1,720,977 research outputs found
BIFURCATION SCENARIOS, DYNAMICAL INTEGRITY AND CONTROL OF NONCONTACT ATOMIC FORCE MICROSCOPES
Get PDFThe research focuses on the description of the global dynamical behavior of a reduced-order model of noncontact Atomic Force Microscope. Different numerical analyses and continuation techniques are carried out to investigate the evolution of the main system periodic solutions and relevant basins of attraction under variations of the most significant system parameters. Local bifurcations, stability boundaries and basin erosion processes around primary and subharmonic resonance regions are studied in presence of both the parametrical horizontal excitation and the external one, and the obtained behavior charts are used not only to compare the results with the literature ones, but also as practical instruments to characterize the operation ranges in terms of the selected parameters. With the same perspective, dynamical integrity concepts, such as detection of basins of attraction, and quantification of their erosion process via integrity measures, are applied to determine acceptable frequency-dependent thresholds associated with a priori safe design targets.
Furthermore, an external feedback control is introduced with the aim to take the system response to a selected reference one, thus providing a simple and efficient method to avoid possible unstable motions. Upon checking the effectiveness of the procedure in the weakly nonlinear regime via a perturbation approach, several numerical analyses in the strongly nonlinear regime are accomplished to achieve a description of its dynamical behavior as a function of the newly inserted parameters, and to critically evaluate the effectiveness of the control actuation on the system dynamics, with also a view to the overall response scenario
Global dynamics and integrity in noncontacting atomic force microscopy with feedback control
No full textDynamical integrity of a noncontact AFM model with external feedback control is investigated to evaluate the effects of such local control procedure on the erosion of the basins of attraction of the system bounded solutions. Two-dimensional cross sections of the five-dimensional basins of attraction have been systematically constructed, and the relevant erosion profiles are obtained for the parametrically excited system. The outcomes, summarized by the so-called isointegrity curves (i.e., frequency-dependent thresholds with constant residual integrity which actually represent
the system practical safety), highlight that around the resonance frequencies, the system undergoes a worsening of its practical stability, with respect to variations in the forcing amplitude and the tip–sample distance, as well, thus underlining the importance of a global analysis to assess the system actual safety in operating conditions
Periodic wave propagation in nonlocal beams resting on a bilinear foundation
Get PDFThe free wave propagation of periodic flexural waves on an infinite elastic Euler-Bernoulli nonlocal beam embedded in bilinear Winkler -type foundation is investigated. A general formulation of the elastic potential energy leads to a nonlinear nonlocal model with spatial derivatives up to the sixth order. The effect of the nonlocal parameters and of the different soil stiffnesses on the dynamical characteristics of the system is critically discussed. An enrichment of the system response with respect to the local beam is unveiled, and the crucial role played by the sixth -order nonlocal term is highlighted
Dynamical properties of a composite microcracked bar based on a generalized continuum formulation
Get PDFThe dynamical behavior of a mono-dimensional bar with distributed microcracks is addressed in terms of free and forced wave propagation. The multiscale model, derived from a generalized continuum formulation, accounts for the microstructure by means of a microdisplacement variable, added to the standard macrodisplacement, and of internal parameters representing density and length of microcracks. The influence of coupling between micro- and macrodisplacement overall response on the system is discussed, as well as the effect of the damage parameters on the propagating waves
Combined effect of wind and sea excitations on the internal resonance response of floating offshore wind turbines
Get PDFThe sea excitation is added into a reduced nonlinear model of floating offshore wind turbine, in order to assess its effect on the system dynamics. To this aim, the sea wave motion is modelled as heave displacement of the turbine tower, which results in a parametric excitation to the along-wind displacement. The occurrence of the 1:1 internal resonance between along-wind and cross-wind oscillations is investigated by means of an asymptotic approach based on the multiple scale method. It is shown that the coupled solutions arising as a result of the wind forcing undergo a significant modification in terms of stability and quality of the response precisely because of the additional presence of the excitation due to the sea waves. A behavior chart is obtained to describe the model response as a function of the forcing parameters. The analytical results are verified by comparison with numerical simulations in terms of bifurcation diagrams and reconstructed solutions
Analytical control of homoclinic bifurcation of the hilltop saddle in a noncontact atomic force microcantilever
Get PDFA control procedure of global dynamics is applied to a reduced order model of noncontact AFM with the aim to shift the homoclinic bifurcation involving the system hilltop saddle. The method consists of adding to the system harmonic excitation controlling superharmonics to be properly identified by solving an optimization problem. The analytical bifurcation threshold is determined through the asymptotic Melnikov method, for the reference system and for the controlled system. The practical effect of the control as regards possibly increasing the system overall robustness by shifting the start of the erosion of the safe basin is then numerically investigated by means of a dynamical integrity analysis based on the evolution of basins of attraction
High order asymptotic dynamics of a nonlinearly coupled electromechanical system
No full textA nonlinearly coupled mathematical model of an electro-magneto-mechanical system is studied via the multiple scale approach in order to investigate its weakly nonlinear dynamics and analytically predict its salient features. The obtained amplitude modulation equations up to the third order perturbation allow to analytically describe the mechanical and electrical responses in terms of frequency-response curves and stability scenarios. A critical threshold of Hopf bifurcation is detected and analyzed as a function of the main system parameters. The subsequent extension of the asymptotic scheme up to the fifth order proves to grasp also the post-critical behavior, providing with the accurate identification of the amplitude of the quasiperiodic responses characterizing the unstable region of the ordinary differential equations system
Influence of a locally-tailored external feedback control on the overall dynamics of a non-contact AFM model
No full textThe dynamical analysis of a single-mode model of non-contact AFM with external feedback control is carried out in the strongly non-linear regime. The aim of the study is to investigate and verify the effects of the control introduction on the system overall behavior, which could be unexpectedly influenced by the local nature of the control technique. For this purpose, a variety of behavior charts around primary and subharmonic resonances are obtained together with several bifurcation diagrams to detect the main local bifurcation thresholds as a function of the most relevant system parameters. The comparison with the results obtained for the corresponding uncontrolled system allows one to comprehensively evaluate the effectiveness and possible criticalities of the control actuation on the system dynamics, with also a view to the overall response scenario
Exploiting global dynamics of a noncontact atomic force microcantilever to enhance its dynamical robustness via numerical control
No full textA control technique exploiting the global dynamical features is applied to a reduced order model of noncontact AFM, aiming to obtain an enlargement of the system's safe region in parameters space. The method consists of optimally modifying the shape of the system excitation by adding controlling superharmonics, to delay the occurrence of the global events (i.e. homo/heteroclinic bifurcations of some saddle) which trigger the erosion of the basins of attraction leading to loss in safety. The system's main saddles and the bifurcations involving the relevant manifolds are detected through accurate numerical investigations, and their topological characterization allows the determination of the global event responsible for the sharp reduction in the system dynamical integrity. Since an analytical treatment is impossible in applying the control, a fully numerical procedure is implemented. Besides being effective in detecting the value of the optimal superharmonic to be added for shifting the global bifurcation to a higher value of forcing amplitude, the method also proves to succeed in delaying the drop down of the erosion profile, thus increasing the overall robustness of the system during operating conditions
Nonlinearity in architecture versus science: borrowing the lexicon of complexity or exploiting its powerfulness?
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