A study of the dynamic of influence through differential equations

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2011.22 - ISSN : 1955-611XThe paper concerns a model of influence in which agents make their decisions on a certain issue. It is assumed that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. The use of continuous variable permits the application of differential equations systems to the analysis of the convergence of agents' decisions in long-time. In particular, by applying the approach based on differential equations of the influence model, we recover the results of the discrete model on classical influence functions and the results on the boss and approval sets for the command games equivalent to some influence functions.Le papier concerne un modèle d'influence dans lequel les agents prennent des décisions sur une proposition. On suppose que chaque agent est incliné à prendre une certaine décision, mais que dû à une influence possible des autres agents, sa décision finale peut être différente de son inclination initiale. Comme dans la réalité l'influence ne s'arrête pas nécessairement après une étape mais peut itérer, nous présentons un modèle qui nous permet d'étudier la dynamique de l'influence. L'utilisation de variables continues permet l'application des systèmes d'équations différentielles à l'analyse de la convergence des décisions des agents. En particulier, en appliquant l'approche basée sur les équations différentielles au modèle d'influence, nous retrouvons les résultats du modèle discret sur les fonctions d'influence classiques, ainsi que les résultats sur les "boss sets" et les ensembles d'approbation pour les jeux de commande équivalents aux fonctions d'influence

Linear Transient Analysis of Laminated Composite Plates using GLPT

The objective of this work is to study the transient response of laminated composite plates under different types of dynamic loading. For this purpose, laminated composite plate is modeled using Reddy’s generalized laminated plate theory (GLPT). This theory assumes layerwise linear variation of displacements components. Transverse displacement is constant through the thickness of the plate. Linear kinematic relations, as well as Hook’s law, are considered. The generalized displacements are expanded in double trigonometric series using Navier-type method. Governing partial differential equations are reduced to a set of ordinary differential equations in time. The equations of motion are solved using constant-average acceleration method. Effect of time step on accuracy of transient response is investigated using a family of simply supported cross-ply (0/90) laminates. Different number of layers, as well as their influence on transient response is considered. Different schemes of transient dynamic loading are investigated. Good agreement is obtained with some results existing from the literature

A Research of Analytical Solution on Tubular Structure which is Subjected to an Axis Expansion in Different Contributions

In this research paper, we proposed a classical mechanical study of the behavior of a tubular structure which is subjected to an expansion following the axis of the material. The first part, is focused on kinematic and dynamic aspects, Gradient tensor, left Cauchy-Green tensor ant isotropic invariants are used to proceed to find an analytical exact logarithmic solution function of the radius, of the problem at the limits through a system of partial differential equations in equilibrium condition. The simulations show that in the case of a sinusoidal, logarithmic and exponential function of time, the solution has a strong dependence to the radius. As a results, sinusoidal function of time has a big influence in the shape of the solution graphic which is negative or positive depending to the value of the time and radius. But logarithmic and exponential contribution has not a big influence in the arc shape of the solution graphic but a great influence in the values and it remains positive whatever the value of the radius.&nbsp

Numerical investigation on nonlinear dynamic responses to fluid-structure interaction in BTA deep-hole drilling shaft system

Numerical investigation is conducted into the nonlinear dynamic responses to fluid-structure interaction in deep-hole drilling shaft system. Based on the theories of pipes and tubes conveying fluid, the governing equation of the drilling shaft system is obtained taking into account of the fluid-structure interaction and the effect of the motion constraints. The nonlinear partial differential governing equation of motion is discretized in modal space using the Galerkin method and then transformed into a set of ordinary different equations. Numerical solutions of these equations are then obtained using the fourth order Runge-Kutta method. The influence of the forcing frequency and the support constraints on the dynamic behaviors of the drilling shaft is examined. The nonlinear dynamic behaviors of the drilling shaft system are presented by the bifurcation diagram and phase diagram. It has been found that the magnitude of support stiffness and the number and position of support constraints have a significant influence on dynamic behaviors of the drilling shaft system. The study in the paper provides an effective guidance to maintain the stability of the BTA deep-hole drilling shaft system through selecting the favorable operation parameters in deep hole drilling process

