Sharif Digital Repository

The flutter of a 3-D rigid fin with double-wedge section and free-play in flapping, plunging and pitching degrees-of-freedom operating in supersonic and hypersonic flight speed regimes have been considered. Aerodynamic model is obtained by local usage of the piston theory behind the shock and expansion analysis, and structural model is obtained based on Lagrange equation of motion. Such model presents fast, accurate algorithm for studying the aeroelastic behavior of the thick supersonic fin in time domain. Dynamic behavior of the fin is considered over large number of parameters that characterize the aeroelastic system. Results show that the free-play in the pitching, plunging and flapping... 

In this study, we deal with passive dynamic object manipulation. During passive dynamic object manipulation, a passive object is manipulated using passive manipulators. Like other passive robotic systems, there are no actuators in these systems. The object follows a path and travels along it under the effect of its own weight, as well as, the interaction force applied by each manipulator on it. The objects are not necessarily rigid, but we manipulate passive multibody objects as well as rigid ones. Thus, for a passive walking system, we assume that the passive walker is a multibody object and is manipulated by the ground (zero degree-of-freedom manipulator). As an example, we show that a... 

In this paper, the whirling frequencies of simply supported and clamped rotating cylindrical shells surrounded by an elastic foundation are investigated. The Love's shell theory is used along with the Winkler foundation to obtain the governing equations of motion. An exact power series solution is obtained for arbitrary boundary conditions and the results are verified with the literature. Several case studies are performed, and the effect of spinning speed, foundation stiffness, and geometrical dimensions of the cylinder on the whirling frequencies are investigated  

In this work, we introduce a category of dynamic manipulation processes, namely passive dynamic object manipulation, according to which an object is manipulated passively. Specifically, we study passive dynamic manipulation here. We define the main concept, discuss the challenges, and talk about the future directions. Like other passive robotic systems, there are no actuators in these systems. The object follows a path and travels along it under the effect of its own weight, as well as the interaction force applied by each manipulator on it. We select some simple examples to show the concept. For each example, dynamic equations of motion are derived and the stability of the process is taken... 

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to... 

Peridynamics is a nonlocal theory of solid mechanics which is suitable for modeling discontinuities and fractures without requiring external theories. In the original peridynamic equation of motion, the internal forces are integrated over the entire domain of the body. Although this equation complies perfectly with physical principles, its heavy calculations make it practically impossible to use. To avoid this difficulty, we can benefit from a special case of the peridynamic equation of motion in which the integration domain of the internal forces is limited to the family of particles. A limitation of this special equation, which is the most common equation in the peridynamic literature, is... 

Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of motion for the dynamics itself, rather than the state. Here we develop a Markovian master equation for the process matrix of an open system interacting with a reservoir, which resembles the Lindblad Markovian master equation. We employ this equation to introduce a scheme for optimal local coherent process control at target times and extend the Krotov technique to obtain optimal control. We illustrate utility of this framework through several quantum... 

A 3D dynamic model with 3 segments and 5 degrees of freedom (DOF) was developed to simulate the gait of a paraplegic patient while wearing a rigid orthosis. The equations of motion were formulated based on Denavit-Hartenberg notation and solved using a combined forward-inverse dynamics approach assuming locked knees, passive hips and actuated pelvis joints. Results showed that the model could take a single step in response to a sinusoidal motion applied to the pelvis joints. It was concluded that a paraplegic patient is able to walk with proper immobilization of the paralyzed joints and appropriate maneuver of the trunk, without the need to a propulsion supply from hands through crutches  

In this Letter, I introduce a generalization of Toda lattice model, in which each site can interact with all other sites with different coupling constants. To show solvability of this model, by introducing new type of quantities (which are referred to as anti-Grassmanian numbers), the equations of motion are transformed to a Lax equation and constants of motion are derived. At last, by finding a proper r matrix involutivity of these constants are shown. © 2002 Elsevier Science B.V. All rights reserved  

We consider general multispecies models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on any type of lattice. We also show that under these conditions the evolution equations for two point functions at different times are also closed. As an example we introduce a class of two species models that may be useful for the description of voting processes or the spreading of epidemics. © 2002 The American Physical Society  

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential... 

Flutter of cantilevered, functionally graded cylindrical shells under an end axial follower force is addressed. The material properties are assumed to be graded along the thickness direction according to a simple power law. Using the Hamilton principle, the governing equations of motion are derived based on the first-order shear deformation theory. The stability analysis is carried out using the extended Galerkin method and minimum flutter loads and corresponding circumferential mode numbers are obtained for different volume fractions, length-to-radius, and thicknesses-to-radius ratios. Two different configurations are considered for the FGM: one in which the metal phase is the outer layer... 

