Sharif Digital Repository

A time domain approach is used to study the cutting conditions in reaming process that leads the system to regenerative chatter vibrations. The dynamic analysis of the system includes inertia of the tool, centripetal and Coriolis terms, damping and the first mode bending of reamer. A model of cutting forces proportional to chip cross sectional area and process damping proportional to cutting speed is considered. Numerical simulation based on the Euler integration scheme is carried out to obtain time domain solution of the equation. Despite linearization in force modelling, the model is nonlinear due to the change in the tool engagement area. Another nonlinearity included in the model jumping... 

This paper investigates the effect of shaft rotation on its natural frequency. Apart from gyroscopic effect, the axial force originated from centrifugal force and the Poisson effect results in change of shaft natural frequency. D'Alembert principle for shaft in cylindrical co-ordinate system, along with the stress-strain relation, gives the non-homogenous linear differential equation, which can be used to calculate axial stress in the shaft. Numerical results of this study show that axial stress produced by shaft rotation has a major effect on the natural frequency of long high-speed shafts, while shaft diameter has no influence on the results. In addition, change in lateral natural... 

Dynamic and stability analysis of non-uniform Timoshenko beam under axial loads is carried out. In the first case of study, the axial force is assumed to be perpendicular to the shear force, while for the second case the axial force is tangent to the axis of the beam column. For each case, a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending was obtained. The parameters of the frequency equation were determined for various boundary conditions. Several illustrative examples of uniform and non-uniform beams with different boundary conditions such as clamped supported, elastically supported, and free end mass have been... 

In this study, an accurate analytical solution for the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities is derived. This solution has been obtained using homotopy analysis method (HAM). Then, homotopy Pade technique is applied to accelerate the convergence rate of the series solution. This study shows that the HAM leads to an accurate analytical solution, which is valid for a wide range of considered system parameters. Unlike the other analytical methods, HAM can control and adjust the convergence region and rate of the approximation series solution. The excellent accuracy of the current results is demonstrated by comparing with the... 

In this paper, free vibration analysis of cross-ply layered composite beams (LCB) with finite length and rectangular cross-section rested on an elastic foundation is investigated by finite element method. Based on the Timoshenko beam theory which includes the shear deformation and rotary inertia, the stiffness and mass matrices of a LCB are obtained using the energy method. Then, the natural frequencies are calculated by employing eigenvalue technique. The obtained results are verified against existing data in the literatures for a LCB with no foundation and uniform cross-section. Good agreements are observed between these cases. In the same way, the natural frequencies of a specific case,... 

We have proposed an efficient parametrization method for a recent variant of the Gay Berne potential for dissimilar and biaxial particles [Phys. Rev. E 67, 041710 (2003)] and demonstrated it for a set of small organic molecules. Compared with the previously proposed coarse-grained models, the new potential exhibits a superior performance in close contact and large distant interactions. The repercussions of thermal vibrations and elasticity have been studied through a statistical method. The study justifies that the potential of mean force is representable with the same functional form, extending the application of this coarse-grained description to a broader range of molecules. Moreover, the... 

In this paper, the large amplitude tree 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... 

Stability analysis of machine tool requires determining of frequency response function (FRF) of spindle. Since this response is changed with a change of tool, Receptance coupling sub-structuring analysis may be used to couple the tool and spindle FRFs. A major difficulty in this regard is the determination of joint model between the two sub-structures. In particular, the identification of rotational DOFs at joints is difficult. In this research, a joint model which accounts for rotational DOFs is proposed and verified which does not require any rotational DOF measurement on machine tool. An optimization method based on genetic algorithm is employed to find parameters of the joint model.... 

In this paper the effect of thrust on the bending behaviour of flexible missiles is investigated. For this purpose, the governing equations of motion of a flexible guided missile are derived following the Lagrangian approach. The missile is idealized as a non-uniform beam where the bending elastic deflections are modelled using the method of modal substitution. The vehicle (time varying) bending modeshapes and natural frequencies are determined by modelling variable mass and stiffness distributions with thrust and mass burning effects accounted for. To solve this problem the missile is divided into several segments of uniform stiffness, density and axial force distribution. This approach... 

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure... 