Linear Transient Analysis of Laminated Composite Plates using GLPT

The objective of this work is to study the transient response of laminated composite plates under different types of dynamic loading. For this purpose, laminated composite plate is modeled using Reddy’s generalized layerwise plate theory (GLPT). This theory assumes layerwise linear variation of displacements components. Transverse displacement is constant through the thickness of the plate. Using the assumed displacement field, linear kinematic relations, as well as Hooke’s constitutive law, equations of motion are derived using Hamilton’s principle. Analytical solution for cross-ply laminates is derived using the Navier method. Numerical solution is obtained using FEM. Governing partial differential equations in both solutions are reduced to a set of ordinary differential equations in time using Newmark integration scheme. The equations of motion are solved using constant-average acceleration method. Effects of time step, mesh refinement and lamination scheme on accuracy of transient response are considered. Illustrative comments are given about the influence of shear deformation on transient response. Finally, different schemes of dynamic loading are investigated. Good agreement is obtained with results from the literature.Obiectivul acestei lucrări este de a studia răspunsul tranzitoriu al plăcilor compozite laminate sub diferite tipuri de încărcare dinamică. În acest scop, placa compozită laminată este modelată folo-sind teoria generalizată a plăcilor propusă de Reddy (GLPT). Această teorie presupune variația liniară a componentelor deplasării în raport cu straturile plăcii. Deplasarea transversală este constantă în grosimea plăcii. Ecuațiile de mișcare sunt derivate folosind principiul lui Hamilton, utilizând câmpul de deplasare asumat, relațiile liniare cinematice, precum și legea constitutivă a lui Hooke. Soluția analitică pentru plăci laminate din fibre din lemn încrucișate este derivată folosind formula lui Navier. Soluția numerică este obținută cu ajutorul metodei elementului finit. Ecuațiile cu derivate parțiale în ambele soluții sunt reduse la un set de ecuații diferențiale ordinare în timp, utilizând Metoda Newmark. Ecuațiile de mișcare sunt rezolvate folosind metoda de inte-grare implicită Newmark β. Sunt luate în considerare efectele integrării numerice în timp, pas cu pas, ale rafinării discretizării și ale sistemului de laminare asupra acurateței răspunsului tranzitoriu. Sunt prezentate comentarii ilustrative despre influența deformării cauzate de forfecare asupra răspunsului tranzitoriu. În cele din urmă, sunt investigate diferite scheme de încărcare dinamică. Rezultatele obținute sunt în concordanță cu cele din literatura de specialitate

Regime change thresholds in flute-like instruments: influence of the mouth pressure dynamics

Since they correspond to a jump from a given note to another one, the mouth pressure thresholds leading to regime changes are particularly important quantities in flute-like instruments. In this paper, a comparison of such thresholds between an artificial mouth, an experienced flutist and a non player is provided. It highlights the ability of the experienced player to considerabily shift regime change thresholds, and thus to enlarge its control in terms of nuances and spectrum. Based on recent works on other wind instruments and on the theory of dynamic bifurcations, the hypothe- sis is tested experimentally and numerically that the dynamics of the blowing pressure influences regime change thresholds. The results highlight the strong influence of this parameter on thresholds, suggesting its wide use by experienced musicians. Starting from these observations and from an analysis of a physical model of flute-like instruments, involving numerical continuation methods and Floquet stability analysis, a phenomenological modelling of regime change is proposed and validated. It allows to predict the regime change thresholds in the dynamic case, in which time variations of the blowing pressure are taken into account

Interception and deviation of near Earth objects via solar collector strategy

A solution to the asteroid deviation problem via a low-thrust strategy is proposed. This formulation makes use of the proximal motion equations and a semi-analytical solution of the Gauss planetary equations. The average of the variation of the orbital elements is computed, together with an approximate expression of their periodic evolution. The interception and the deflection phase are optimised together through a global search. The low-thrust transfer is preliminary designed with a shape based method; subsequently the solutions are locally refined through the Differential Dynamic Programming approach. A set of optimal solutions are presented for a deflection mission to Apophis, together with a representative trajectory to Apophis including the Earth escape