Analytical investigation of air squeeze film damping for bi‐axial micro‐scanner using eigenfunction expansion method

Atabak, Ruhollah; Sedighi, Hamid M.; Reza, Arash; Mirshekari, Erfan

doi:10.1002/mma.6658

Cited by 9 publications

(1 citation statement)

References 29 publications

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“…A fractionally damped beam has been analyzed by [32]. The influence of dispersion force and squeezed film damping was incorporated in the dynamic instability of the nanowire-fabricated sensor subjected to centrifugal and constant acceleration [33,34]. Even though Eq.…”

Section: Introductionmentioning

confidence: 99%

A heuristic approach to the prediction of a periodic solution for a damping nonlinear oscillator with the non-perturbative technique

2023

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The present work attracts attention to obtaining a new result of the periodic solution of a damped nonlinear Duffing oscillator and a damped Klein–Gordon equation. It is known that the frequency response equation in the Duffing equation can be derived from the homotopy analysis method only in the absence of the damping force. We suggest a suitable new scheme successfully to produce a periodic solution without losing the damping coefficient. The novel strategy is centered on establishing an alternate equation apart from any difficulty in handling the influence of the linear damped term. This alternative equation was obtained with the rank upgrading technique. The periodic solution of the problem is presented using the non-perturbative method and validated by the modified homotopy perturbation technique. This technique is successful in obtaining new results toward a periodic solution, frequency equation, and the corresponding stability conditions. This methodology yields a more effective outcome of the damped nonlinear oscillators. With the help of this procedure, one can analyze many problems in the domain of physical engineering that involve oscillators and a linear damping influence. Moreover, this method can help all interested plasma authors for modeling different nonlinear acoustic oscillations in plasma.

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Section: Introductionmentioning

confidence: 99%

A heuristic approach to the prediction of a periodic solution for a damping nonlinear oscillator with the non-perturbative technique

2023

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Two‐phase local/nonlocal gradient mechanics of elastic torsion

Faghidian

2020

Math Methods in App Sciences

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The higher order two‐phase local/nonlocal elasticity model and the higher order strain gradient theory are unified via an abstract variational scheme. The higher order constitutive integral convolution is established in a consistent variational framework governed by ad hoc functional space of test fields. Equivalent differential constitutive law equipped with nonclassical boundary conditions of constitutive type is determined. The proposed higher order elasticity theory provides as special cases a range of well‐known size‐dependent elasticity models such as nonlocal, two‐phase local/nonlocal, strain gradient, modified nonlocal strain gradient, and nonlocal strain‐driven gradient models. Evidences of well‐posedness of the introduced higher order two‐phase local/nonlocal gradient problems are elucidated by rigorous examination of the elastostatic torsional response of structural schemes of applicative interest in nano‐mechanics. The exact analytical solution of the torsion problem of elastic nano‐beams is derived, graphically demonstrated, and compared with analogous outcomes in the literature. The conceived higher order elasticity theory can efficiently characterize advanced nano‐materials and structural elements of modern nano‐systems.

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Higher order mixture nonlocal gradient theory of wave propagation

Faghidian

2020

Math Methods in App Sciences

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The higher order mixture nonlocal gradient theory of elasticity is conceived via consistent unification of the higher order stress‐ and strain‐driven mixture nonlocal elasticity and the higher order strain gradient theory. The integro‐differential constitutive law is established applying an abstract variational approach and appropriately replaced with the equivalent differential condition subject to nonclassical boundary conditions. The introduced higher order elasticity theory provides, as special cases, a variety of generalized elasticity theories adopted in nanomechanics to assess size effects in continua with nanostructural features. The well‐posed higher order mixture nonlocal gradient theory is elucidated and invoked to examine the flexural wave propagation. The closed‐form wave propagation relation between the phase velocity and the wave number is analytically derived. The determined wave propagation response and ensuing results are compared and calibrated with the pertinent molecular dynamic simulations. The demonstrated results of the phase velocity of the flexural wave propagation detect new benchmarks for numerical analyses. The proposed higher order size‐dependent elasticity approach can be profitably employed in rigorous analysis of pioneering nanotechnological devices.

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Analytical investigation of air squeeze film damping for bi‐axial micro‐scanner using eigenfunction expansion method

Cited by 9 publications

References 29 publications

A heuristic approach to the prediction of a periodic solution for a damping nonlinear oscillator with the non-perturbative technique

A heuristic approach to the prediction of a periodic solution for a damping nonlinear oscillator with the non-perturbative technique

Two‐phase local/nonlocal gradient mechanics of elastic torsion

Higher order mixture nonlocal gradient theory of wave propagation

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