• Structural Engineering and Mechanics
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• v.48 no.3
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• pp.415-434
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• 2013

This work is concerned with transverse vibrations of axially traveling nanobeams including strain gradient and thermal effects. The strain gradient elasticity theory and the temperature field are taken into consideration. A new higher-order differential equation of motion is derived from the variational principle and the corresponding higher-order non-classical boundary conditions including simple, clamped, cantilevered supports and their higher-order "offspring" are established. Effects of strain gradient nanoscale parameter, temperature change, shape parameter and axial traction on the natural frequencies are presented and discussed through some numerical examples. It is concluded that the factors mentioned above significantly influence the dynamic behaviors of an axially traveling nanobeam. In particular, the strain gradient effect tends to induce higher vibration frequencies as compared to an axially traveling macro beams based on the classical vibration theory without strain gradient effect.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.223-232
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• 2019

Since the actuators with small- scale structures may be exposed to external reciprocal actions lead to create undesirable loads causing instability, the buckling behaviors of them are interested to make reliable or accurate actions. Therefore, the purpose of this paper is to analyze plastic buckling behavior of the micro beam structures by adopting a Conventional Mechanism-based Strain Gradient plasticity (CMSG) theory. The effect of length scale on critical force is considered for three types of boundary conditions, i.e. the simply supported, cantilever and clamped - simply supported micro beams. For each case, the stability equations of the buckling are calculated to obtain related critical forces. The constitutive equation involves work hardening phenomenon through defining an index of multiple plastic hardening exponent. In addition, the Euler-Bernoulli hypothesis is used for kinematic of deflection. Corresponding to each length scale and index of the plastic work hardening, the critical forces are determined to compare them together.

• Journal of the Korea Concrete Institute
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• v.18 no.2 s.92
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• pp.283-290
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• 2006

The paper describes m experimental study on the shear strengthening of concrete beams with exposed wire rope. The strengthening method is using the mechanical bolting of wire rope tensioned on the exterior of beam section. There are two shear strengthening types. The first is closed type wrapped beam section with wire rope like as closed stirrup. The second is U type tensioned at the anchor located in the side of beam section. The main parameters of specimens are strengthening spacings of wire rope with 150, 200, and 250mm for the closed and U type respectively. The shear span ratio of specimens applied by 3-point loading is 4. The results showed that the ultimate shear strength and ductility of strengthened beams increased significantly compared with non-strengthened beams. Especially, the strengthening effect of closed type was very preferable to U type. Therefore, the shear strengthening method with wire rope is very reasonable in view of repair and rehabilitation of beams.

• Smart Structures and Systems
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• v.18 no.2
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• pp.355-374
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• 2016

This paper presents and compares a one-dimensional (1D) bending theory for piezoelectric thin beam-type structures with resistive-inductive electrodes to ANSYS$^{(R)}$ three-dimensional (3D) finite element (FE) analysis. In particular, the lateral deflections and vibrations of slender piezoelectric beams are considered. The peculiarity of the piezoelectric beam model is the modeling of electrodes in such a manner that is does not fulfill the equipotential area condition. The case of ideal, perfectly conductive electrodes is a special case of our 1D model. Two-coupled partial differential equations are obtained for the lateral deflection and for the voltage distribution along the electrodes: the first one is an extended Bernoulli-Euler beam equation (second-order in time, forth order in space) and the second one the so-called Telegrapher's equation (second-order in time and space). Analytical results of our theory are validated by 3D electromechanically coupled FE simulations with ANSYS$^{(R)}$. A clamped-hinged beam is considered with various types of electrodes for the piezoelectric layers, which can be either resistive and/or inductive. A natural frequency analysis as well as quasi-static and dynamic simulations are performed. A good agreement between the extended beam theory and the FE results is found. Finally, the practical relevance of this type of electrodes is shown. It is found that the damping capability of properly tuned resistive or resistive-inductive electrodes exceeds the damping performance of beams, where the electrodes are simply linked to an optimized impedance.

• Structural Engineering and Mechanics
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• v.14 no.5
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• pp.611-624
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• 2002

In this paper, a complete solution is presented for dynamic plastic response of a rigid, perfectly plastic hinged-free beam, of which one end is simply supported or hinged and the other end free, subjected to a transverse strike by a travelling mass at an arbitrary location along its span. The governing differential equations are expressed in non-dimensional forms and solved numerically to obtain the instantaneous deflection of the beam and the plastic dissipated energy in the beam. The dynamic behavior for a hinged-free beam is more complicated than that of a free-free beam. It transpires that the mass ratio and impact position have significant influence on the final deformation. In the aspect of energy dissipation, unlike simply supported or clamped beams for which the plastic deformation consumes almost the total input energy, a considerable portion of the input energy would be transferred as rigid-body motion of hinged-free beam, and the energy dissipated in its plastic deformation is greatly reduced.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.501-518
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• 2007

