Mathematical Justification of an Obstacle Problem in the Case of a Plate

In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified.Starting from the three-dimensional nonlinear Signorini problem,by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied.It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.     

Numerical treatment of Casson nanofluid Bioconvectional flow with heat transfer due to stretching cylinder/plate: Variable physical properties

PurposeThe purpose of the current framework is to scrutinize the two-dimensional flow and heat transfer of Casson nanofluid over cylinder/plate along with impacts of thermophoresis and Brownian motion effects. Also, the effects of exponential thermal sink/source, bioconvection, and motile microorganisms are taken.Methodology/ApproachThe resulting non-linear equations (PDEs) are reformed into nonlinear ODEs by using appropriate similarity variables. The resultant non-linear (ODEs) were numerically evaluated by the use of the Bvp4c package in the mathematical solver MATLAB.FindingsThe numerical and graphical illustration regarding outcomes represents the performance of flow-involved physical parameters on velocity, temperature, concentration, and microorganism profiles. Additionally, the skin friction coefficient, local Nusselt number, local Sherwood number, and local microorganism density number are computed numerically for the current presented system. We noted that the velocity profile diminishes for the rising estimations of magnetic and mixed convection parameters. The Prandtl number corresponds with the declining performance of the temperature profile observed. The enhancement in the values of the Solutal Biot number and Brownian motion parameter increased in the concentration profile.OriginalityIn specific, this framework focuses on the rising heat transfer of Casson nanofluid with bioconvection by using a shooting mathematical model. The novel approach of the presented study is the use of motile microorganisms with exponential thermal sink/source in a Casson nano-fluid through a cylinder/plate. A presented study performed first time in the author’s opinion. Understanding the flow characteristics and behaviors of these nanofluids is crucial for the scientific community in the developing subject of nanofluids.     

Oscillatory behavior of supersonic impinging jet flows

Oscillatory flows of a choked underexpanded supersonic impinging jet issuing from a convergent nozzle have been computed using the axisymmetric unsteady Navier--Stokes system. This paper focuses on the oscillatory flow features associated with the variation of the nozzle-to-plate distance and nozzle pressure ratio. Frequencies of the surface pressure oscillation and flow structural changes from computational results have been analyzed. Staging behavior of the oscillation frequency has been observed for both cases of nozzle-to-plate distance variation and pressure ratio variation. However, the staging behavior for each case exhibits different features. These two distinct staging behaviors of the oscillation frequency are found to correlate well if the frequency and the distance are normalized by the length of the shock cell. It is further found that the staging behavior is strongly correlated with the change of the pressure wave pattern in the jet shear layer, but not with the shock cell structure. Communicated by K. Takayama PACS 02.60.Cb; 47.40.−x; 47.40.Nm; 47.35.+I; 47.15.−x     

薄板结构的安定性分析

本文关于薄板的分析采用样条函数插值及结构中的残余应力场用温度参数模拟，解决了薄板结构在交变载荷作用下的安定问题。由于温度参数的引用，使得研究的问题的自由度大幅度减少，文中还对薄板的Ｍｉｓｅｓ型屈服函数进行了线性化处理，它是安定定理的求解线性化的基础，算例表明本文所提出的方法及程序的可行和有效。     

The Kinematics of Plate Models: A Geometrical Deduction

We present a deduction of the Kirchhoff–Love and Reissner–Mindlin kinematics of a simply-connected plate by using the formal asymptotic development method applied to the compatibility conditions of Saint-Venant and the formula of Cesàro–Volterra. This formal deduction is purely geometrical because we do not use any information coming from the loading or the constitutive behavior.      

Heat transfer due to harmonic variation in the free stream temperatures in a flat plate exposed on both sides

The heat transfer through an infinite flat plate is studied when the temperatures of the two free streams surrounding it are varying harmonically with time and out of phase, with a delay period τ_d. The configuration is a simplified model for the heat transfer through the separating wall in the isochoric counter-current heat exchanger. The results show that apart from the τ_d effect, the perturbation parameters depend mainly on the cavity passing frequency f. At the thick plate solution, the combined passing frequency–delay time influences are significant only when the dimensionless frequency is smaller than 10. Within this range τ_d affects seriously not only the temperature perturbation amplitudes (which determine the thermal stresses) but also the heat fluxes and the accumulated energy ones. When f ≥ 10, the plate behaves as two separate semi-infinite slabs. Heat penetration delays greater than one cavity passing period may be possible.     

Finite Element Analysis of Dynamically Loaded Homogeneous Viscous Beams

The paper is concerned with impulsively loaded beams in which the material is treated as homogeneous viscous as an approximation of a rigid-viscoplastic constitutive relation. As opposed to the standard displacement method finite element formulation, where interpolation functions describing the velocity field across elements is given, a mixed formulation is used in which nodal velocities and nodal moments are carried as parameters. At each instant the accelerations (by the Tamuzh principle) and the rates of change of moment (by a virtual velocities formulation) are found, and velocities and moments are integrated forward independently. The properties of the mode solution are also introduced, and the forward integration is carried through only for the difference between the mode solution and the actual solution. This leads to a very efficient scheme for the numerical solution of a cantilever beam problem shown as an illustration.     

Electromechanical control of vibration on a plate submitted to a non-ideal excitation

This paper deals with the enhancement of electromechanical control of vibration on a thin plate submitted to non-ideal excitation. Modelling of the systems displays the non-ideal source used as external excitation above the structure on a particular surface and control force acting at specific points under the structure. The electromechanical device is composed by a RL circuit with a saturated inductance and stings connected to the plate is used as connection between the structure and the controller. Routh–Hurwitz criteria are used to obtain the stability condition of the controlled system and some dynamics exploration leads us to the condition for which the amplitude of vibration is reduced in the mechanical structure.