In this paper, the dynamic characteristics of skewed bridges are explored analytically. Closed form solutions for translational and torsional periods of free vibration and mode shapes are given for slab-girder skewed bridges. Moreover, the seismic displacement of the deck of skewed bridges is calculated using the response spectrum method and its skew term is compared with the requirement of AASHTO. The effects of seismic force resisting elements, such as elastomeric bearings and end diaphragms are included. It is shown that the skew term in AASHTO's equation can underestimate the seat width requirement for some bridges. A new skew term for the bridge seat width requirement is suggested  

Phase noise is one of the most important specifications of microwave oscillators. External factors such as mechanical vibrations increase the phase noise of the oscillator. A novel technique is introduced to reduce vibration-induced phase noise using inter-injection locking of two coupled oscillators. Two similar oscillators with equal free running frequencies are chosen and are subjected to sinusoidal vibration. The mechanical configuration is such that vibration sensitivity vector increases the frequency of one oscillator and decreases the other one's frequency of oscillation. Coupling these two oscillators using inter-injection locking, the common after-lock frequencies of both... 

In this paper, a tunable vibration absorber (TVA) is designed to suppress regenerative chatter in milling of cantilever plates. In machining industry, the majority of work-piece materials or the interaction of work-piece/cutting tool causes the cutting forces to demonstrate nonlinear behavior. The application of TVA (as a semi-active controller) is investigated for the process with an extensive nonlinear model of cutting forces. Under regenerative chatter conditions, optimum values of the absorber position and its spring stiffness are found such that the plate vibration is minimized. For this purpose, an optimal algorithm is developed based on mode summation approach. Results are presented... 

Modern Latticed composite materials whose high specific strength and stiffness are utilized in spacecraft and rocket structures to a sufficiently high extent are now widely used in primary airframe structures. In this work a comparison between squared latticed composite cylinder shells and the equivalent hollow cylinder with same weight, outer radius, length and material is done. An analytical equation is derived for natural frequency of square latticed composite shells. The first fifth modes are taken to be compared. The analytical and FEM results are shown and compared to each other. Also, as discussed, the squared lattice cylinder shell reaches to their natural frequencies easily than the... 

Nanocars are artificial molecular machines with chassis, axles, and wheels designed for nanoscale transport at materials' surfaces. Understanding the dependence of surface dynamics of nanocars on the substrate's physicochemical properties is critical to the design of the transport properties of such man-made nanoscale devices. Among the multitude of potential substrates for the nanotransporters, graphene exhibits intrinsic ripples on its surface, which may affect the surface dynamics of nanocars. In this work, we report our molecular dynamics study of motion of C60, a popular nanocar wheel, on the graphitic substrates with systematically controllable surface ripples. We find that surface... 

We introduce a new scheme for determining radiation pressure coupling to microresonator devices. It is shown that for the input pump powers there exists a threshold value for instability behavior. Radiation pressure can couple mechanical modes of a cavity to it's optical modes, leading to parametric oscillation instability. Here we present an approximate analysis of such nonlinear effect with Hamilton's least action principle. Our Lagrangian includes no interaction term, but interaction between optical and mechanical modes has been taken into account through integration limit. © 2008 Elsevier B.V. All rights reserved  

A general modeling framework is presented for the development of the frequency equation of a microgyroscope, which is modeled as a suspended cantilever beam with a tip mass under general base excitation. Specifically, the beam is considered to vibrate in all the three directions, while subjected to a base rotational motion around its longitudinal direction. This is a common configuration utilized in many vibrating beam gyroscopes and well drilling systems. The governing equations are derived by using the Extended Hamilton's Principle with a general 6-dof base motion. The natural frequency equation is then extracted in a closed-form for the case where the beam support undergoes longitudinal... 

Coordinate Measuring Machines (CMMs) are designed for precision inspection of complex industrial products. The mechanical accuracy of CMMs depends on both static and dynamic sources of error. In automated CMMs, one of the dynamic error sources is vibration of the probe, due to inertia forces resulting from parts acceleration and deceleration. Modeling of a gantry type CMM, based on the Timoshenko beam theory with moving mass effects, is developed and the dynamic errors of the probe resulting from the acceleration and deceleration of moving parts, are calculated. Findings from analytical solution and dynamic modeling software indicate high accuracy and good agreement between the results. ©... 

This paper presents a novel approach for the analysis of a fourth-order parabolic equation dealing with vibration of beams by using the decomposition method. In this regard, a general approach based on the generalized Fourier series expansion is applied. The obtained analytic solution is simplified in terms of a given set of orthogonal basis functions. The result is compared with the classical modal analysis technique which is widely used in the field of structural dynamics. It is shown that the result of the decomposition method leads to an exact closed-form solution which is equivalent to the result obtained by the modal analysis method. Some examples are given to demonstrate the validity... 

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...