In this work, a new approach is developed for dynamic analysis of a composite beam with an interply crack, based on finite element solution of partial differential equations with the use of the COMSOL Multiphysics package, allowing for fast and simple change of geometric characteristics of the delaminated area. The use of COMSOL Multiphysics package facilitates automatic mesh generation, which is needed if the problem has to be solved many times with different crack lengths. In the model, a physically impossible interpenetration of the crack faces is prevented by imposing a special constraint, leading to taking account of a force of contact interaction of the crack faces and to nonlinearity of the formulated boundary value problem. The model is based on the first order shear deformation theory, i.e., the longitudinal displacement is assumed to vary linearly through the beam's thickness. The shear deformation and rotary inertia terms are included into the formulation, to achieve better accuracy. Nonlinear partial differential equations of motion with boundary conditions are developed and written in the format acceptable by the COMSOL Multiphysics package. An example problem of a clamped-free beam with a piezoelectric actuator is considered, and its finite element solution is obtained. A noticeable difference of forced vibrations of the delaminated and undelaminated beams due to the contact interaction of the crack's faces is predicted by the developed model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.256-263
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• 2008

The assumed modes method is developed to derive a set of linear differential equations describing the motion of a flexible wind turbine blade and to propose an approach to investigate the forced responses result from various wind excitations. In this work, we have adopted Euler beam theory and considered that the root of the blade is clamped at the rigid hub. And the aerodynamic parameters and forces are determined based on Blade Element Momentum (BEM) theory and quasi-steady airfoil aerodynamics. Numerical calculations show that this method gives good results and it can be used fur modeling and the forced vibration analysis including the coupling effect of wind-turbine blades, as well as turbo-machinery blades, aircraft propellers or helicopter rotor blades which may be considered as straight non-uniform beams with built-in pre-twist.

• Journal of Korean Society of Steel Construction
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• v.9 no.1 s.30
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• pp.65-79
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• 1997

Composite materials are consist of two or more different materials to produce desirable properties for structural strength. Because of their superiority in strength, corrosion resistance, and weight reduction, they are used extensively as structural members. The objective of this study is to present the effectivness of the laminated composite elements by analyzing in-plane displacement and stress of the anisotropic laminated annular elements. Anisotropic laminated structures are very difficult to analyze and apply, compared with isotropic and orthotropic cases for arbitrary boundaries and fiber angle -ply. Boundary conditions for the examples used in this study consist of two opposite edges clamped and the other two edges free, and finite difference method is used in this study for numerical analysis. From the numerical result, it is found that the program used in this study can be used to obtain the displacement of the straight beams considering it's transverse shear deformation as well as anisotropic laminated elements. Several numerical examples show the advantages of the stiffness increase when the angle-ply composite materials are used. Therefore it gives a guide in deciding how to make use of fiber's angle for the subtended angle, load cases, and boundary conditions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2812-2818
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• 1996

A cantilever beam with a mass and a spring at the end can be use to model a miniature flexible arm. It is necessary to know the natural frequencies and mode shapes to discuss its free vibration, especially when modal analysis is employed. A beam is clamped-free. In this paper we look at the lateral vibration of beams that have step changes in the properties of their cross sections. The frequency equation is derived by Bernoulli-Euler formulation and is sloved by the separation of variable. The parameters of the beam, 'mass and spring stiffness' are defined as nondimensionalized parameters for wide application of the results. According to the change of eigenvalues and mode shape are presented for this beam. The results presented are the eigenvalues and the natural frequencies for the first three modes of vibration. Results show that the parameters have a significant effect on the natural frequency.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1311-1320
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• 2000

In this study, shape memory alloy(SMA) wires and piezoceramic actuators(PZT's) are employed in order to generate higher modes on the beam deformations. Compressive force is generated and applied to the beam by the pre-strained SMA wires attached at both ends of the beam. PZT's apply concentrated moments to several locations on the beam. Combinations of the compressive force and concentrated moments are investigated in order to understand the higher-mode deformation of beams. The first desired mode shape is obtained by controlling the temperature of the SMA wires. The first and third mode shapes are performed experimentally by heating SMA wires up to phase transformation temperature. The adaptive wing is defined as a wing whose shape parameters such as the camber, wing twist and thickness can be varied in order to change the wing shape for various flight conditions. In this research, control of the camber has been studied. The wing model consists of three plates and many ribs. Two of the plates are placed parallel to each other and they are clamped at one edge. Third plate connects the other edges of the parallel plates together. Each rib is made of SMA wire and connected to the parallel plates. It generates concentrated force and applies to the plates in oblique directions. The PZT's are bonded onto the plates and exert concentrated moments upon the plate at several locations. The object of this research is to generate various shape of wing by combining the concentrated forces and moments.