1,720,969 research outputs found
Frequency domain modeling of nonlinear end stop behavior in Tuned Mass Damper systems under single- and multi-harmonic excitations
No full textNonsmooth dynamics of a Tuned Mass Damper system with lateral stops are studied using an alternating frequency/time harmonic balancing (AFT-HB) method. To this end, an extremely stiff end stop nonlinearity is considered. The application range of AFT-HB is investigated by including up to 250 harmonics in the external force, as well as in the motion description. Numerical simulations are performed by making use of a Newmark time integration algorithm for numerical verification of the results. The results for single harmonic excitations are further verified with an existing pseudo-arclength path-following tool. Two excitation scenarios are considered: single harmonic- and a wide-spectrum excitation with uniform distribution and random phase correlation between the harmonics. The AFT-HB algorithm is found to accurately reproduce the time integration results, for all considered cases. Finally, insights are gained into the differences between the system responses to single- and multi-harmonic excitations.Accepted Author ManuscriptDynamics of Micro and Nano System
Non-linear static bending and forced vibrations of rectangular plates retaining non-linearities in rotations and thickness deformation
No full textGeometrically non-linear static bending and forced vibrations of rectangular plates are studied allowing full non-linear terms associated with Green-Lagrange strain-displacement relations, second-order thickness stretching, third-order shear deformation and rotary inertia by using seven independent parameters to describe the shell kinematics. In particular, in addition to non-linearities in membrane and transverse deflection, non-linear terms associated with rotations and thickness deformation parameters are also included. In order to obtain the governing equations of motion, the three-dimensional constitutive equations are used, removing the assumption of zero transverse normal strain. The boundary conditions of the plate are assumed to be simply supported immovable and the equations of motion are derived by using a Lagrangian approach. The numerical solutions are obtained by using pseudo arc-length continuation and collocation scheme. In order to compare the non-linear static response, another analysis has also been carried out by using the finite element code ANSYS and three-dimensional solid modeling. Results reveal that the new theory with full geometric non-linearities provides significant accuracy improvement for rotational and thickness deformation parameters, and, unlike other shear deformation theories, predicts the correct thickness stretching along the plate
Robustness of attractors in tapping mode atomic force microscopy
Full text linkIn this work, we perform a comprehensive analysis of the robustness of attractors in tapping mode atomic force microscopy. The numerical model is based on cantilever dynamics driven in the Lennard–Jones potential. Pseudo-arc-length continuation and basins of attraction are utilized to obtain the frequency response and dynamical integrity of the attractors. The global bifurcation and response scenario maps for the system are developed by incorporating several local bifurcation loci in the excitation parameter space. Moreover, the map delineates various escape thresholds for different attractors present in the system. Our work unveils the properties of the cantilever oscillation in proximity to the sample surface, which is governed by the so-called in-contact attractor. The robustness of this attractor against operating parameters is quantified by means of integrity profiles. Our work provides a unique view into global dynamics in tapping mode atomic force microscopy and helps establishing an extended topological view of the system.Dynamics of Micro and Nano SystemsMicro and Nano Engineerin
Linear and non-linear vibrations of fluid-filled hollow microcantilevers interacting with small particles
No full textLinear and non-linear vibrations of a U-shaped hollow microcantilever beam filled with fluid and interacting with a small particle are investigated. The microfluidic device is assumed to be subjected to internal flowing fluid carrying a buoyant mass. The equations of motion are derived via extended Hamilton's principle and by using Euler-Bernoulli beam theory retaining geometric and inertial non-linearities. A reduced-order model is obtained applying Galerkin's method and solved by using a pseudo arc-length continuation and collocation scheme to perform bifurcation analysis and obtain frequency response curves. Direct time integration of the equations of motion has also been performed by using Adams-Moulton method to obtain time histories and analyze transient cantilever-particle interactions in depth. It is shown that exploiting near resonant non-linear behavior of the microcantilever could potentially yield enhanced sensor metrics. This is found to be due to the transitions that occur as a matter of particle movement near the saddle-node bifurcation points of the coupled system that lead to jumps between coexisting stable attractors.Accepted Author ManuscriptMicro and Nano Engineerin
Imperfection-induced internal resonance in nanotube resonators
Full text linkThrough molecular dynamics simulations, we demonstrate the possibility of internal resonances in single-walled carbon nanotubes. The resonant condition is engineered with a lack of symmetry in the boundary condition and activated by increasing the energy exchange with a coupled thermal bath. The critical temperature threshold for initiating modal interaction is found to be chirality-dependent. By applying the proper orthogonal decomposition algorithm to molecular dynamics time responses, we show how the thermal fluctuations influence the vibrational behaviour of the nanotube leading to both flexural–flexural and flexural–longitudinal resonances. Understanding the interaction between nanotube resonators and the thermal bath is crucial for designing and optimizing their performance for various nanoscale sensing, actuation, and signal processing applications.Dynamics of Micro and Nano System
Non-Smooth Dynamics of Tapping Mode Atomic Force Microscopy
No full textThis study examines the nonlinear dynamics in tapping-mode atomic force microscopy (AFM) with tip-surface interactions that include van der Waals and Derjaguin-Muller-Toporov contact forces. We investigate the periodic solutions of the hybrid system by performing numerical pseudo-arclength continuation. Through the use of bifurcation locus maps in the set of parameters of the discontinuous model, the overall dynamical response scenario is assessed. We demonstrate the influence of various dissipation mechanisms that are related with the AFM touching or lacking contact with the sample. Local and global analyses are used to investigate the stability of the stable solution in the repulsive regime. The impacting nonsmooth dynamics framed within a higher-mode Galerkin discretization is able to capture windows of irregular and complex motion
Non-linear vibrations and stability of a periodically supported rectangular plate in axial flow
No full textIn the present study, the geometrically non-linear vibrations of thin infinitely long rectangular plates subjected to axial flow and concentrated harmonic excitation are investigated for different flow velocities. The plate is assumed to be periodically simply supported with immovable edges and the flow channel is bounded by a rigid wall. The equations of motion are obtained based on the von Karman non-linear plate theory retaining in-plane inertia and geometric imperfections by employing Lagrangian approach. The fluid is modeled by potential flow and the flow perturbation potential is derived by applying the Galerkin technique. A code based on the pseudo-arc-length continuation and collocation scheme is used for bifurcation analysis. Results are shown through bifurcation diagrams of the static solutions, frequency-response curves, time histories, and phase-plane diagrams. The effect of system parameters, such as flow velocity and geometric imperfections, on the stability of the plate and its geometrically non-linear vibration response to harmonic excitation are fully discussed and the convergence of the solutions is verified
Mode Coupling in Dynamic Atomic Force Microscopy
Full text linkIncreasing the signal-to-noise ratio in dynamic atomic force microscopy plays a key role in nanomechanical mapping of materials with atomic resolution. In this work, we develop an experimental procedure for increasing the sensitivity of higher harmonics of an atomic-force-microscope cantilever without modifying the cantilever geometry but instead by utilizing dynamical mode coupling between its flexural modes of vibration. We perform experiments on different cantilevers and samples and observe that via nonlinear resonance frequency tuning we can obtain a frequency range where strong modal interactions lead to 7-fold and 16-fold increases in the sensitivity of the 6th and 17th harmonics while reducing sample indentation. We derive a numerical model that captures the observed physics and confirms that nonlinear mode coupling is the reason for the increase of the amplitude of higher harmonics during tip-sample interactions
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