• Earthquakes and Structures
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• v.2 no.1
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• pp.89-107
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• 2011

In this paper a simple mathematical model is presented for estimating the natural frequencies and corresponding mode shapes of a tall building with outrigger-belt truss system. For this purposes an equivalent continuum system is analyzed in which a tall building structure is replaced by an idealized cantilever continuum beam representing the structural characteristics. The equivalent system is comprised of a cantilever shear beam in parallel to a cantilever flexural beam that is constrained by a rotational spring at outrigger-belt truss location. The mathematical modeling and the derivation of the equation of motion are given for the cantilevers with identically paralleled and rotational spring. The equation of motion and the associated boundary conditions are analytically obtained by using Hamilton's variational principle. After obtaining non-trivial solution of the eigensystem, the resulting is used to determine the natural frequencies and associated mode shapes of free vibration analysis. A numerical example for a 40 story tall building has been solved with proposed method and finite element method. The results of the proposed mathematical model have good adaptation with those obtained from finite element analysis. Proposed model is practically suitable for quick evaluations during the preliminary design stages.

• Journal of Radiation Industry
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• v.9 no.2
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• pp.57-62
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• 2015

In this study, we fabricated effect of storage conditions on graft of polypropylene (PP) non-woven fabric induced by electron beam. The electron beam irradiations on PP non-woven fabric were carried out over a range of irradiation doses from 25 to 100 kGy to make free radicals on fabric surface. The radical measurement was established by electron spin resonance (ESR) for confirming the changes of the alkyl radical and peroxy radical according to effect of storage time, storage temperature and atmosphere. It was observed that the free radicals were increased with irradiation dose and decreased with storage time due to the continuous oxidation. However, the radical extinction was significantly delayed due to reduced mobility of radicals at extremely low temperature. The degree of graft based on the analysis of ESR was investigated. The conditions of graft reaction were set at a temperature: $60^{\circ}C$, reaction time: 6 hours and styrene monomer concentration: 20 wt%.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.62-69
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• 1995

The differential equations governing both the free vibrations and buckling loads of the beam-columns with constant volumes are derived and solved numerically. The axial load effects are included in the differential equations. The Runge-Kutta method and Regula-Falsi method are used to compute the eigenvalues corresponding to the natural frequencies. and buckling loads. In numerical examples, the simple end constraint is considered.

• Ocean Systems Engineering
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• v.1 no.1
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• pp.59-72
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• 2011

The objective of this work is to investigate the possibility of using the longitudinal strain on the surface of a pipe to determine the inception of dangerous free spanning. The long term objective is to develop an online monitoring technique to detect the development of dangerous free spanning in subsea pipelines. This work involves experimental study as well as finite element modeling. In the experiments, the strains at four points on a cross section of a pipeline inside the free span zone are measured. Pipes with different boundary conditions and different diameter to length ratios were tested. The pipe is treated as a simple beam with fixed-fixed or simply supported boundary conditions. The variation of the strains as a function of the diameter to length ratio gives a pointer to the inception of dangerous free spanning. The finite element results agree qualitatively with the experiments. The quantitative discrepancy is a result of the difficulty to replicate the exact boundary conditions that is used by the finite element program.

• Smart Structures and Systems
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• v.19 no.3
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• pp.309-322
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• 2017

