A coupled nonlinear continuum model for bifurcation behaviour of fluid-conveying nanotubes incorporating internal energy loss

Abstract

A coupled continuum model incorporating size influences and geometric nonlinearity is presented for the coupled motions of viscoelastic nonlinear nanotubes conveying nanofluid.A modified model of nanobeams incorporating nonlocal strain gradient effects is utilised for describing size influences on the bifurcation behaviour of the fluid-conveying nanotube. Furthermore, size influences on the nanofluid are taken into account via Beskok-Karniadakis theory. To model the geometric nonlinearity, nonlinear strain-displacement relations are employed. Utilising Hamilton's principle and the Kelvin-Voigt model, the coupled equations of nonlinear motions capturing the internal energy loss are derived. A Galerkin procedure with a high number of shape functions and a direct time-integration scheme are then employed to extract the bifurcation characteristics of the nanofluid-conveying nanotube with viscoelastic properties. A specific attention is paid to the chaotic response of the viscoelastic nanosystem. It is found that the coupled viscoelastic bifurcation behaviour is very sensitive to the flow velocity.

Nonlinear Vibration and Stability Analysis of Functionally Graded Nanobeam Subjected to External Parametric Excitation and Thermal Load

“…In order to investigate the effect of changing the temperature to the top surface on vibrational behaviour and instability regions, in Figs. [19][20][21][22] we assume that the distribution of temperature is linear and power-law exponents change also, in Figs. 23-25 power-law exponent is held constant while the distribution of temperature changes.…”

“…In the framework of Euler-Bernoulli nanobeam theory, the modified couple stress theory and Gurtin-Murdoch surface elasticity are employed to take account the size effects of nanoscale structures [19]. Eringen's nonlocal elasticity model of the nanotube is established to inquire the effect of size on the bifurcation characteristic of fluid-conveying nanobeam [20]. Free vibration and resonance of frequencies of nano-resonator is investigated by Eltaher et al [21].…”

Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams

“…In the above relations, large deformations are also incorporated since large deformations happen in many engineering problems at both ultrasmall and large-scale levels [70][71][72][73][74][75][76][77][78]. An internal-damping-related work is:…”

Buckling Behaviour of Protein Microtubules

“…The microtubule has a hollow cylindrical geometry and consists of α and β tubulins, as shown in (Figure 1). It has been proven that size influences have a significant impact on the mechanica0000000l behavior at small-scales [29][30][31][32][33][34][35][36]. Since the inner and outer radii of microtubules are of several nanometers, the nonlocal theory is mostly used to describe size influences.…”