Sharif Digital Repository

Using Hamilton's principle the coupled nonlinear partial differential motion equations of a flying 3D Euler-Bernoulli beam are derived. Stress is treated three dimensionally regardless of in-plane and out-of-plane warpings of cross-section. Tension, compression, twisting, and spatial deflections are nonlinearly coupled to each other. The flying support of the beam has three translational and three rotational degrees of freedom. The beam is made of a linearly elastic isotropic material and is dynamically modeled much more accurately than a nonlinear 3D Euler-Bernoulli beam. The accuracy is caused by two new elastic terms that are lost in the conventional nonlinear 3D Euler-Bernoulli beam... 

The purpose of this paper is to present efficient and accurate analytical expressions for deflection of a shape memory polymer (SMP) beam employing Euler-Bernoulli beam theory in a thermomechanical SMP cycle. Material behavior is considered using a recently 3D thermodynamically consistent constitutive model available in literature. In different steps of an SMP thermomechanical cycle, closed form expressions for internal variables variations, stresses and beam curvature distribution are presented. We show that during the cooling process, stored strains evolve to fix the temporary shape and then during the heating process they relax to recover the permanent shape. Effects of applying external... 

In this paper, static behavior and pull-in of micro tweezers is studied. The micro tweezer is modelled as two cantilever beams. Static behavior of the micro tweezer under the effect of electrostatic actuation is modelled using the Euler-Bernoulli beam theory. In order to capture size effects on the behavior of micro tweezers, modified couple stress theory is utilized. It is shown when the voltage between two electrodes increased from some specific value, micro beams adhere to each other and it is observed that the pull-in voltage predicted by the modified couple stress theory considerably differs with that of the classical theory of elasticity. Results of this paper can be used for accurate... 

Shape memory polymers (SMPs) are a class of smart materials which can recover their shape even after many shape changes in application of an external stimulus. In this paper, flexural behavior of a composite beam, constructed of a corrugated part filled with SMPs, is studied. This composite beam is applicable in sensor and actuator applications. Since the corrugated profiles display higher stiffness-to-mass ratio in the transverse to the corrugation direction, the beams with a corrugated part along the transverse direction are stiffer than ones with a corrugated part along the length. Employing a developed constitutive model for SMPs and the Euler–Bernoulli beam theory, the behavior of the... 

This paper presents vibration and buckling analysis of functionally graded beams with different boundary conditions, using reproducing kernel particle method (RKPM). Vibration of simple Euler-Bernoulli beam using RKPM is already developed and reported in the literature. Modeling of FGM beams using theoretical method or finite element technique is not evolved with accurate results for power law form of FGM with large power of "n" value so far. Accuracy of the RKPM results is very good and is not sensitive to n value. System of equations of motion is derived using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of the beam are taken into account using... 

This paper investigates the dynamic behavior of microcantilevers under suddenly applied DC voltage based on the modified couple stress theory. The cantilever is modeled based on the Euler-Bernoulli beam theory and equation of motion is derived using Hamilton's principle. Both analytical and numerical methods are utilized to predict the dynamic behavior of the microbeam. Multiple scales method is used for analytical analysis and the numerical approach is based on a hybrid finite element/finite difference method. The results of the modified couple stress theory are compared with those from the literature as well as the results predicted by the classical theory. It is shown that the modified... 

This paper investigates the deflection and static pull-in of microbridges based on the modified couple stress theory, a non-classic continuum theory able to predict the size effects for structures in micron and sub-micron scales. The beam is modeled using EulerBernoulli beam theory and the nonlinearities caused by mid-plane stretching have been considered. It is shown that modified couple stress theory predicts size dependent normalized deflection and pull-in voltage for microbeams while according to classical theory the normalized behavior of microbeams is independent of the size of the beam. According to results, when the thickness of the beam is in order of length scale of the beam... 

This paper presents free vibration analysis of functionally graded material (FGM) beams with different boundary conditions, using RKPM (Reproducing Kernel Particle Method), which is a meshless method. System of equations of motion is derived by using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of beam are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is applied to obtain eigenvalue equation of vibration and natural frequencies are obtained. It should be noted that for special cases where the beam is uniform,... 

In this paper, simple analytical expressions are presented for geometrically non-linear vibration analysis of thin nanobeams with both simply supported and clamped boundary conditions. Gurtin-Murdoch surface elasticity together with Euler-Bernoulli beam theory is used to obtain the governing equations of motions of the nanobeam with surface effects consideration. The governing nonlinear partial differential equation is reduced to a single nonlinear ordinary differential equation using Galerkin technique. He's variational approach is employed to obtain analytical solution for the resulted nonlinear governing equation. The effects of different parameters such as vibration amplitude, boundary... 

This paper undertakes to facilitate appraisal of aeroelastic interaction of a locally distributed, flap-type control surface with aircraft wings operating in a subsonic potential flow field. The extended Hamilton's principle serves as a framework to ascertain the Euler-Lagrange equations for coupled bending-torsional-flap vibration. An analytical solution to this boundary-value problem is then accomplished by assumed modes and the extended Galerkin's method. The developed aeroelastic model considers both the inherent flexibility of the control surface displaced on the wing and the inertial coupling between these two flexible bodies. The structural deformations also obey the Euler-Bernoulli... 

