• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.609-617
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• 2002

A three-dimensional(3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular rings with isosceles trapezoidal and triangular cross-sections. Displacement components u/sub s/, u/sub z/, and u/sub θin the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the ψ and z directions. Potential(strain) and kinetic energies of the circular ring are formulated, and upper bound values of the frequencies we obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Novel numerical results are presented for the circular rings with isosceles trapezoidal and equilateral triangular cross-sections having completely free boundaries. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rings. The method is applicable to thin rings, as well as thick and very thick ones.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.399-407
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• 2002

A three-dimensional method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components$U_\Phi, U_z, U_\theta$ in the meridional, normal and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in$\theta$, and algebraic polynomials in the$\Phi$and z directions. Potential(strain) and kinetic energies of the entire body are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degrees of the polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations. Convergence to four digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.

• Smart Structures and Systems
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• v.15 no.3
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• pp.683-698
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• 2015

Railroad bridges form an integral part of railway infrastructure throughout the world. To accommodate increased axel loads, train speeds, and greater volumes of freight traffic, in the presence of changing structural conditions, the load carrying capacity and serviceability of existing bridges must be assessed. One way is through system identification of in-service railroad bridges. To dates, numerous researchers have reported system identification studies with a large portion of their applications being highway bridges. Moreover, most of those models are calibrated at global level, while only a few studies applications have used globally and locally calibrated model. To reach the global and local calibration, both ambient vibration tests and controlled tests need to be performed. Thus, an approach for system identification of a railroad bridge that can be used to assess the bridge in global and local sense is needed. This study presents system identification of a railroad bridge using free vibration data. Wireless smart sensors are employed and provided a portable way to collect data that is then used to determine bridge frequencies and mode shapes. Subsequently, a calibrated finite element model of the bridge provides global and local information of the bridge. The ability of the model to simulate local responses is validated by comparing predicted and measured strain in one of the diagonal members of the truss. This research demonstrates the potential of using measured field data to perform model calibration in a simple and practical manner that will lead to better understanding the state of railroad bridges.

• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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• pp.113-128
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• 2004

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.197-206
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• 2003

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid and hollow hemispherical shells of revolution of arbitrary wall thickness having arbitrary constraints on their boundaries. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components μ/sub Φ/, μ/sub z/, and μ/sub θ/ in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the Φ and z directions. Potential (strain) and kinetic energies of the hemispherical shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Novel numerical results are presented for solid and hollow hemispheres with linear thickness variation. The effect on frequencies of a small axial conical hole is also discussed. Comparisons are made for the frequencies of completely free, thick hemispherical shells with uniform thickness from the present 3-D Ritz solutions and other 3-D finite element ones.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.3
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• pp.251-260
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• 2003

A three dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of deep, tapered rods and beams with circular cross section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sup r/, u/sub θ/ and u/sub z/, in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in , and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler-Bernoulli beam theory.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.2
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• pp.119-129
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• 2004

A three dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike conventional plate theories, which are mathematically two dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u/sub s/, u/sub z/, and u/sub θ/ in the radial, thickness, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the s and z directions. Potential (strain) and kinetic energies of the plates are formulated, and the Ritz method is used to solve the eigenvalue problem thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the plates. Numerical results we presented for completely free, annular and circular plates with uniform linear, and quadratic variations in thickness. Comparisons are also made between results obtained from the present 3D and previously published thin plate (2D) data.