Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions

This work is motivated by the self-powered component of biomedical nano-robotic device which is expected to move in arterial blood vessels. The transverse vibrations and steady-state responses of axially moving viscoelastic piezoelectric two-dimensional nanostructures are investigated based on the nonlocal viscoelasticity thin plate theory. The constitutive relations of viscoelastic piezoelectric nanoplate containing the thermal effect are performed and the governing partial differential equations of the problem model are derived using the Hamilton's principle. The natural frequencies are numerically determined via the Galerkin method, the complex mode method, as well as the finite element method for comparison. Moreover, the theoretical calculations are compared with those in previous literature to verify effects in nonlocal nanoscale framework and average speed on natural frequency. Afterwards, the instable behaviors of axially non-uniformly moving viscoelastic piezoelectric nanoplate characterized as a sine variation about the constant average speed are addressed using the method of multiple scales. The analyses are mainly focused on the boundaries of instable regions in combination parametric resonance and principal parametric resonance. The non-dimensional numerical results imply the existences of nonlocal nanoscale parameter and average speed contribute to reduce the rigidity, and further produce the coupled vibrations and flutter instabilities for complex frequencies. Additionally, the instable regions of combination and principal parametric resonances decrease with increases in the biaxial compression, change of temperature, positive electric voltage and viscoelastic coefficient. The dynamic responses of axially moving viscoelastic piezoelectric nanoplate under the coupling of thermo-electro-mechanical multi-fields are expected to play significant roles in designing biomedical nano-robots.

Nonlocal vibrations and stabilities in parametric resonance of axially moving viscoelastic piezoelectric nanoplate subjected to thermo-electro-mechanical forces

An analytical answer to the natural vibration problem of a composite plate consisted of multi-scale hybrid nanocomposites, is presented here for the first time. In this paper, the constituent material of the structure is made of an epoxy matrix which is reinforced by both macro- and nano-size reinforcements, namely carbon fiber (CF) and carbon nanotube (CNT). The effective material properties like Young's modulus or density are derived utilizing a micromechanical scheme incorporated with the Halpin-Tsai model. To present a more realistic problem, the plate is placed on a two-parameter elastic substrate. Then, on the basis of an energy-based Hamiltonian approach, the equations of motion are derived using the classical theory of plates. Finally, the governing equations will be solved analytically to obtain the natural frequency of the system's oscillation. Afterward, the normalized form of the results will be presented to put emphasis on the impact of each parameter on the dimensionless frequency of nanocomposite plates. It is worth mentioning that the effects of various boundary conditions on the frequency of the plate are covered, too. To show the efficiency of presented modeling, the results of this article are compared to those of former attempts. Numerical results declare that plates fabricated from the hybrid nanocomposites can endure higher frequencies compared with those consisted of conventional composites.

Vibration analysis of multi-scale hybrid nanocomposite plates based on a Halpin-Tsai homogenization model

Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment

In this paper, a detailed review on the dynamics of axially moving systems is presented. Over the past 60 years, vibration control of axially moving systems has attracted considerable attention owing to the board applications including continuous material processing, roll-to-roll systems, flexible electronics, etc. Depending on the system’s flexibility and geometric parameters, axially moving systems can be categorized into four models: String, beam, belt, and plate models. We first derive a total of 33 partial differential equation (PDE) models for axially moving systems appearing in various fields. The methods to approximate the PDEs to ordinary differential equations (ODEs) are discussed; then, approximated ODE models are summarized. Also, the techniques (analytical, numerical) to solve both the PDE and ODE models are presented. The dynamic analyses including the divergence and flutter instabilities, bifurcation, and chaos are outlined. Lastly, future research directions to enhance the technologies in this field are also proposed. Considering that a continuous manufacturing process of composite and layered materials is more demanding recently, this paper will provide a guideline to select a proper mathematical model and to analyze the dynamics of the process in advance.

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Dynamic models of axially moving systems: A review

In the present research, vibration and instability of axially moving single-layered graphene sheet (SLGS) subjected to magnetic field is investigated. Orthotropic visco-Pasternak foundation is developed to consider the influences of orthotropy angle, damping coefficient, normal and shear modulus. Third order shear deformation theory (TSDT) is utilized due to its accuracy of polynomial functions than other plate theories. Motion equations are obtained by means of Hamilton’s principle and solved analytically. Influences of various parameters such as axially moving speed, magnetic field, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of SLGS on the vibration characteristics of moving system are discussed in details. The results indicated that the critical speed of moving SLGS is strongly dependent on the moving speed. Therefore, the critical speed of moving SLGS can be improved by applying magnetic field. The results of this investigation can be used in design and manufacturing of marine vessels in nanoscale.

Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field

In the present research, modeling and vibration analysis of the double of sandwich beams which are coupled by visco-Pasternak medium are investigated. Also, this system is rested on Winkler foundat...

Vibration behavior of visco-elastically coupled sandwich beams with magnetorheological core and three-phase carbon nanotubes/fiber/polymer composite facesheets subjected to external magnetic field:

In this research, vibration analysis of a viscoelastic sandwich plate rested on a visco-Pasternak foundation is investigated. Sandwich plate consists of a magnetorheological (MR) fluid core and vis...

Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets:

Differential quadrature method for vibration analysis of electro-rheological sandwich plate with CNT reinforced nanocomposite facesheets subjected to electric field

In this study, the nonlinear thermo-electro vibrations of double-walled boron nitride nanopeapods (DWBNNPPs) and double-walled carbon nanopeapods (DWCNPPs) under magnetic field embedded in an elastic medium is investigated. DWBNNPPs are made of piezoelectric and smart materials therefore, electric field is effective on them; meanwhile, DWCNPPs are made of carbon thus, magnetic field can be useful to control them. The Pasternak model is used to simulate the effects of elastic medium which surrounds the system. Nanotubes are modeled with assumption of the Euler-Bernoulli beam (EBB) theory and the surface effects are considered to achieve accurate response of the system. Moreover, interaction between two layers is modeled by van der Waals (vdW) forces. The equations of motion are derived using the energy method and the Hamilton principle. Then the governing equations are solved by using Galerkin’s method and incremental harmonic balance method (IHBM). The influences of various parameters such as the magnetic field, different types of DWCNPPs and DWBNNPPs, elastic medium, existence of fullerene and surface effect on the vibration behavior of the system are investigated. The results demonstrate that DWBNNPPs have more influence on the frequency of the system than DWCNPPs. In addition, the presence of fullerene in nanotubes has a negative impact on the frequency behavior of revisionthe system.

H. BabaAkbar Zarei

Papers

Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field

Vibration behavior of visco-elastically coupled sandwich beams with magnetorheological core and three-phase carbon nanotubes/fiber/polymer composite facesheets subjected to external magnetic field:

Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets:

Differential quadrature method for vibration analysis of electro-rheological sandwich plate with CNT reinforced nanocomposite facesheets subjected to electric field

Nonlinear vibration of double-walled boron nitride and carbon nanopeapods under multi-physical fields with consideration of surface stress effects