Sharif Digital Repository

An innovative 1D finite element (FE) approach is developed to analyze the 3D static, transient, and dynamic problems in the coupled and uncoupled thermoelasticity for the nonhomogeneous anisotropic materials. The Galerkin method is directly applied to the governing equations to obtain a weak formulation of the thermoelasticity problems with arbitrary loads and boundary conditions. To surmount the restrictions of the classical beam theories, a 1D FE procedure is proposed in the context of the Carrera Unified Formulation (CUF). Since coupled thermoelastic analyses are computationally demanding, the proposed 1D FE approach can be used as a powerful means to simulate the generalized coupled... 

In this paper, based on the modified couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The findings are compared with classical beam... 

Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the non-uniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution... 

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... 

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,... 

Dynamic stability of machine tools during operations is dependent on many parameters including the spindle speed. In high and ultra high speed machining, the gyroscopic on the spindle dynamics becomes more pronounced and can affect the borders of stability of the rotating system. In this paper, a finite element based model of spindle, tool holder and cutting tool based on Timoshenko beam theory is used to obtain the dynamic response of the system when gyroscopic terms are included. An iterative scheme is used to update the speed dependent frequency response of the system for obtaining system stability characteristics. It is shown that the gyroscopic effect reduces the critical depth of cut... 

This paper presents a numerical parametric study on design parameters of multispan viscoelastic shear deformable beams subjected to a moving mass via generalized moving least squares method (GMLSM). For utilizing Lagrange's equations, the unknown parameters of the problem are stated in terms of GMLSM shape functions and the generalized Newmark-β scheme is applied for solving the discrete equations of motion in time domain. The effects of moving mass weight and velocity, material relaxation rate, slenderness, and span number of the beam on the design parameters and possibility of mass separation from the base beam are scrutinized in some detail. The results reveal that for low values of beam... 

Micro actuators are irreplaceable part of motion control in minimized systems. The current study presents an analytical model for a new Hybrid Thermo Piezoelectric micro actuator based on the combination of piezoelectric and thermal actuation mechanisms. The micro actuator structure is a double PZT cantilever beam consisting of two arms with different lengths. The presented micro actuator uses the structure of electrothermal micro actuator in which polysilicon material is replaced by PZT. Also the voltage and poling directions are considered in the lengthwise of PZT beams. As a result, the piezoelectric actuation mechanism is based on d33 strain coefficient. The tip deflection of micro... 

In this investigation, the stability analysis of a rotating elastic stepped shaft is studied and the sufficient condition for system stability in the sense of Lyapunov is derived. The model consists of an elastic stepped shaft which is clamped rigidly to a rotary device. From the model's point of view, the entire length of shaft is partitioned into uniform segments with different characteristics. The Lyapunov direct method is applied in this survey where the Hamilton function has been chosen as the candidate Lyapunov function. Since the dynamical mode shapes of the shaft are required for the stability analysis, the shaft has been modeled by the Euler- Bernoulli beam theory and the... 

This paper presents the linear dynamic response of uniform beams with different boundary conditions excited by a moving load, based on the Elder-Bernouli beam theory. Using a dynamic green function, effects of different boundary conditions, velocity of load and other parameters are. assessed and some of the numerical results are compared with those given in the. references. © Sharif University of Technology, June 2009  

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... 

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. ©... 

The vibration of a simply supported beam with rotary springs at either ends is studied. The governing equations of motion are investigated considering the nonlinear effect of stretching. These equations are made non-dimensional and then solved to first order approximation using the two methods of the multiple scales and the mode summation. The first five natural frequencies of the beam for few pairs of the boundary condition parameters are evaluated. A multilayer feed-forward back-propagation artificial neural network is trained using these natural frequencies. The artificial neural network used in this study shows high degree of accuracy for the natural frequency of the beam with general... 

Energy methods such as Energy Flow and Statistical Energy Analyses have been popularly used to predict the medium to high frequency vibro-acoustic response of several structures. In these energy methods, usually the common simple structural theories are used for simplicity. Since, the effects of shear deformation and rotary inertia at high frequency regions are unavoidable, it is necessary to determine the validity of these theories in each frequency domain. This paper aims to propose a method for defining a criteria to select a proper structural theory based on the order of shear deformation and rotary inertia to be used in vibration analyses. Several common as well as higher-order beam... 

There are two different ways of using shape memory alloy (SMA) wire as an actuator for shape control of flexible structures: it can be either embedded within the composite laminate or externally attached to the structure. As the actuator can be placed at different offset distances from the beam, external actuators produce more bending moment and, consequently, considerabnle shape changes with the same magnitude of actuation force compared with the embedded type. Such a configuration also provides faster heat transfer rate owing to convection, which is very important in shape control applications that require a highfrequency response of SMA actuators. Although combination and physics-based... 

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, 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... 

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... 

In this paper, the modified couple stress theory is employed to develop a size-dependent beam element able to predict the size-dependency observed in microbeams. The stiffness matrix is obtained for the aforementioned beam element. As an example, the deflection of a microcantilever is evaluated using the proposed beam elements and the results of the finite element method are compared to the analytical results obtained by the classical beam theory. The maximum deflection of the beam is depicted versus the ratio of the beam thickness to the material length scale parameter, the parameter appearing in non-classical continuum theories. The results show that when the characteristic size of the...