• Steel and Composite Structures
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• v.29 no.5
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• pp.579-590
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• 2018

Size-dependent free vibration responses and magneto-electro-elastic bending results of a three layers piezomagnetic curved beam rest on Pasternak's foundation are presented in this paper. The governing equations of motion are derived based on first-order shear deformation theory and nonlocal piezo-elasticity theory. The curved beam is containing a nanocore and two piezomagnetic face-sheets. The piezomagnetic layers are imposed to applied electric and magnetic potentials and transverse uniform loadings. The analytical results are presented for simply-supported curved beam to study influence of some parameters on vibration and bending results. The important parameters are spring and shear parameters of foundation, applied electric and magnetic potentials, nonlocal parameter and radius of curvature of curved beam. It is concluded that the increase in radius of curvature tends to an increase in the stiffness of curved beam and consequently natural frequencies increase and bending results decrease. In addition, it is concluded that with increase of nonlocal parameter of curved beam, the stiffness of structure is decreased that leads to decrease of natural frequency and increase of bending results.

• Structural Engineering and Mechanics
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• v.86 no.6
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• pp.751-764
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• 2023

In practical engineering such as aerial refueling pipes, the boundary of the fluid-conveying pipe is difficult to be completely immovable. Pipes under movable and immovable boundaries are controlled by different dominant nonlinear factors, where the boundary mobility will affect the nonlinear dynamic characteristics, which should be focused on for adopting different strategies for vibration suppression and control. The nonlinear dynamic instability characteristics of functionally graded fluid-conveying pipes lying on a viscoelastic foundation under movable and immovable boundary conditions are systematically studied for the first time. Nonlinear factors involving nonlinear inertia and nonlinear curvature for pipes with a movable boundary as well as tensile hardening and nonlinear curvature for pipes with an immovable boundary are comprehensively considered during the derivation of the governing equations of the principal parametric resonance. The stability boundary and amplitude-frequency bifurcation diagrams are obtained by employing the two-step perturbation- incremental harmonic balance method (TSP-IHBM). Results show that the movability of the boundary of the pipe has a great influence on the vibration amplitude, bifurcation topology, and the physical meanings of the stability boundary due to different dominant nonlinear factors. This research has guidance significance for nonlinear dynamic design of fluid-conveying pipe with avoiding in the instability regions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.1014-1019
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• 2003

A dynamic modeling method for beams undergoing overall rigid body motion is presented in this paper. Two special deformation variables are introduced to represent the stretching and the curvature and are approximated by the assumed mode method. Geometric constraint equations that relate the two special deformation variables and the cartesian deformation variables are incorporated into the modeling method. By using the special deformation variables, all natural as well as geometric boundary conditions can be satisfied. It is shown that the geometric nonlinear effects of stretching and curvature play important roles to accurately predict the dynamic response when overall rigid body motion is involved.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.157-166
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• 2006

In order to model blending surfaces with curvature continuity, in this paper we apply sixth order partial differential equations (PDEs), which are solved with a composite power series based method. The proposed composite power series based approach meets boundary conditions exactly, minimises the errors of the PDEs, and creates almost as accurate blending surfaces as those from the closed form solution that is the most accurate but achievable only for some simple blending problems. Since only a few unknown constants are involved, the proposed method is comparable with the closed form solution in terms of computational efficiency. Moreover, it can be used to construct 3- or 4-sided patches through the satisfaction of continuities along all edges of the patches. Therefore, the developed method is simpler and more efficient than numerical methods, more powerful than the analytical methods, and can be implemented into an effective tool for the generation and manipulation of complex free-form surfaces.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2002.09a
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• pp.322-329
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• 2002

The purpose of this study is to develop a reasonable design for transverse confinement reinforcement considering ductility and required transverse confinement reinforcement of RC bridge columns. In order to develop relationships between the curvature ductility and the displacement ductility, the analysis for total 21,600 columns using the computer program NARCC have been carried out for parametric studies. Based on the results from the parametric studies, a correlation equation between the curvature ductility and the displacement ductility was developed. In addition, an equation for calculating the required transverse confinement reinforcement based on ductility demand was developed for seismic design of RC bridge columns. The equations proposed by this study will provide more reasonable and more effective design guidelines for performance-based seismic design of RC bridge columns.

