Effects of a slow harmonic displacement on an Atomic Force Microscope system under Lennard-Jones forces

We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM). The microbeam is subjected to a low frequency harmonic displacement of its base and to the Lennard-Jones (LJ) forces at its free end. Static and modal analysis are performed for various gaps between the tip of the microbeam and a sample. The Galerkin method is employed to reduce the equations of motion to a fast-slow dynamical system. We show that the dynamics of the AFM system is governed by the contact and the noncontact invariant slow manifolds. The tapping mode is triggered via two saddle-node bifurcations of these manifolds. Moreover, the contact time is computed and the effects of the base motion amplitude and the initial gap are discussed

Linear flexural natural frequencies and stability analysis of spinning Rayleigh beams: application to clamped-clamped beams.

In the present paper 3D bending linear free vibrations of spinning Rayleigh beams are investigated. Four linear models, that differ in the linearization process, are studied. A focus on analytical computation of natural frequencies for a broad range of boundary conditions is highlighted. Then, the conditions of occurrence of divergence and flutter instabilities are determined. Finally, a case study consisting of a clamped-clamped Rayleigh beam is studied. It is found that the free vibrations destabilization process depends on the used linearization approach

Invariant slow manifolds of an Atomic Force Microscope system under the Derjaguin-Muller-Toporov forces and a slow harmonic base motion

In the present work, we study the nonlinear vibrations of an AFM system, modeled as a linear mass-spring-damper system, under the Derjaguin-Muller-Toporov forces and subject to imposed slow harmonic base displacement. The invariant slow manifolds of the system are approximated and their bifurcations are investigated. Then, the charts of behaviors of the different operating modes of the AFM are determined. The dynamic saddle-node bifurcations of the contact and the noncontact invariant slow manifolds are found to be responsible for the occurrence of the tapping mode

A nonlinear model of the hand-arm system and parameters identification using vibration transmissibility

In the present paper a lumped single degree-of-freedom nonlinear model is used to study biodynamic responses of the hand arm system (HAS) under harmonic vibrations. Then, the harmonic balance method is implemented to derive the vibration transmissibility. Furthermore,Padé approximations are used in the identification process of biodynamic characteristics of the HAS model. This process is based on minimizing the distance between the theoretical and the experimentally measured transmissibilities. The proposed identification workflow is applied to vibrations at the wrist in two cases: 1) the transmissibility versus the grip force for fixed excitation frequencies, and 2) the transmissibility versus the excitation frequency for fixed grip force

Linear flexural natural frequencies and stability analysis of spinning Rayleigh beams: application to clamped-clamped beams.

In the present paper 3D bending linear free vibrations of spinning Rayleigh beams are investigated. Four linear models, that differ in the linearization process, are studied. A focus on analytical computation of natural frequencies for a broad range of boundary conditions is highlighted. Then, the conditions of occurrence of divergence and flutter instabilities are determined. Finally, a case study consisting of a clamped-clamped Rayleigh beam is studied. It is found that the free vibrations destabilization process depends on the used linearization approach

Effects of a slow harmonic displacement on an Atomic Force Microscope system under Lennard-Jones forces

We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM). The microbeam is subjected to a low frequency harmonic displacement of its base and to the Lennard-Jones (LJ) forces at its free end. Static and modal analysis are performed for various gaps between the tip of the microbeam and a sample. The Galerkin method is employed to reduce the equations of motion to a fast-slow dynamical system. We show that the dynamics of the AFM system is governed by the contact and the noncontact invariant slow manifolds. The tapping mode is triggered via two saddle-node bifurcations of these manifolds. Moreover, the contact time is computed and the effects of the base motion amplitude and the initial gap are discussed

A nonlinear model of the hand-arm system and parameters identification using vibration transmissibility

In the present paper a lumped single degree-of-freedom nonlinear model is used to study biodynamic responses of the hand arm system (HAS) under harmonic vibrations. Then, the harmonic balance method is implemented to derive the vibration transmissibility. Furthermore,Padé approximations are used in the identification process of biodynamic characteristics of the HAS model. This process is based on minimizing the distance between the theoretical and the experimentally measured transmissibilities. The proposed identification workflow is applied to vibrations at the wrist in two cases: 1) the transmissibility versus the grip force for fixed excitation frequencies, and 2) the transmissibility versus the excitation frequency for fixed grip force

Invariant slow manifolds of an Atomic Force Microscope system under the Derjaguin-Muller-Toporov forces and a slow harmonic base motion

In the present work, we study the nonlinear vibrations of an AFM system, modeled as a linear mass-spring-damper system, under the Derjaguin-Muller-Toporov forces and subject to imposed slow harmonic base displacement. The invariant slow manifolds of the system are approximated and their bifurcations are investigated. Then, the charts of behaviors of the different operating modes of the AFM are determined. The dynamic saddle-node bifurcations of the contact and the noncontact invariant slow manifolds are found to be responsible for the occurrence of the tapping mode