Sharif Digital Repository

To account for certain essential features of material such as dispersive behaviour and optical branches in dispersion curves, a fundamental departure from classical elasticity to polar theories is required. Among the polar theories, micromorphic elasticity of appropriate grades and anisotropy is capable of capturing these physical phenomena completely. In the mathematical framework of micromorphic elasticity, in addition to the traditional elastic constants, some additional constants are introduced in the pertinent governing equations of motion. A precise evaluation of the numerical values of the aforementioned elastic constants in the realm of the experimentations poses serious... 

This is the first research on the nonlinear frequency analysis of a multi-scale hybrid nanocomposite (MHC) disk (MHCD) resting on an elastic foundation subjected to nonlinear temperature gradient and mechanical loading is investigated. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. We present a modified Halpin–Tsai model to predict the effective properties of the MHCD. The displacement–strain of nonlinear vibration of multi-scale laminated disk via third-order shear deformation theory (TSDT) and using Von Karman nonlinear shell theory is obtained. Hamilton’s principle is employed to establish the governing... 

In this study, the dynamics of the accelerated and steady-state motion of a single bubble in a quiescent highly viscous Newtonian liquid was investigated theoretically and experimentally. The presented mathematical model was based on Newton's second law of motion and a balance of buoyancy, drag, history, and added-mass forces. Due to the presence of non-linear terms in the equation of motion, homotopy perturbation method was used as a powerful analytical method to calculate the velocity analytically. To obtain accurate results in the experiments, a high-speed camera was used to record the bubble motion from the moment of detachment to the time at which the terminal velocity is reached.... 

In this work, after formulating the weakly nonlocal micromorphic equations of motion for non-Bravais crystals with general anisotropy, specialization to diamond structures is made. A critical dilemma is the determination of the elastic moduli tensor appearing in the equations of motion. From the equivalency of these equations with the pertinent equations obtained in the context of lattice dynamics, the expressions of the components of the elastic moduli tensors in terms of the atomic force constants are derived analytically. Subsequently, the atomic force constants are calculated via ab initio density functional perturbation theory (DFPT) with high precision. As a benchmark for the accuracy... 

Based on the first-order shear deformation (FSD) model and nonlocal elasticity theory, the simultaneous effects of shear and small scale on the nonlinear vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams are investigated for the first time. To this end, the governing equations of bending and stretching with von Kármán geometric nonlinearity are decoupled into one fourth-order partial differential equation in terms of transverse deflection. A closed-form solution of the nonlinear natural frequency, which can be used in conceptual design and optimization algorithms of FG- CNTRC beams with different boundary conditions, is developed using a hybrid... 

The radiation loss in the whispering gallery resonators causes the eigenvalues of the Maxwell equations with the corresponding boundary conditions complex. The corresponding operators are nonhermitian and for these operators the standard perturbation techniques have some difficulties. In this paper by employing the Floquet theorem a new technique for the φ periodic perturbations is developed. The method is applied to obtain the change of resonance frequencies and losses of φ -perturbed microresonators with cylindrical symmetry. The results are compatible with that are obtained by the Volume Current Method  

New gains tuning and impedance control method were addressed for flexible base moving manipulators. Slow and fast dynamics of robot are decoupled using singular perturbation method. Then, using sliding mode control method, an impedance control law was derived for the slow dynamics. Combined control law was proposed comprising the impedance control law and a feedback control law for the fast dynamics. As fist time, we proposed a new online particle swarm optimization algorithm for gain tuning of impedance control at the contact moments of end effector and unknown environments. This proposed Sliding Mode Impedance Controller and online PSO were simulated for a Flexible Base Moving Manipulator.... 

In this paper, the general problem of impedance control for a robotic manipulator with a moving flexible base is addressed. Impedance control imposes a relation between force and displacement at the contact point with the environment. The concept of impedance control of flexible base mobile manipulator is rather new and is being considered for first time using singular perturbation and new sliding mode control methods by authors. Initially slow and fast dynamics of robot are decoupled using singular perturbation method. Slow dynamics represents the dynamics of the manipulator with rigid base. Fast dynamics is the equivalent effect of the flexibility in the base. Then, using sliding mode... 

In this study, we applied the homotopy perturbation (HP) method for solving linear and nonlinear fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of a convergent series with easily computable components. Comparisons between the results of the HP method and the analytical solution showed that this method gives very precise results with a few terms. In the implied HP method, some unknown parameters in the initial guess are introduced, which are identified after applying boundary conditions. This improvement results in higher accuracy. © 2008 The Royal Swedish Academy of Sciences  

We present a perturbation theory to find the response of an anisotropic DNA to the external tension. It is shown that the anisotropy has a nonzero but small contribution to the force-extension curve of the DNA. Thus an anisotropic DNA behaves like an isotropic one with an effective bending constant equal to the harmonic average of its soft and hard bending constants. © 2008 American Institute of Physics  

We have derived an analytical equation of state (EOS) based on the soft-core statistical mechanical perturbation theory for fluids, using the Weeks-Chandler-Andersen (WCA) theory recently developed by Ben-Amotz-Stell (BAS) for the choice of the hard-sphere diameter, but with a new algorithm for calculation of the pair and many-body interactions. We have used Carnahan-Starling expression with the Boltzmann factor criterion (BFC) as an effective hard-sphere diameter for the reference system, and also decomposed the perturbed pair potential to symmetric and asymmetric terms. The former term is due to the many-body interactions at high densities as was used in the linear isotherm regularity... 