• Journal of Mechanical Science and Technology
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• v.20 no.3
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• pp.345-357
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• 2006

By employing the concept of equivalent linkage, this paper presents an analytical method for analyzing the mechanical errors of disk cam mechanisms with a flat-faced follower. The resulting error equations do not really involve the location of the curvature center of the cam profile, and locating the curvature center of the cam profile is not essential. The resulting errors are significantly affected by the pressure angle, and the smaller pressure angle will result in the smaller mechanical error. In the worst case, owing to the joined effects of various design parameters, the accuracy of the follower motion may degrade considerably. For the oscillating follower case, all acceleration error functions have a sudden change at every beginning and at every end of the motion even though the theoretical follower displacement is cycloidal motion.

• Structural Engineering and Mechanics
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• v.39 no.2
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• pp.169-186
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• 2011

This paper is devoted to the development of the equations which describe the elastic response of a curved laminate subjected to in-plane loads and bending moments. Similar to the classic $6{\times}6$ ABD matrix constitutive relation of a flat laminate, a new $6{\times}6$ matrix constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved laminate is formulated. This curved lamination theory will provide the fundamental basis for the analyses of curved laminated structures. The stress predictions by the present curved lamination theory are compared to those by the curved laminate analysis that neglected the nonlinear terms in the derivation of the constitutive relation. The results show that the curved laminate analysis that neglected the nonlinear terms cannot reflect the effect of curvature and can no longer predict the stresses accurately as the curvature becomes noticeable. In this paper, a curved lamination theory that retains the nonlinear terms and, therefore, accounts for the effect of the non-flat geometry of the structure will be developed.

• Structural Engineering and Mechanics
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• v.36 no.6
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• pp.679-695
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• 2010

In-plane vibrations of slightly curved beams having cracks are investigated numerically and experimentally. The curvature of the beam is circular and stays in the plane of vibration. Specimens made of steel with different lengths but with the same radius of curvature are used in the experiments. Cracks are opened using a hand saw having 0.4 mm thickness. Natural frequencies depending on location and depth of the cracks are determined using a Bruel & Kjaer 4366 type accelerometer. Then the beam is assumed as a Rayleigh type slightly curved beam in finite element method (FEM) including bending, extension and rotary inertia. A flexural rigidity equation given in literature for straight beams having a crack is used in the analysis. Frequencies are obtained numerically for different crack locations and depths. Experimental results are presented and compared with the numerical solutions. The natural frequencies are affected too much due to larger moments when the crack is around nodes. The effect can be neglected when it is at the location of maximum displacements. When the crack is close to the clamped end, the decrease in the frequencies in all modes is very high. The consistency of the results and validity of the equations are discussed.

• Advances in nano research
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• v.5 no.2
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• pp.179-192
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• 2017

The transverse vibration of double walled carbon nanotube (DWCNT) embedded in elastic medium with an initial imperfection is considered. In this paper, Timoshenko beam theory is employed. However the nonlocal theory is used for modeling the nano scale of nanotube. In addition, the governing Equations of motion are obtained utilizing the Hamilton's principle and simply-simply boundary conditions are assumed. Furthermore, the Navier method is used for determining the natural frequencies of DWCNT. Hence, some parameters such as nonlocality, curvature amplitude, Winkler and Pasternak elastic foundations and length of the curved DWCNT are analyzed and discussed. The results show that, the curvature amplitude causes to increase natural frequency. However, nonlocal coefficient and elastic foundations have important role in vibration behavior of DWCNT with imperfection.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1099-1120
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• 2015

External prestressing has been applied to both new construction and retrofitting of existing reinforced and prestressed concrete structures. Continuous beams are preferred to simply supported beams because of economy, fewer movement joints and possible benefits from moment redistribution. However, this paper argues that continuous prestressed concrete beams with external unbonded tendons demonstrate different full-range behaviour compared to reinforced concrete (RC) beams. Applying the same design approach for RC to external prestressing may lead to design with a lower safety margin. To better understand the behaviour of continuous prestressed concrete beams with unbonded tendons, an experimental investigation is performed in which nine such specimens are tested to failure. The full-range behaviour is investigated with reference to moment-curvature relationship and moment redistribution. The amounts of moment redistribution measured in the experiments are compared with those allowed by BS 8110, EC2 and ACI 318. Design equations are also proposed to estimate the curvature ductility index of unbonded prestressed concrete beams.