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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

Analytical and parametric analysis of thermoelastic damping in circular cylindrical nanoshells by capturing small-scale effect on both structure and heat conduction

Li Ming, Cai Youjie, Bao Li, Fan Rui, Zhang Hongbin, Wang Hongyan, Borjalilou Vahid

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e14, 2022

EN

This article intends to examine thermoelastic damping (TED) in circular cylindrical nanoshells by considering small-scale effect on both structural and thermal areas. To fulfill this aim, governing equations are extracted with the aid of nonlocal elasticity theory and dual-phase-lag (DPL) heat conduction model. Circular cylindrical shell is also modeled on the basis of Donnell–Mushtari–Vlasov (DMV) equations for thin shells. By inserting asymmetric simple harmonic oscillations of nanoshell into motion, compatibility and heat conduction equations, the size-dependent thermoelastic frequency equation is obtained. By solving this equation and deriving the frequency of nanoshell affected by thermoelastic coupling, the value of TED can be calculated through complex frequency approach. Results of this investigation are given in two sections. First, to appraise the validity of presented formulation, a comparison study is conducted between the results of this work in special cases and those reported in the literature. Next, by providing several numerical data, a detailed parametric study is performed to highlight the profound impact of nonlocality and dual-phase-lagging on TED value in simply supported cylindrical nanoshells. The influence of some determining factors such as mode number and type of material on TED is also evaluated.

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.