The effects of selected metal ions on the gas-phase acidity of weak organic acids have been explored using the DFT and Moller-Plesset Perturbation Theory (MP2) calculations. The three organic acids selected for this study were acetic acid (aliphatic), benzoic acid (aromatic), and glycine (amino acid). The acidities of these compounds are compared with the acidity of their Li +-, Na+-, and K+ -complexed species. The results indicate that upon complexation with Li+, Na+, and K+ at 298K, the gas-phase acidity of acetic acid, for example, varies from 345.3 to 218.8, 230.2, and 240.1 kcal/mol, respectively (i.e., its dissociation becomes much less endothermic). These values indicate that a weak... 

A computational method for simulation of 3-D movement of the trunk under the control of 48 anatomically oriented muscle actions was developed. Neural excitation of muscles was set based on inverse dynamics approach along with the stability-based optimization. The effect of muscle spindle reflex response on the trunk movement stability was evaluated upon the application of a perturbation moment. The method was used to simulate the trunk movement from the upright standing to 60° of flexion. Incorporation of the stability condition as an additional constraint in the optimization resulted in an increase in antagonistic activities demonstrating that the antagonistic co-activation acts to increase... 

In this paper, the general problem of impedance control for a robotic manipulator with a moving flexible base is addressed. Impedance control imposes a relation between force and displacement at the contact point with the environment. The concept of impedance control of flexible base mobile manipulator is rather new and is being considered for first time using singular perturbation and new sliding mode control methods by authors. Initially slow and fast dynamics of robot are decoupled using singular perturbation method. Slow dynamics represents the dynamics of the manipulator with rigid base. Fast dynamics is the equivalent effect of the flexibility in the base. Then, using sliding mode... 

We present N-body simulations of unstable spiral modes in a dynamically cool collisionless disc. We show that spiral modes grow in a thin collisionless disk in accordance with the analytical perturbation theory. We use the particle-mesh code SUPERBOX with nested grids to follow the evolution of unstable spirals that emerge from an unstable equilibrium state. We use a large number of particles (up to N = 40 & 106) and high-resolution spatial grids in our simulations (1283 cells). These allow us to trace the dynamics of the unstable spiral modes until their wave amplitudes are saturated due to nonlinear effects. In general, the results of our simulations are in agreement with the analytical... 

A two-dimensional depth-integrated numerical model is developed using a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundary and is applied for submarine-landslide-generated waves. The mathematical formulation of model is an extension of (4,4) Padé approximant for moving bottom boundary. The mathematical formulations are derived based on a higher-order perturbation analysis using the expanded form of velocity components. A sixth-order multi-step finite difference method is applied for spatial discretization and a sixth-order Runge-Kutta method is applied for temporal discretization of the higher-order depth-integrated governing equations and boundary... 

The dynamic response of the leg (tether) of a Tension Leg Platform (TLP), subjected to axial load at the top of the leg, is presented. The structural model is very simple, but several complicated factors, such as foundation effect, buoyancy and simulated ocean wave load, are considered. As an application, the effect of added mass fluctuation on the dynamic response of the leg subjected to such a load is presented. This effect is important in the fatigue life study of tethers. A first order perturbation method is used, in order to formulate and solve the problem. The differential equation is solved by means of non-harmonic Fourier expansion, in terms of eigenfunctions obtained from a... 

The absolute free energy of solvation of methane (CH4) and its fluorinated forms (CH3F, CH2F2, CHF3 and CF4) have been computed via statistical perturbation theory (SPT) in the NPT ensemble at four thermodynamical states (whitin liquid and supercritical regions), in the context of Monte Carlo Simulations. Thermodynamical interpretation of the observed trend in the absolute free energy of solvation in different states reveals an exothermic solvation with ΔSslv < 0 (entropically unfavorable solvation) that the intermolecular interactions play an important role in the solvation process. The fluorinated methanes are confirmed to control the mutual arrangement of neighboring CO2 molecules and the... 

Total motion in waves can be considered as a superposition of the motion of the body in still water and the forces on the restrained body. In this study the effect of added mass fluctuation on vertical vibration of tension leg platforms (TLP) in the case of vibration in still water for both free and forced vibration subjected to axial load at the top of the leg is presented. This effect is more important when the amplitude of vibration is large. Also this is important in fatigue life study of tethers. The structural model used here is very simple. Perturbation method is used to formulate and solve the problem. First- and second-order perturbations are used to solve the free and forced... 

In this paper, the large amplitude free vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton's principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second-order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the...