• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.83-95
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• 2020

In this work, a mathematical model of beam-column system carrying a double eccentric end mass system is investigated, and solved analytically based on the exact solution analysis. The model considers the case in which the double eccentric end mass is a rigid storage tank containing fluid. Both Timoshenko and Bernoulli-Euler beam bending theories are considered. Equation of motion, general solution and boundary conditions for the present system model are developed and presented in dimensional and non-dimensional format. Several important non-dimensional design parameters are introduced. Symbolic and/or explicit formulae of the frequency and mode shape equations are formulated. To the authors knowledge, the present reduced closed form symbolic and explicit frequency equations have not appeared in literature. For different applications, the results are validated using commercial finite element package, namely ANSYS. The beam-column system investigated in this paper is significant for many engineering applications, especially, in mechanical and structural systems.

• Advances in nano research
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• v.7 no.2
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• pp.99-108
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• 2019

Higher-order theories are very important to investigate the mechanical properties and behaviors of nanoscale structures. In this study, a free vibration behavior of SiNW resting on elastic foundation is investigated via Eringen's nonlocal elasticity theory. Silicon Nanowire (SiNW) is modeled as simply supported both ends and clamped-free Euler-Bernoulli beam. Pasternak two-parameter elastic foundation model is used as foundation. Finite element formulation is obtained nonlocal Euler-Bernoulli beam theory. First, shape function of the Euler-Bernoulli beam is gained and then Galerkin weighted residual method is applied to the governing equations to obtain the stiffness and mass matrices including the foundation parameters and small scale parameter. Frequency values of SiNW is examined according to foundation and small scale parameters and the results are given by tables and graphs. The effects of small scale parameter, boundary conditions, foundation parameters on frequencies are investigated.

• Steel and Composite Structures
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• v.50 no.4
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• pp.459-474
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• 2024

Classical and first-order nonlocal beam theory are employed in this study to assess the thermal buckling performance of a small-scale conical, cylindrical beam. The beam is constructed from functionally graded (FG) porosity-dependent material and operates under the thermal conditions of the environment. Imperfections within the non-uniform beam vary along both the radius and length direction, with continuous changes in thickness throughout its length. The resulting structure is functionally graded in both radial and axial directions, forming a bi-directional configuration. Utilizing the energy method, governing equations are derived to analyze the thermal stability and buckling characteristics of a nanobeam across different beam theories. Subsequently, the extracted partial differential equations (PDE) are numerically solved using the generalized differential quadratic method (GDQM), providing a comprehensive exploration of the thermal behavior of the system. The detailed discussion of the produced results is based on various applied effective parameters, with a focus on the potential application of nanotubes in enhancing sports bikes performance.

• Journal of Mechanical Science and Technology
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• v.19 no.2
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• pp.589-604
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• 2005

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analysis. For this, the displacement field is expressed by introducing displacement parameters defined at the centroid and shear center axes, respectively. Next the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are rigorously derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to the solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.1033-1039
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• 2006

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analyses. For this, the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to tl1e solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.4
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• pp.335-341
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• 2017

In this paper, beam finite elements with higher-order derivatives' continuity are formulated and evaluated for various boundary conditions. All the beam elements are based on Euler-Bernoulli beam theory. These higher-order beam elements are often required to analyze structures by using newly developed higher-order beam theories and/or non-classical beam theories based on nonlocal elasticity. It is however rare to assess the performance of such elements in terms of boundary and loading conditions. To this end, two higher-order beam elements are formulated, in which $C^2$ and $C^3$ continuities of the deflection are enforced, respectively. Three different boundary conditions are then applied to solve beam structures, such as cantilever, simply-support and clamped-hinge conditions. In addition to conventional Euler-Bernoulli beam boundary conditions, the effect of higher-order boundary conditions is investigated. Depending on the boundary conditions, the oscillatory behavior of deflections is observed. Especially the geometric boundary conditions are problematic, which trigger unstable solutions when higher-order deflections are prescribed. It is expected that the results obtained herein serve as a guideline for higher-order derivatives' continuous finite elements.

• Advances in nano research
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• v.2 no.4
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• pp.199-210
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• 2014

Carbon nanotubes have exceptional mechanical, thermal and electrical properties, and are considered for high performance structural and multifunctional composites. In the present study, the natural frequencies of aligned single walled carbon nanotube (CNT) reinforced composite beams are obtained using shear deformable composite beam theories. The Ritz method with algebraic polynomial displacement functions is used to solve the free vibration problem of composite beams. The Mori-Tanaka method is applied to find the composite beam mechanical properties. The continuity conditions are satisfied among the layers by modifying the displacement field. Results are found for different CNT diameters, length to thickness ratio of the composite beam and different boundary conditions. It is found that the use of smaller CNT diameter in the reinforcement element gives higher fundamental frequency for the composite beam.

• Structural Engineering and Mechanics
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• v.62 no.5
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• pp.577-585
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• 2017

To study the mechanical performances of prestressed steel-concrete composite box beam under combination of bending-shear-torsion, nine composite beams with different ratio of torsion to bending were designed. Torsion was applied to the free end of the beam with jacks controlled accurately with peripherals, as well as concentrated force on the mid-span with jacks. Based on experimental data and relative theories, mechanical properties of composite beams were analyzed, including torsional angle, deformation and failure patterns. The results showed that under certain ratio of torsion to bending, cracking and ultimate torsion increased and reached to its maximum at the ratio of 2. Three phases of process is also discussed, as well as the conditions of each failure mode.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.1
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• pp.82-88
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• 2002

This paper deals with the free vibrations of horizontally curved beams with transition curve. Based on the dynamic equilibrium equations of a curved beam element subjected to the stress resultants and inertia forces, the governing differential equations are derived for the out-of-plane vibration of curved beam wish variable curvature. This equations are applied to the beam having transition curve in which the third parabolic curve is chosen in this study. The differential equations are solved by the numerical procedures for calculating the natural frequencies. As the numerical results, the various parametric studies effecting on natural frequencies are investigated and its results are presented in tables and figures. Also the laboratory scaled experiments were conducted for verifying the theories developed herein.

• Structural Engineering and Mechanics
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• v.32 no.6
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• pp.811-833
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• 2009

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.