Motivated by specific applications, electrostatically actuated bistable arch shaped micro-nano resonators have attracted growing attention in the research community in recent years. Nevertheless, some issues relating to their nonlinear dynamics, including the possibility of chaos, are still not well known. In this paper, we investigate the chaotic vibrations of a bistable resonator comprised of a double clamped initially curved microbeam under combined harmonic AC and static DC distributed electrostatic actuation. A reduced order equation obtained by the application of the Galerkin method to the nonlinear partial differential equation of motion, given in the framework of Euler-Bernoulli beam... 

In this paper, two lowest resonant frequencies and sensitivities of an AFM V-Shaped microcantilever made of functionally graded materials are studied. The beam is modeled by Euler-Bernoulli beam theory in which rotary inertia and shear deformation is neglected. It is assumed that the beam is made of a mixture of metal and ceramic with properties varying through the thickness of the beam. This variation is function of volume fraction of beam material constituents. The interaction between AFM tip and surface is modeled by two linear springs which expresses the normal and lateral contact stiffness. A relationship is developed to evaluate the sensitivity of FGM micro cantilever beam. Effect of... 

The motion of a stick-slip microrobot propelled by its piezoelectric unimorph legs is mathematically modeled. Using a continuously distributed mass model for the robot's body, the working equation of the mechanism is derived based on the assumption of linear Euler-Bernoulli beam theory and linear piezoelectric behavior. Moreover, the required condition for generating net motion is calculated in terms of physical characteristics of the microrobot. It is demonstrated that the higher the friction constant, then a lower average speed is obtained. Also, it is shown that a microrobot with heavier legs can move in a rougher environment. Regardless of the mass proportion between robot's main body... 

The dynamics of the flexible robot arm subjected to tip mass during an actual deployment is studied. The Euler-Bernoulli beam theory and the real deployment are considered in the simulation. A new real axial velocity profile is developed. This new suggested profile simulates the actual deployment such that the arm movement starts from immovability and after attaining the final required length comes back again to the static state. Using Lagrange's equation, the equations of motion of the system are derived to study the system dynamics in this suggested deployment profile. A series approximation is used to represent the lateral elastic displacements. Using variables separation and also some... 

The purpose of this paper is the enhancement of the AFM sensitivity through the selection of an optimized FGM micro cantilever beam. In this paper, resonant frequencies and sensitivities of first two modes of micro cantilever which is made of functionally graded materials are investigated and a relationship is developed to evaluate the sensitivity of FGM micro cantilever. Effect of volume fraction of materials and surface contact stiffness on the resonant frequencies and sensitivities are studied. The rectangular FGM beam is modeled by an Euler-Bernoulli beam theory. It is assumed that beam is made of a mixture of metal and ceramic with properties varying through the thickness following a... 

In this paper, the static stability of the variable cross section columns, subjected to distributed axial force, is considered. The presented solution is based on the singular perturbation method of Wentzel-Kramers-Brillouin and the column is modeled using Euler-Bernoulli beam theory. Closed-form solutions are obtained for calculation of buckling loads and the corresponding mode shapes. The obtained results are compared with the results in the literature to verify the present approach. Using numerous examples, it is shown that the represented solution has a very good convergence and accuracy for determination of the instability condition  

The purpose of this paper is the enhancement of the AFM sensitivity through the selection of an optimized FGM micro cantilever beam. In this paper, resonant frequencies and sensitivities of first two modes of micro cantilever which is made of functionally graded materials are investigated and a relationship is developed to evaluate the sensitivity of FGM micro cantilever. Effect of volume fraction of materials and surface contact stiffness on the resonant frequencies and sensitivities are studied. The rectangular FGM beam is modeled by an Euler-Bernoulli beam theory. It is assumed that beam is made of a mixture of metal and ceramic with properties varying through the thickness following a... 

In the present study, dynamic stability of a viscoelastic cantilevered pipe conveying fluid which fluctuates harmonically about a mean flow velocity is considered; while the fluid flow is exhausted through an inclined end nozzle. The Euler-Bernoulli beam theory is used to model the pipe and fluid flow effects are modelled as a distributed load along the pipe which contains the inertia, Coriolis, centrifugal and induced pulsating fluid flow forces. Moreover, the end nozzle is modelled as a follower force which couples bending vibrations with torsional ones. The extended Hamilton's principle and the Galerkin method are used to derive the bending-torsional equations of motion. The coupled... 

Using some agent variables, the general structure of the dynamic model of a spatial mobile robot with N long spatially flexible links and N revolute joints has been exposed. It is composed of a set of 5N + 6 nonlinear coupled partial differential motion equations under the influence of the boundary conditions. Non-conservative forces/moments have been neglected. While being considered, the general structure of the dynamic model will not change, but a few exciting/damping terms will arise within the agent variables. The base of the robot is an unconstrained rigid body in space and the links as 3D Euler-Bernoulli beams undergo tension-compression, torsion and two spatial bendings while elastic... 

In this paper, the stability of pipes conveying fluid with viscoelastic fractional foundation is investigated. The pipe is fixed at the beginning while the pipe end is constrained with two lateral and rotational springs. The fluid flow effect is modeled as a lateral distributed force, containing the fluid inertia, Coriolis and centrifugal forces. The pipe is modeled using the Euler-Bernoulli beam theory and a fractional Kelvin-Voigt model is employed to describe the viscoelastic foundation. The equation of motion is derived using the extended Hamilton's principle. Presenting the derived equation in Laplace domain and applying the Galerkin method, a set of algebraic equations is extracted....