In this paper, the buckling, and free vibration analysis of tapered functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro Reddy beam under longitudinal magnetic field using finite element method (FEM) is investigated. It is noted that the material properties of matrix is considered as Poly methyl methacrylate (PMMA). Using Hamilton's principle, the governing equations of motion are derived by applying a modified strain gradient theory and the rule of mixture approach for micro-composite beam. Micro-composite beam are subjected to longitudinal magnetic field. Then, using the FEM, the critical buckling load, and natural frequency of micro-composite Reddy beam is solved. Also, the influences of various parameters including ${\alpha}$ and ${\beta}$ (the constant coefficients to control the thickness), three material length scale parameters, aspect ratio, different boundary conditions, and various distributions of CNT such as uniform distribution (UD), unsymmetrical functionally graded distribution of CNT (USFG) and symmetrically linear distribution of CNT (SFG) on the critical buckling load and non-dimensional natural frequency are obtained. It can be seen that the non-dimensional natural frequency and critical buckling load decreases with increasing of ${\beta}$ for UD, USFG and SFG micro-composite beam and vice versa for ${\alpha}$. Also, it is shown that at the specified value of ${\alpha}$ and ${\beta}$, the dimensionless natural frequency and critical buckling load for SGT beam is more than for the other state. Moreover, it can be observed from the results that employing magnetic field in longitudinal direction of the micro-composite beam increases the natural frequency and critical buckling load. On the other hands, by increasing the imposed magnetic field significantly increases the stability of the system that can behave as an actuator.

• Computational Structural Engineering
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• v.3 no.2
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• pp.67-75
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• 1990

A stepped beam with immovable ends under the free and forced vibrations with large amplitude is investigated by using the finite element method to show the effects of longitudinal displacement, shear deformation and rotary inertia. A modified harmonic force matrix is introduced for analysis of finite amplitude vibration of the stepped beam under uniform harmonic loading and a beam under nonuniform harmonic loading. Numerical examples are analysed for deflections and natural frequencies of stepped beam under various support conditions. Results show that the proposed method is valid and efficient.

• Wind and Structures
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• v.27 no.4
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• pp.247-254
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• 2018

In this paper, a simple first-order shear deformation theory is presented for dynamic behavior of functionally graded beams. Unlike the existing first-order shear deformation theory, the present one contains only three unknowns and has strong similarities with the classical beam theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported FG beam are obtained and the results are compared with Euler-Bernoulli beam and the other shear deformation beam theory results. Comparison studies show that this new first-order shear deformation theory can achieve the same accuracy of the existing first-order shear deformation theory.

• Journal of Power System Engineering
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• v.9 no.2
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• pp.65-72
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• 2005

A new approach is presented to design a robust sampled-data controller for an experimental flexible beam carrying an unknown payload at its free end. The purpose of this paper is to move the free end of the beam to a desired position in the specified time under vibration suppression. We derive a transfer function nominal model for the beam and quantitative description of model uncertainties based on experimentally obtained frequency response data. Robust controllers are designed by applying the sampled-data $H_{\infty}$ control and ${\mu}m-theory$, in which two types of uncertainties, structured and unstructured uncertainties, are adopted for satisfactory performance in terms of hinge position regulation and vibration damping, besides obviously asymptotic stability. The effectiveness of the proposed method is confirmed through simulation and experimentation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.396-400
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• 2006

We studied the influences of open cracks in free vibrating beam with rectangular section using a numerical model. The crack was assumed to be single and always open during the free vibration and equivalent bending stiffness of a cracked beam was calculated based on the strain energy balance. By Galerkin's method, the frequencies of cantilever beam could he obtained with respect to various crack depths and locations. Also, the experiments on the cracked beams were carried out to find natural frequencies. The cracks were initiated at five locations and the crack depths were increased by five steps at each location. The experimental results were compared with the numerical results and the comparison results were discussed.

• Steel and Composite Structures
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• v.9 no.5
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• pp.473-497
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• 2009

For the spatially coupled free vibration analysis of composite box beams resting on elastic foundation under the axial force, the exact solutions are presented by using the power series method based on the homogeneous form of simultaneous ordinary differential equations. The general vibrational theory for the composite box beam with arbitrary lamination is developed by introducing Vlasov°Øs assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Finally, the dynamic stiffness matrix is calculated using force-displacement relationships. In addition, the finite element model based on the classical Hermitian interpolation polynomial is presented. To show the performances of the proposed dynamic stiffness matrix of composite box beam, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the results from other researchers. Particularly, the effects of the fiber orientation, the axial force, the elastic foundation, and the boundary condition on the vibrational behavior of composite box beam are investigated parametrically. Also the emphasis is given in showing the phenomenon of vibration mode change.