An analytical approach for calculating natural frequencies of finite one-dimensional acoustic metamaterials

In this paper, an analytical matrix method is presented to drive closed-form characteristic equations for natural frequencies of finite monoatomic and diatomic metamaterials with various boundary conditions. Here, we extend the matrix method introduced by Louck for monoatomic lattice chains. The proposed method is used to calculate the vibration frequencies of the monoatomic metamaterials with fixed–fixed, fixed-free and free-free boundary conditions. In addition, the natural frequencies of fixed–fixed diatomic metamaterials are calculated. The existence of band gaps in the frequencies of the metamaterials is numerically shown.

     

Analytical analysis of the static interaction of fluid and cylindrical membrane structures

The static behavior of an inflated cylindrical membrane is theoretically investigated under different conditions of internal pressures, upstream and downstream fluid parameters. The membrane is attached to a horizontal base along two generators and can be inflated with a compressible fluid (air), an incompressible fluid (water), or a combination of them. The base width, curved perimeter, internal pressure, upstream and downstream fluid properties are given. Large deformation of the membrane due to the internal and external pressures makes the governing equation of the problem to be non-linear. In the present study, an analytical approach for the non-linear analysis of the static interaction of the fluid and the cylindrical membrane with different load distributions and boundary conditions is developed. Both geometric and equilibrium relations of the membrane element are used to obtain the membrane profile in explicit closed form. The validity of the present analytical approach is confirmed by comparing the results with experimental and numerical results obtained from the literature. It is shown that the present formulation is an appropriate method and a new approach to predict the static non-linear interaction of the fluid and the membrane structures with a good accuracy and less numerical effort.     

Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid

The flexural vibration of viscoelastic carbon nanotubes (CNTs) conveying fluid and embedded in viscous fluid is investigated by the nonlocal Timoshenko beam model. The governing equations are developed by Hamilton's principle, including the effects of structural damping of the CNT, internal moving fluid, external viscous fluid, temperature change and nonlocal parameter. Applying Galerkin’s approach, the resulting equations are transformed into a set of eigenvalue equations. The validity of the present analysis is confirmed by comparing the results with those obtained in literature. The effects of the main parameters on the vibration characteristics of the CNT are also elucidated. Most results presented in the present investigation have been absent from the literature for the vibration and instability of the CNT conveying fluid.     

Coupled free vibration analysis of a fluid-filled rectangular container with a sagged bottom membrane

In the present paper, two-dimensional coupled free vibrations of a fluid-filled rectangular container with a sagged bottom membrane are investigated. This system consists of two rigid walls and a membrane anchored along two rigid vertical walls. It is filled with incompressible and inviscid fluid. The membrane material is assumed to act like an inextensible material with no bending resistance. First, the nonlinear equilibrium equation is solved and the equilibrium shape of the membrane is obtained using an analytical formulation neglecting the membrane weight. The small vibrations about the equilibrium configuration are then investigated. Along the contact surface between the bottom membrane and the fluid, the compatibility requirement is applied for the fluid–structure interactions and the finite element method is used to calculate the natural frequencies and mode shapes of the fluid–membrane system. The vibration analysis of the coupled system is accomplished by using the displacement finite element for the membrane and the pressure fluid-finite element for the fluid domain. The variations of natural frequencies with the pressure head, the membrane length, the membrane weight and the distance between two rigid walls are examined. Moreover, the mode shapes of system are investigated.     

Nanoscale mass sensing based on vibration of single-layered graphene sheet in thermal environments简

Based on vibration analysis, single-layered graphene sheet （SLGS） with multiple attached nanoparticles is developed as nanoscale mass sensor in thermal environments. Graphene sensors are assumed to be in simplysupported configuration. Based on the nonlocal plate the- ory which incorporates size effects into the classical theory, closed-form expressions lot the frequencies and relative fre- quency shills of SLGS-based mass sensor are derived using the Galerkin method. The suggested model is justified by a good agreement between the results given by the present model and available data in literature. The effects of tem- perature difference, nonlocal parameter, the location of the nanoparticle and the number of nanoparticles on the relative frequency shift of the mass sensor are also elucidated. The obtained results show that the sensitivity of the SLGS- based mass sensor increases with increasing temperature difference.     

A semi-analytical approach for the nonlinear two-dimensional analysis of fluid-filled thin-walled pliable membrane tubes

Pliable tubes are tubular membranes of low rigidity and may collapse or substantially deform easily. The governing equations of these tubes are nonlinear because the tube shape depends on the internal pressure and the deformation of the tube can be very large. In the present study, a semi-analytical approach for the nonlinear analysis of the fluid-filled thin-walled pliable tubes with different load distributions and boundary conditions is developed. Both geometric and equilibrium relations of the tube element are used to obtain the tube profile in explicit closed form. Several applications of the pliable tubes are considered and the equilibrium shape and wave propagation velocity in these tubes are also obtained. The validity of the present semi-analytical approach is confirmed by comparing the results with those obtained from the literature. It is shown that the present formulation is an appropriate method and a new approach to predict the nonlinear behavior of the pliable tubes with a good accuracy.     

Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect

Single-walled carbon nanotubes (SWCNTs) exhibit remarkable chirality-dependent mechanical phenomena. In present paper, an anisotropic elastic shell model is developed to study the vibration characteristics of chiral SWCNTs. Analytical solution is presented by using the Flügge shell theory and complex method. The suggested model is justified by a good agreement between the present results and some experimental and numerical available data in literature. Furthermore, the model is used to elucidate the effect of tube chirality on the frequencies of SWCNTs. Finally, the influences of the externally applied mid-face axial force and torque on longitudinal, radial and torsional frequencies of SWCNTs are investigated.