Large deflections of shallow conical membrane

Large deflections of a shallow elastic conical membrane fixed at the outer edge and loaded by either uniform or hydrostatic pressure are investigated. The overning equations were solved by the method of matched asymptotic expansions and by a finite difference method. Agreement between the two methods was excellent for the small values of the perturbation parameter

One-dimensional wave propagation in particulate suspensions

One-dimensional small-amplitude wave motion in a two-phase system consisting of an inviscid gas and a cloud of suspended particles is analyzed using a continuum theory of suspensions. Laplace transform methods are used to obtain several approximate solutions. Properties of acoustic wave motion in particulate suspensions are inferred from these solutions

Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation

Vibration responses were investigated for a viscoelastic Single-walled carbon nanotube (visco-SWCNT) resting on a viscoelastic foundation. Based on the nonlocal Euler-Bernoulli beam model, velocity-dependent external damping and Kelvin viscoelastic foundation model, the governing equations were derived. The Transfer function method (TFM) was then used to compute the natural frequencies for general boundary conditions and foundations. In particular, the exact analytical expressions of both complex natural frequencies and critical viscoelastic parameters were obtained for the Kelvin-Voigt visco-SWCNTs with full foundations and certain boundary conditions, and several physically intuitive special cases were discussed. Substantial nonlocal effects, the influence of geometric and physical parameters of the SWCNT and the viscoelastic foundation were observed for the natural frequencies of the supported SWCNTs. The study demonstrates the efficiency and robustness of the developed model for the vibration of the visco-SWCNT-viscoelastic foundation coupling system

Dynamic stability of a nonlinear multiple-nanobeam system

We use the incremental harmonic balance (IHB) method to analyse the dynamic stability problem of a nonlinear multiple-nanobeam system (MNBS) within the framework of Eringen’s nonlocal elasticity theory. The nonlinear dynamic system under consideration includes MNBS embedded in a viscoelastic medium as clamped chain system, where every nanobeam in the system is subjected to time-dependent axial loads. By assuming the von Karman type of geometric nonlinearity, a system of m nonlinear partial differential equations of motion is derived based on the Euler–Bernoulli beam theory and D’ Alembert’s principle. All nanobeams in MNBS are considered with simply supported boundary conditions. Semi-analytical solutions for time response functions of the nonlinear MNBS are obtained by using the single-mode Galerkin discretization and IHB method, which are then validated by using the numerical integration method. Moreover, Floquet theory is employed to determine the stability of obtained periodic solutions for different configurations of the nonlinear MNBS. Using the IHB method, we obtain an incremental relationship with the frequency and amplitude of time-varying axial load, which defines stability boundaries. Numerical examples show the effects of different physical and material parameters such as the nonlocal parameter, stiffness of viscoelastic medium and number of nanobeams on Floquet multipliers, instability regions and nonlinear amplitude–frequency response curves of MNBS. The presented results can be useful as a first step in the study and design of complex micro/nanoelectromechanical systems