The main objective of this paper is to present the modeling and simulation of open loop dynamics of a rigid body insect-like flapping wing. The most important aerodynamic mechanisms that explain the nature of the flapping flight, including added mass, rotational lift and delayed stall, are modeled. Wing flapping kinematics is described using appropriate reference frames and three degree of freedom for each wing with respect to the insect body. In order to simulate nonlinear differential equations of motion, 6DOF model of the insect-like flapping wing is developed, followed by an evaluation of the simulation results in hover condition  

In this paper, a size-dependent formulation is presented for vibration analysis of micro-end mill tool. The formulation is developed based on the strain gradient elasticity theory in order to enhance the modeling capability of micro-size structures. Due to stubby geometry of micro-tool, the shear deformation and rotary inertia effects are considered in the derivation of equations. Hence, based on the strain gradient Timoshenko beam theory, the extended Hamilton's principle is used to formulate a detailed dynamical model of the rotating micro-tool. The dynamical model includes a set of partial differential equations with gyroscopic coupling produced due to the spindle rotation. The governing... 

This paper aims at investigating the interaction of two flexible permanent magnet beams facing each other. The governing equations of motion are obtained based on the Euler-Bernoulli beam model along with Hamiltons principle. Assuming that the beams tips are far enough, each magnet beam is considered as a series of dipole segments and the external force and moment distributions over each beam due to the magnetic field of the other one is calculated in the deformed configuration. The transverse deflections of the beams are written as series expansions of the mode shapes of an unloaded cantilever beam and the Galerkin method is applied to determine the stability and resonance frequencies.... 

A nonlocal continuum shell model is developed to study the stability of nanocones under combined loading: external pressure and compression force. The nonlinear governing equations of motion of nanocone are obtained using Hamiltons principle and the external loads are considered as prestress. Based on Eringens nonlocal elasticity theory the small-scale effect is accounted in the governing equations of motion. To obtain the critical loads, the equations are solved using Galerkin technique and the effect of small-scale parameter and geometry on the stability of nanocone is studied  

In this paper, the nonlinear oscillation of a pendulum wrapping and unwrapping on two cylindrical bases is studied, and an analytical solution is obtained using the multiple scales method. The equation of motion is derived based on an energy conservation technique. By applying the perturbation method to the differential equation, the nonlinear natural frequency of the system is calculated, along with its time response. Analytical results are compared with numerical findings and good agreement is found. The effect of large amplitude and radius of cylinders on system frequency is evaluated. The results indicate that as the radius of the cylinder increases, the system frequency is increased.... 

This paper focuses on developing a new configuration on magnetorheological (MR) brake damper as prosthetic knee. Knee uses magnetic fields to vary the viscosity of the MR fluid, and thereby its flexion resistance. Exerted transmissibility torque of the knee greatly depends on the magnetic field intensity in the MR fluid. In this study a rotary damper using MR fluid is addressed in which a single rotary disc will act as a brake while MR fluid is activated by magnetic field in different walking gait. The main objective of this study is to investigate a prosthetic knee with one activating rotary disc to accomplish necessary braking torque in walking gait via implementing of Newton's equation of... 

In the present study, free vibrations and stability of rotating single walled carbon nanotubes (SWCNT) is investigated by nonlocal theory of elasticity; while the CNT is partially resting on an elastic foundation. The governing equations of motion are presented by using Love's shell assumptions. An exact series expansion method of solution is employed and very accurate results are obtained. Some parameter studies including the effects of rotating speed, foundation stiffness, slenderness ratio and nonlocal parameter on the natural frequency and stability margins of the current model are studied. The studies show that rotation rates and foundation elasticity can contribute significantly in the... 

In this paper, motion of a micro-robot with two perpendicular vibrational actuators is studied. In this work, separation of the micro-robot body from the substrate of motion is modeled. If the applied vertical force to the micro-robot body is greater than its weight, body of the micro-robot jumps apart from the substrate and then returns to it. This motion will continue intermittently until it is damped. In this condition, the motion mechanism of “stick-slip” is not valid, and a hybrid motion according to “stick-slip-jump” mode is governed. By increasing the applied vertical force, the motion velocity of the micro-robot becomes disordered and unrepeatable. By numerical solving of the...