Effects of initial geometric imperfections on dynamic behavior of rectangular plates

The present work deals with the influence of initial geometric imperfections on the dynamic behavior of simply supported rectangular plates subjected to the action of periodic in-plane forces. The nonlinear large-deflection plate theory used in this analysis corresponds to the dynamic analog of von Karman's theory. The temporal response is analyzed by the first-order generalized asymptotic method. The solution for the temporal equations of motion takes into account the possibility of existence of simultaneous forced and parametric vibrations. The results indicate that the presence of initial imperfections may significantly raise the resonance frequencies, cause the plate to exhibit a soft spring behavior and improve slightly the stability of the plate by reducing the area of its instability zones. Furthermore, the presence of initial imperfections induces forced vibrations which interact with parametric vibrations in order to generate a competitive hesitation phenomenon in the transition zone.     

Asymptotics for the eigenelements of vibrating membranes with very heavy thin inclusionsComportement asymptotique des éléments propres pour des membranes vibrantes avec des couches très minces et très lourdes

We consider the vibrations of a membrane that contains a very thin and heavy inclusion around a curve γ. We assume that the membrane occupies a domain $\text{Ω}$ of $\text{R}{}^2$. The inclusion occupies a layer-like domain $\text{ω}{}_{\mathrm{\epsilon }}\text{?Ω}$ of width 2ε and it has a density of order O(ε^?3). The density is of order O(1) outside this inclusion, the concentrated mass around the curve γ. ε is a positive parameter, ε∈(0,1). By means of asymptotic expansions, we describe the behaviour, as ε→0, of the eigenelements (λ^ε,u^ε) of the associated spectral problem. We provide complete asymptotic series for the low frequencies λ^ε=O(ε²), the medium frequencies λ^ε=O(ε) and the corresponding eigenfunctions u^ε. To cite this article: Y. Golovaty et al., C. R. Mecanique 330 (2002) 777–782.     

Nonaxisymmetric Vibrations of Discretely Reinforced Inhomogeneous Multilayer Cylindrical Shells under Nonstationary Loads

The equations of nonaxisymmetric vibrations of discretely reinforced multilayer cylindrical shells are analyzed. A refined Timoshenko model of shells and beams is used to analyze elements of an elastic structure. The vibration equations for an inhomogeneous elastic system are derived using the Reissner variational principle. The numerical solver of the dynamic equations is based on the integro-interpolation method used to construct finite-difference schemes for equations with discontinuous coefficients. The dynamic behavior of a five-layer cylindrical shell under distributed nonstationary loading is analyzed     

On the radial oscillations of incompressible, isotropic, elastic and limited elastic thick-walled tubes

The finite amplitude, free radial oscillations of a thick-walled circular cylindrical tube are studied for an arbitrary incompressible, isotropic and homogeneous rubber-like material having limiting molecular chain extensibility. First, based on classical results for hyperelastic tubes, some results for thick-walled Mooney-Rivlin tubes are described graphically in the phase plane. Then the periodicity of the finite amplitude, free oscillations of a general limited elastic, thick-walled tube is studied; and some analytical results for the Gent model are illustrated in several numerical examples. Results for thick-walled Gent tubes are compared with those for corresponding Mooney-Rivlin tubes; and the motion of thin-walled Gent tubes is illustrated in the phase plane. Physical conclusions are presented. The period of small amplitude oscillations of an arbitrary elastic or limited elastic tube is derived from relations obtained by a linearization of a general class of equations of which the tube problem is a special case. Classical results of the linear theory are thereby recovered and compared with results for Mooney-Rivlin and Gent tubes.     

Collective Behavior in Quantum Interference: A Supplementary Superposition Principle

An interferometer in which all of its components are treated as quantum bodies is examined with the standard interpretation and with a model in which its uncoupled spatially separated components act collectively. These models utilize superposition principles that differ when applied to systems composed of three or more bodies. Interferometric discrepancies between these models that involve frequency shifts and recoil are shown to be difficult to measure. More pronounced differences involve quantum correlated interference. The collective model provides a missing connection between quantum and semiclassical theories. Scattering from an entangled state, which cannot be divided into disjoint parts, is proposed to involve such collective recoil. Collective scattering offers a viable supplement to the standard model, thereby providing insight into constructing tests of the superposition principle in systems with three or more bodies.     

A high-order solver for simulating vortex-induced vibrations using the sliding-mesh spectral difference method and hybrid grids

We present a high-order solver for simulating vortex-induced vibrations (VIVs) at very challenging situations, for example, VIVs of a row of very closely placed objects with large relative displacements. This solver works on unstructured hybrid grids by employing the high-order tensor-product spectral difference method for quadrilateral grids and the Raviart-Thomas spectral difference method for triangular grids. To deal with the challenging situations where a traditional conforming moving mesh is incapable, we split a computational domain into nonoverlapping subdomains, where each interior subdomain encloses an object and moves freely with respect to its neighbors. A nonuniform sliding-mesh method that ensures high-order accuracy is developed to deal with sliding interfaces between subdomains. A monolithic approach is adopted to seamlessly couple the fluid and solid vibration equations. Moreover, the solver is parallelized to further improve its efficiency on distributed-memory computers. Through a series of numerical tests, we demonstrate that this solver is high-order accurate for both inviscid and viscous flows and has good parallel efficiency, making it ideal for VIV studies.     

Enhance limit cycle oscillation in a wind flow energy harvester system with fractional order derivatives

Advances in material science and mathematics in conjunction with technological needs have triggered the use of material and electric components with fractional order physical properties. This paper considers the mathematical model of a piezoelectric wind flow energy harvester system for which the capacitance of the piezoelectric material has fractional order current-voltage characteristics. Additionally the mechanical element is assumed to have fractional order damping. The analysis is focused on the effects of order of derivatives on the appearance and characteristics of limit circle oscillations (LCO). It is obtained that, the order of derivatives to enhance the amplitude of LCO and lower the threshold condition leading to LCO. The domains of efficiency of the system are illustrated in various parameters spaces.     

The Complexity of Collective Decision

This paper is about the dynamics of collective decision when an individual adapts his rational decision to the others'. We consider an organization of heterogeneous agents, in which each agent faces the binary decision problem. The standard way of modeling a collective decision is to assume everyone has the same value or payoff structure. This paper considers collective decision of agents with heterogeneous payoffs. We obtain and classify rational decision rules of heterogeneous agents into a few categories depending on their idiosyncratic payoff structure. We also obtain the micro–macro dynamics that relate the aggregate collective decision with the underlying individual decisions. We investigate the roles of particular types of agents such as hardcore, conformists, and nonconformists. We show that agents' rational behavior combined with the others produce stable orders, and sometimes complex cyclic behavior.     

Vibrations and Dissipative Heating of a Cylindrical Panel under a Periodic Moving Load

An analytic solution is obtained to describe the vibrations and dissipative heating of a simply supported infinite cylindrical panel under periodic normal loads moving over its surface with a constant velocity. Special attention is focused on resonant vibrations, which result in the most intensive dissipative heating. It is additionally assumed that the material of the panel is viscoelastic, its properties are independent of temperature, and Poisson’s ratio is real. The influence of thickness, radius of curvature, load velocity, and viscoelastic properties on the thermal state of the panel is analysed against the thermal state of the plate__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 100–109, April 2005.