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Nonlinear forced vibration analysis of micro-rotating shaft-disk systems through a formulation based on the nonlocal strain gradient theory

Panahi Ramin, Asghari Mohsen, Borjalilou Vahid

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 2

art. no. e85, 2023

EN

The paper presents an upgraded size-dependent formulation for micro-rotating shaft-disks system to study their nonlinear forced vibration behavior. The novel formulation is based on the nonlocal strain gradient theory (NSGT). To achieve this goal, first of all, by incorporating the geometrical nonlinearity within the Rayleigh beam theory, the governing equations of the lateral motion of the system are derived by the Hamilton principle and then converted into a complex form. By defning some dimensionless parameters, the normalized form of the complex governing equation is also extracted. In the next step, the Galerkin method is implemented to establish an infinite set of ordinary differential equations (ODEs). Then, with the help of the method of multiple scales, the nonlinear ODE is solved to attain the vibrational amplitude of the system as well as its forward and backward natural frequencies. Lastly, an all-out parametric study is conducted to appraise the impact of some important factors like the nonlocal theory parameter, the strain gradient length scale parameter, the rotational speed, the amount of mass eccentricity and the internal damping coeffcient on the motion amplitude and natural frequencies. The numerical outcomes illuminate well that depending on the relative value of two non-classical parameters of NSGT, this theory have the potential to reflect the hardening or softening attribute of small-scaled mechanical elements.

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Forced and free vibrational analysis of viscoelastic nanotubes conveying fluid subjected to moving load in hygro-thermo-magnetic environments with surface effects

Sarparast Hoda, Alibeigloo Akbar, Borjalilou Vahid, Koochakianfard Omid

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 4

art. no. e172, 2022

EN

Forced and free vibrational analyses of viscoelastic nanotubes containing fluid under a moving load in complex environments incorporating surface effects are conducted based on the nonlocal strain gradient theory and the Rayleigh beam model. To model the internal nanoflow, the slip boundary condition is employed. Adopting the Galerkin discretization approach, the reduced-order dynamic model of the system is acquired. Analytical and numerical methods are exploited to determine the dynamic response of the system. The impacts of geometry, scale parameter ratio, Knudsen number, fluid velocity, rotary inertia parameter, viscoelastic parameter, surface residual stress, surface elastic modulus, and hygro-thermo-magnetic environments on the dynamic magnification factor, critical moving load speed, cancellation, and maximum free vibration of the system are evaluated. The results indicate that the effects of the viscoelastic parameter on the dynamic behavior of the system differ significantly from those of other parameters. It is indicated that the dynamic magnification factor and critical moving load speed are enhanced by increasing the surface residual stress and the surface elastic modulus. The model and results of the current investigation can serve as a comprehensive benchmark for the optimum design of nanoflow sensors and targeted drug delivery systems.

3

On the nonlocal interaction range for stability of nanobeams with nonlinear distribution of material properties

Jankowski Piotr

Acta Mechanica et Automatica

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2022

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Vol. 16, no. 2

151--161

EN

The present study analyses the range of nonlocal parameters’ interaction on the buckling behaviour of nanobeam. The intelligent nonhomogeneous nanobeam is modelled as a symmetric functionally graded (FG) core with porosity cause nonlinear distribution of material parameters. The orthotropic face-sheets are made of piezoelectric materials. These kinds of structures are widely used in nanoelectromechanical systems (NEMS). The nanostructure model satisfies the assumptions of Reddy third-order beam theory and higher-order nonlocal elasticity and strain gradient theory. This approach allows to predict appropriate mechanical response of the nanobeam regardless of thin or thick structure, in addition to including nano-sized effects as hardening and softening. The analysis provided in the present study focuses on differences in results for nanobeam stability obtained based on classical and nonlocal theories. The study includes the effect of diverse size-dependent parameters, nanobeams’ length-to-thickness ratio and distributions of porosity and material properties through the core thickness as well as external electro-mechanical loading. The results show a dependence of nonlocal interaction range on geometrical and material parameters of nanobeam. The investigation undertaken in the present study provides an interpretation for this phenomenon, and thus aids in increasing awareness of nanoscale structures’ mechanical behaviour.

4

Generalized thermoelasticity model of nonlocal strain gradient Timoshenko nanobeams

Yue Xuejie, Yue Xuezheng, Borjalilou Vahid

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 3

655--674

EN

The aim of this study is to establish a thorough model for appraisal of size-dependent thermoelastic vibrations of Timoshenko nanobeams by capturing small-scale effect on both structural and thermal fields. With the intention of incorporating size effect within motion and heat conduction equations, nonlocal strain gradient theory (NSGT) as well as nonclassical heat conduction model of Guyer and Krumhansl (GK model) are exploited. For the sake of generalization and clarifying the impact of nonclassical scale parameters on results, by introducing some nondimensional quantities, the size-dependent coupled thermoelastic equations are written in dimensionless form. By applying the Laplace transform to this system of differential equations, thermoelastic responses of a simply supported Timoshenko nanobeam under dynamic load are extracted in closed forms. In order to highlight the influence of scale parameters on thermoelastic behavior of Timoshenko nanobeams, a variety of numerical results is provided. The discrepancy between classical and nonclassical outcomes betokens the salient role of structural and thermal scale parameters in accurate analysis of nanobeams. In addition, findings reveal that utilization of NSGT gives the means to capture both stiffness softening and stiffness enhancement characteristic of small-sized structures, so that according to the relative values of two scale parameters of NSGT, the nonclassical model of Timoshenko nanobeam can exhibit either softening or hardening behavior in comparison with the classical one.

5

Effect of kerr foundation and in-plane forces on free vibration of fgm nanobeams with diverse distribution of porosity

Jankowski Piotr

Acta Mechanica et Automatica

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2020

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Vol. 14, no. 3

135--143

EN

In the present paper, the effect of diverse distribution of functionally graded porous material and Kerr elastic foundation on natu-ral vibrations of nanobeams subjected to in-plane forces is investigated based on the nonlocal strain gradient theory. The displacement field of the nanobeam satisfies assumptions of Reddy higher-order shear deformation beam theory. All the displacements gradients are assumed to be small, then the components of the Green-Lagrange strain tensor are linear and infinitesimal. The constitutive relations for functionally graded (FG) porous material are expressed by nonlocal and length scale parameters and power-law variation of material pa-rameters in conjunction with cosine functions. It created possibility to investigate an effect of functionally graded materials with diverse dis-tribution of porosity and volume of voids on mechanics of structures in nano scale. The Hamilton’s variational principle is utilized to derive governing equations of motion of the FG porous nanobeam. Analytical solution to formulated boundary value problem is obtained in closed-form by using Navier solution technique. Validation of obtained results and parametric study are presented in tabular and graphical form. Influence of axial tensile/compressive forces and three different types of porosity distribution as well as stiffness of Kerr foundation on natural frequencies of functionally graded nanobeam is comprehensively studied.