• Journal of Korean Tunnelling and Underground Space Association
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• v.6 no.4
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• pp.279-290
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• 2004

The differential quadrature method (DQM) for a system of coupled differential equations governing the elastic stability of thin-walled curved members is presented, and is applied to computation of the eigenvalues of out-of-plane buckling of curved beams subjected to uniformly distributed radial loads including a warping contribution. Critical loads with warping, which were found to be significant, are calculated for a single-span wide-flange beam with various end conditions, opening angles, and stiffness parameters. The results are compared with the exact methods available. New results are given for the case of both ends clamped and clamped-simply supported ends without comparison since no data are available The differential quadrature method gives good accuracy and stability compared with previous theoretical results.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.442-448
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• 2008

This paper presents an approach to define an optimal piezoactuator length to actively control structural vibration. The optimal ratio of the piezoactuator length against beam length when a pair of piezoceramic actuator and accelerometer is used to suppress unwanted vibration with direct velocity feedback (DVFB) control strategy is not clearly defined so far. It is well known that direct velocity feedback (DVFB) control can be very useful when a pair of sensor and actuator is collocated on structures with a high gain and excellent stability. It is considered that three different collocated pairs of piezoelectric actuators (20, 50 and 100 mm) and accelerometers installed on three identical clamped-clamped beams (300 * 20 * 1 mm). The response of each sensor-actuator pair requires strictly positive real (SPR) property to apply a high feedback gain. However the length of the piezoactuator affects SPR property of the sensor-actuator response. Intensive simulation and experiment shows the effect of the actuator length variation is strongly related with the frequency range of SPR property. A shorter actuator gave a wider SPR frequency range as a longer one had a narrower range. The shorter actuator showed limited control performance in spite of a higher gain was applied because the actuation force was relatively small. Thus an optimal length ratio (actuator length/beam length) was suggested to obtain relevant performance with good stability with DVFB strategy. The result of this investigation could give important information in the design of active control system to suppress unwanted vibration of smart structures with piezoelectric actuators and accelerometers.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.3
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• pp.37-46
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• 1991

A method is developed for solving the natural frequencies and mode shapes of linearly variable tapered beams. The governing differential equation for the tapered beam is derived. Three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and the determinant search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, damped-clamped and free-damped end constraints are investigated in numerical examples. The lowest four nondimensional natural frequencies are obtained as functions of $d_b/d_a$. ratio. The effects of end constraints and cross sectional shapes on frequencies are analyzed and typical mode shapes are also presented.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.371-379
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• 2001

This paper deals with the free vibrations of horizontally curved members resting on elastic foundations with continuity effect. Taking into account the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which the Pasternak foundation model is considered as the elastic foundation with continuity effect. The differential equations are solved numerically to calculate natural frequencies and mode shapes. The experiments were performed in which the natural frequencies of such curved beams in laboratorial scale were measured and these results agree quite well with the present numerical studies. In numerical examples, the circular, parabolic, sinusoidal and elliptic curved members with the hinged-hinged, hinged-clamped and clamped end constraints are considered. The parametric studies are conducted and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Advances in Computational Design
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• v.5 no.4
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• Smart Structures and Systems
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• v.15 no.5
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• pp.1233-1252
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• 2015

This study investigates the problem of crack detection in post-buckled beam-type structures. The beam under the axial compressive force has a crack, assumed to be open and through the width. The crack, which is modeled by a massless rotational spring, divides the beam into two segments. The crack detection is considered as an optimization problem, and the weighted sum of the squared errors between the measured and computed natural frequencies is minimized by the bees algorithm. To find the natural frequencies, the governing nonlinear equations of motion for the post-buckled state are first derived. The solution of the nonlinear differential equations of the two segments consists of static and dynamic parts. The differential quadrature method along with an arc length strategy is used to solve the static part, while the same method is utilized for the solution of the linearized dynamic part and the extraction of the natural frequencies of the cracked beam. The investigation includes several numerical as well as experimental case studies on the post-buckled simply supported and clamped-clamped beams having open cracks. The results show that several parameters such as the amount of applied compressive force and boundary conditions influences the outcome of the crack detection scheme. The identification results also show that the crack position and depth can be predicted well by the presented method.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1767-1772
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• 2008

A microcantilever is a well-known MEMS structure for sensing bio-chemical molecules. When bio-chemical molecules are adsorbed on the microcantilever's surface, resonance frequency shift is generated. There are two issues in this phenomena. The first one is which one between mass change and surface stress change effects is more dominant on the resonance frequency shift. The second one is what will be the performance change when the boundary condition is changed from cantilevers to double clamped beams. We have studied the effect of surface stress change and compared it with that of mass change by using FEM analysis. Furthermore, for microstructures having different boundary conditions, we have studied Q-factor, which determines the detection limit of micro/nano mechanical sensors.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.53-67
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• 1996

The dynamic characteristics of mechanical structure are strongly affected by the properties of joint parameters. In this study, the test structures are constructed with two beams which are clamped by bolts, and a bolted joint which is modelled as a lumped stiffness element. To idientify the dynamic joint parameters with variance of clamping torque of bolts, the sensitivity analysis and the mode energy analysis methods are investigated experimentally. As a reult of these two methods, stiffnesses of bolted joint are experimentally found to increase as the clamping torque increases. These stiffnesses identified from the sensitivity analysis and the mode energy analysis method have some difference.

• Smart Structures and Systems
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• v.26 no.3
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• pp.311-318
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• 2020

The goal of this study is to analytically and non-stochastically generate structural uncertainty behaviors of isotropic beams and laminated composite plates under plane stress conditions by using an interval finite element method. Uncertainty parameters of structural properties considering resistance and load effect are formulated by interval arithmetic and then linked to the finite element method. Under plane stress state, the isotropic cantilever beam is modeled and the laminated composite plate is cross-ply lay-up [0/90]. Triangular shape with a clamped-free boundary condition is given as geometry. Through uncertainties of both Young's modulus for resistance and applied forces for load effect, the change of structural maximum deflection and maximum von-Mises stress are analyzed. Numerical applications verify the effective generation of structural behavior uncertainties through the non-stochastic approach using interval arithmetic and immediately the feasibility of the present method.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.785-799
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hyperboloidal shells free at the top edge and clamped at the bottom edge like a hyperboloidal cooling tower by the Ritz method based upon the circular cylindrical coordinate system instead of related 3-D shell coordinates which are normal and tangent to the shell midsurface. The Legendre polynomials are used as admissible displacements. Convergence to four-digit exactitude is demonstrated. Natural frequencies from the present 3-D analysis are also compared with those of straight beams with circular cross section, complete (not truncated) conical shells, and circular cylindrical shells as special cases of hyperboloidal shells from the classical beam theory, 2-D thin shell theory, and other 3-D methods.