the analysis of modal contribution and solution convergence of various resonant cables, hints are obtained on proper reduced-order model selections from the asymptotic solution accounting for higher-order effects of quadratic nonlinearities. The dependence of resonant dynamics on coupled vibration amplitudes, and the significant effects of cable sag, inclination and extensibility on system non-linear behavior are highlighted, along with meaningful contributions of longitudinal dynamics. The spatio-temporal variation of non-linear dynamic configurations and dynamic tensions associated with 2:1 resonant non-linear normal modes is illustrated. Overall, the analytical predictions are validated by finite difference-based numerical investigations of the original partial-differential equations of motion

The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables

This study aims at comparing non-linear modal interactions in shallow horizontal cables with kinematically non-condensed vs. condensed modeling, under simultaneous primary external and internal resonances. Planar 1:1 or 2:1 internal resonance is considered. The governing partial-differential equations of motion of non-condensed model account for spatio-temporal modification of dynamic tension, and explicitly capture non-linear coupling of longitudinal/ vertical displacements. On the contrary, in the condensed model, a single integro-differential equation is obtained by eliminating the longitudinal inertia according to a quasi-static cable stretching assumption, which entails spatially uniform dynamic tension. This model is largely considered in the literature. Based on a multi-modal discretization and a second-order multiple scales solution accounting for higher-order quadratic effects of a infinite number of modes, coupled/uncoupled dynamic responses and the associated stability are evaluated by means of frequency- and force-response diagrams. Direct numerical integrations confirm the occurrence of amplitude-steady or -modulated responses. Non-linear dynamic configurations and tensions are also examined. Depending on internal resonance condition, system elasto-geometric and control parameters, the condensed model may lead to significant quantitative and/or qualitative discrepancies, against the non-condensed model, in the evaluation of resonant dynamic responses, bifurcations and maximal/minimal stresses. Results of even shallow cables reveal meaningful drawbacks of the kinematic condensation and allow us to detect cases where the more accurate non-condensed model has to be used

Comparing Statistical Feature and Artificial Neural Networks for Control Chart Pattern Recognition: A Case Study

Control chart has been widely used for monitoring production process, especially in evaluating the quality performance of a product. An uncontrolled process is usually known by recognizing its chart pattern, and then performing some actions to overcome the problems. In high speed production process, real-time data is recorded and plotted almost automatically, and the control chart pattern needs to be recognized immediately for detecting any unusual process behavior. Neural networks for automatic control chart recognition have been studied in detecting its pattern. In the field of computer science, the performance of its automatic and fast recognition ability can be a substitution for a conventional method by human. Some researchers even have developed newer algorithm to increase the recognition process of this neural networks control chart. However, artificial approaches have some difficulties in implementation, especially due to its sophisticated programming algorithm. Another competing method, based on statistical feature also has been considered in recognition process. Control chart is related to applied statistical method, so it is not unreasonable if statistical properties are developed for its pattern recognition. Correlation coefficient, one of classic statistical features, can be applied in control chart recognition. It is a simpler approach than the artificial one. In this paper, the comparison between these two methods starts by evaluating the behavior of control chart time series point, and measured for its closeness to some training data that are generated by simulation and followed some unusual control chart pattern. For both methods, the performance is evaluated by comparing their ability in detecting the pattern of generated control chart points. As a sophisticated method, neural networks give better recognition ability. The statistical features method simply calculate the correlation coefficient, even with small differences in recognizing the generated pattern compared to neural networks, but provides easy interpretation to justify the unusual control chart pattern. Both methods are then applied in a case study and performances are then measured

Optimization of a pseudoelastic absorber for vibration mitigation

Damic vibration absorbers (DVAs) have received special attention in recent years due to their capability to reduce structural vibrations of a primary structure. In this work, a DVA of the Tuned Mass Damper type based on a Shape Memory Alloy (SMA) element with pseudoelastic behavior is considered. Owing to their rich thermomechanical response, SMAs can exhibit hysteresis loops with rather different features in terms of overall energy dissipation and of pseudoelastic stiffness. As a first step towards the comprehensive evaluation of the performances of such a device, the optimization of a TMD based on SMA devices with different features is studied. Numerical simulations show that the size and the shape of the pseudoelastic loops can influence in a significant way the performances of the DVA