Nonlinear micromechanically analysis of forced vibration of the rectangular-shaped atomic force microscopes incorporating contact model and thermal influences

Saeidi, Hossein; Zajkani, Asghar; Ghadiri, Majid

doi:10.1080/15397734.2020.1721299

Cited by 5 publications

(2 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, putting the coefficients containing ϵ3 equal to zero, the following equation is extracted in which Dk indicate the operation of time differentiation and is written as the general solution of equations (39) and (40) can be expressed by expanding Fourier as follows where ψ1m is the time unknown function of the mth mode and for the Euler-Bernoulli beam with fixed-free boundary conditions, the characteristic functions Φm are expressed by 57 , 58 so that ηm is the mth root of coshηmcosηm+1 = 0 and the lowest five roots are 1.8751, 4.6941, 7.8548, 10.9955, 14.1372 and also false∫01ΦjΦk=δjk…”

Section: Equation Solving Methodsmentioning

confidence: 99%

Nonlinear vibration and stability analysis of a size-dependent viscoelastic cantilever nanobeam with axial excitation

Noroozi

Ghadiri

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

Self Cite

View full text Add to dashboard Cite

In the present paper, nonlinear forced vibrations of an axial moving nanobeam which is vertically influenced by an external harmonic excitation and gravity is analyzed by considering the effects of linear damping. Considering certain assumptions, a nonlinear Euler-Bernoulli beam theory is developed. With the implementation of the nonlocal elasticity theory, the governing integro-partial-differential equation is obtained by using the Hamilton principle. The multiple scale method is employed to obtain a steady-state response for the size-dependent viscoelastic nanobeam with fixed-free boundary conditions. Subsequently, the trivial and non-trivial steady-state response and the bifurcation point types are examined. Finally, the effects of damping coefficient and nonlocal parameter on stability and bifurcation of trivial and non-trivial solutions are studied. It is found that the effect of nonlocal parameter on the steady-state response and the bifurcation point types is quite important.

show abstract

Section: Equation Solving Methodsmentioning

confidence: 99%

Nonlinear vibration and stability analysis of a size-dependent viscoelastic cantilever nanobeam with axial excitation

Noroozi

Ghadiri

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

Self Cite

View full text Add to dashboard Cite

show abstract

“…Mahmoudi et al [ 18 ] studied the resonance of a non-contact AFM using harmonic balance and multiple time-scale methods. Saeidi et al [ 19 ] explored forced vibrations of an AFM, taking the temperature and contact effects into account. Ahmadi and co-workers [ 20 ] studied free and forced oscillations of AFM with rectangular and V-shaped and employed the finite element analysis.…”

Section: Introductionmentioning

confidence: 99%

Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance

et al. 2022

View full text Add to dashboard Cite

The impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made from a hyperelastic material, providing large deformation under small excitation amplitude. A nonlinear strain energy function is proposed to capture the elastic energy stored in the flexible component of the device. The tip–sample interaction is modeled based on the van der Waals non-contact force. The nonlinear equation governing the AFM’s dynamics is established using the extended Hamilton’s principle, obeying the Euler–Bernoulli beam theory. As a result, the vibration behavior of the system is introduced by a nonlinear equation having a time-dependent boundary condition. To capture the steady-state numerical response of the system, a developed Galerkin method is utilized to discretize the partial differential equation to a set of nonlinear ordinary differential equations (ODE) that are solved by the combination of shooting and arc-length continuation method. The output reveals that while the resonator is set to be operating near twice the fundamental natural frequency, the response amplitude undergoes a significant drop to the trivial stable branch as the sample’s profile experiences depression in the order of the picometer. According to the performed sensitivity analysis, the proposed working principle based on principal parametric resonance is recommended to design AFMs with ultra-high detection resolution for surface profile scanning.

show abstract

Flexural resonant frequencies of an AFM cantilever in viscoelastic surface contact mode using modified nonlocal elasticity theory

Mamandi

2024

Arch Appl Mech

View full text Add to dashboard Cite

Nonlinear micromechanically analysis of forced vibration of the rectangular-shaped atomic force microscopes incorporating contact model and thermal influences

Cited by 5 publications

References 39 publications

Nonlinear vibration and stability analysis of a size-dependent viscoelastic cantilever nanobeam with axial excitation

Nonlinear vibration and stability analysis of a size-dependent viscoelastic cantilever nanobeam with axial excitation

Hyperelastic Microcantilever AFM: Efficient Detection Mechanism Based on Principal Parametric Resonance

Flexural resonant frequencies of an AFM cantilever in viscoelastic surface contact mode using modified nonlocal elasticity theory

Contact Info

Product

Resources

About