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Determination of hazardous metal ions in the water with resonant MEMS biosensor frequency shift – concept and preliminary theoretical analysis

Rahimi Z., Yazdani J., Hatami H., Sumelka W., Baleanu D., Najafi S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2020

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Vol. 68, nr 3

529--537

EN

Heavy metal ions (e.g. cadmium, chromium, copper, nickel, arsenic, lead, zinc) have significantly serious side effects on the human health. They can bind with proteins and enzymes, altering their activity, increasing neurotoxicity, generating reactive oxygen species (ROS), promote cellular stress and resulting in their damage. Furthermore, the size, shape and type of metal are important for considering nano- or microtoxicity. It then becomes clear that the levels of these metals in drinking water are an important issue. Herein, a new micro-mechanical sensor is proposed to detect and measure these hazardous metals. The sensor consists of a micro-beam inside a micro-container. The surface of the beam is coated with a specific protein that may bind heavy metals. The mass adsorbed is measured using the resonant frequency shift of the micro-beam. This frequency shift due to the admissible mass (which is considered acceptable for drinking water based on the World Health Organization (WHO) standard) of manganese (Mn), lead (Pb), copper (Cu) and cadmium (Cd) is investigated for the first, second and third mode, respectively. Additionally, the effects of micro-beam off-center positions inside the micro-container and the mass location and investigated.

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The analysis of non-linear free vibration of FGM nano-beams based on the conformable fractional non-local model

Rahimi Z., Sumelka W., Shafiei S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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Vol. 66, nr 5

737--745

EN

Continuum models generalized by fractional calculus are used in different mechanical problems. In this paper, by using the conformable fractional derivative (CFD) definition, a general form of Eringen non-local theory as a fractional non-local model (FNM) is formulated. It is then used to study the non-linear free vibration of a functional graded material (FGM) nano-beam in the presence of von-Kármán non-linearity. A numerical solution is obtained via Galerkin and multiple scale methods and effects of the integer and non-integer (fractional) order of stress gradient (in the non-local stress-strain relation) on the ratio of the non-local non-linear natural frequency to classical non-linear natural frequency of simply-supported (S-S) and clamped-free (C-F) FGM nano-beams are presented.

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A study of critical point instability of micro and nano beams under a distributed variable-pressure force in the framework of the inhomogeneous non-linear nonlocal theory

Rahimi Z., Rezazadeh G., Sumelka W., Yang X.-J.

Archives of Mechanics

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2017

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Vol. 69, nr 6

413--433

EN

Fractional derivative models (FDMs) result from introduction of fractional derivatives (FDs) into the governing equations of the differential operator type of linear solid materials. FDMs are more general than those of integer derivative models (IDMs) so they are more fixable to describe physical phenomena. In this paper the inhomogeneous nonlocal theory has been introduced based on conformable fractional derivatives (CFD) to study the critical point instability of micro/nano beams under a distributed variable-pressure force. The phase of distributed variable-pressure force is used for electrostatic force, electromagnetic force and so on. This model has two free parameters: i) parameter to control the order of inhomogeneity in constitutive relations that gives a general form to the model, and ii) a nonlocal parameter to consider size dependence effects in micron and sub-micron scales. As a case study the theory has been used to model micro cantilever (C-F) and doubly-clamped (C-C) silicon beams under a distributed uniform electrostatic force in the presence of von-Karman nonlinearity and their static critical point (static pull-in instability), moreover, effects of different inhomogeneity have been shown on the pull-in instability.