In the present study, nonlinear vibration of coupled carbon nanotubes (CNTs) in presence of surface effect is investigated based on nonlocal Euler-Bernoulli beam (EBB) theory. CNTs are embedded in a visco-elastic medium and placed in the uniform longitudinal magnetic field. Using von Karman geometric nonlinearity and Hamilton’s principle, the nonlinear higher order governing equations are derived. The differential quadrature (DQ) method is applied to obtain the nonlocal frequency of coupled visco-CNTs system. The effects of various parameters such as the longitudinal magnetic field, visco-Pasternak foundation, Knudsen number, surface effect, aspect ratio and velocity of CONVEYING viscous are specified. It is shown that the longitudinal magnetic field is responsible for an up shift in the frequency and an improvement of the instability of coupled system. Results also reveal that the surface effect and internal CONVEYING FLUID plays an important role in the instability of nano coupled system. Also, it is found that trend of figures have good agreement with previous researches. It is hoped that the nonlinear results of this work could be used in design and manufacturing of nano/micro mechanical system in advanced nanomechanics applications where in this study the magnetic field is a controller parameter.

In this paper, the nonlinear dynamic buckling of double-walled boron-nitride nanotube (DWBNNT) CONVEYING viscous FLUID is investigated based on Eringen's theory. BNNT is modeled as an Euler-Bernoulli beam and is subjected to combine mechanical, electrical and thermal loading. The effect of viscosity on FLUID-BNNT interaction is considered based on Navier-Stokes relation. The van der Waals (vdW) interaction between the inner and outer nanotubes is taken into account and the surrounding elastic medium is simulated as Winkler and Pasternak foundation. Considering the charge equation for coupling of mechanical and electrical fields, Hamilton's principle is utilized to derive the motion equations based on the von Karman theory. Dynamic buckling load is evaluated using differential quadrature method (DQM). Results show that dynamic buckling load depends on small scale factor, viscosity, elastic medium parameters and temperature changes. Also, dynamic instability region is discussed for various conditions.

This paper investigates the parametric excitation of a micro-pipe CONVEYING FLUID suspended between two symmetric electrodes. Electrostatically actuated micro-pipes may become unstable when the exciting voltage is greater than the pull-in value. It is demonstrated that the parametric excitation of a micro-pipe by periodic (ac) voltages may have a stabilizing effect and permit an increase of the steady (dc) component of the actuation voltage beyond the pull-in value. Mathieu type equation of the system is obtained by applying Taylor series expansion and Galerkin method to the nonlinear partial differential equation of motion. Floquet theory is used to extract the transition curves and stability margins in physical parameters space (Vdc-Vac). In addition, the stability margins are plotted in flow velocity and excitation amplitude space (u-Vac space). The results depict that the micro-pipe remains stable even if the flow velocity is more than the critical value for a certain dc voltage. For instance, in absence of the (ac) component, it is shown that pull-in voltages associated to critical velocities 3 and 6 are 14. 06 and 5. 4 volt, respectively. However, transition curves show that superimposing an (ac) component with forcing frequency Ω =10 increases the pull-in voltage beyond these values. Furthermore, for the present pull-in voltages the critical velocities 3 and 6 could be increases with imposing some (ac) component. These results are discussed in detail in simulation results section where the transion curves are ploted quantitatively.

In this article, derivation of a nonlinear model and nonlinear controller design for a micropipe CONVEYING FLUID, which is excited with a piezoelectric actuator, are accomplished. The governing equations are derived by using Hamilton’ s principle. The difference between the equations in micro-scales and macro-scales is established by using the modified couple stress theory. Unlike the classical Timoshenko beam theory, this new theorem includes a material length scale parameter which could help capturing the size effect. In addition, for thin members, so long as the deformation in the order of thickness, they do not remain in the elastic zone. Therefore, the linear theorem produces error in predicting in-plane movement of the member. In this way, the nonlinear terms are considered in the equations by applying mid-plane stretching theory. After this derivation, a frequency analysis is performed on the model. In addition, the effective parameters on the peak value of the response are studied as well. Finally, a sliding mode controller for the input voltage of the system is designed. It has been observed that by using this type of nonlinear controller, the behavior of the system could be improved significantly.

Vibration analysis of vessels CONVEYING blood flow embedded in viscous FLUID is studied based on the modified strain gradient theory. The viscoelastic vessels are simulated as a non-classical EulerBernoulli beam theory. Employing Hamilton’ s principle, the governing equations for size-dependent vessels are derived. The Galerkin method is used in order to transform the resulting equations into general eigenvalue equations. The effects of the blood flow profile and its modification factors, red blood cells (RBCs) and hematocrit are considered in the blood flow. Besides, the influences of the constitutional material gradient scale, blood flow, internal pressure, structural damping coefficient, viscous FLUID substrate and various boundary conditions on the natural frequencies and critical buckling velocities are studied. It is revealed that as the hematocrit, FLUID viscosity of substrate, internal pressure and mass ratio increase, the natural frequencies and critical buckling velocities decrease. Furthermore, the results indicated that the strain gradient theory predicts the highest natural frequencies and critical buckling velocities among others. The results are compared with those available in the literature and good agreement has been observed.