• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.673-691
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• 1998

In this paper, an analytic method to examine the random vibration of multispan Timoshenko frames due to a concentrated load traversing at a constant velocity is presented. A load's magnitude is a stationary process in time with a constant mean value and a variance. Two types of variances of this load are considered: white noise process and cosine process. The effects of both velocity and statistical characteristics of load and span number of the frame on both the mean value and variance of deflection and moment of the structure are investigated. Results obtained from a multispan Timoshenko frame are compared with those of a multispan Bernoulli-Euler frame.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.12
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• pp.1547-1557
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• 2013

A forced vibration model of a rail system was established using the Timoshenko beam theory to determine the dynamic response of a rail under time-varying load considering the damping effect and stiffness of the elastic foundation. By using a Fourier series and a numerical method, the critical velocity and dynamic response of the rail were obtained. The forced vibration model was verified by using FEM and Euler beam theory. The permanent deformation of the rail was predicted based on the forced vibration model. The permanent deformation and wear were observed through the experiment. Parametric studies were then conducted to investigate the effect of five design factors, i.e., rail cross-section shape, rail material density, rail material stiffness, containment stiffness, and damping coefficient between rail and containment, on four performance indices of the rail, i.e., critical velocity, maximum deflection, maximum longitudinal stress, and maximum shear stress.

• Steel and Composite Structures
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• v.43 no.2
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• pp.185-200
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• 2022

A Closed-form solution for dynamic response of a functionally graded (FG) nonlocal nanobeam due to action of moving harmonic load is presented in this paper. Due to analyzing in small scale, a nonlocal elasticity theory is utilized. The governing equation and boundary conditions are derived based on the Euler-Bernoulli beam theory and Hamilton's principle. The material properties vary through the thickness direction. The harmonic moving load is modeled by Delta function and the FG nanobeam is simply supported. Using the Laplace transform the dynamic response is obtained. The effect of important parameters such as excitation frequency, the velocity of the moving load, the power index law of FG material and the nonlocal parameter is analyzed. To validate, the results were compared with previous literature, which showed an excellent agreement.

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Smart Structures and Systems
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• v.7 no.5
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• pp.417-432
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• 2011

The present paper is devoted to vibration canceling and shape control of piezoelastic slender beams. Taking into account the presence of electric networks, an extended electromechanically coupled Bernoulli-Euler beam theory for passive piezoelectric composite structures is shortly introduced in the first part of our contribution. The second part of the paper deals with the concept of passive shape control of beams using shaped piezoelectric layers and tuned inductive networks. It is shown that an impedance matching and a shaping condition must be fulfilled in order to perfectly cancel vibrations due to an arbitrary harmonic load for a specific frequency. As a main result of the present paper, the correctness of the theory of passive shape control is demonstrated for a harmonically excited piezoelelastic cantilever by a finite element calculation based on one-dimensional Bernoulli-Euler beam elements, as well as by the commercial finite element code of ANSYS using three-dimensional solid elements. Finally, an outlook for the practical importance of the passive shape control concept is given: It is shown that harmonic vibrations of a beam with properly shaped layers according to the presented passive shape control theory, which are attached to an resistor-inductive circuit (RL-circuit), can be significantly reduced over a large frequency range compared to a beam with uniformly distributed piezoelectric layers.

• Journal of Ocean Engineering and Technology
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• v.34 no.6
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• pp.419-427
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• 2020

In this study, a particle image velocimetry (PIV)-based pressure estimation method was investigated, with application to the wave-in-deck loading phenomenon. An experimental study was performed in a two-dimensional wave tank using a fixed deck structure under a focused wave, obtaining local pressures by pressure sensors, global loads by load cells, and instantaneous velocity fields using the PIV measurement technique. The PIV-based pressure estimation method was applied using the Euler equation as the governing equation, and the proper time step for the wave impact pressure was studied using the normalized root-mean-square deviation. The pressure estimation method showed good agreement for the local impact pressure in comparison with the measured pressure by the pressure sensors. However, some differences were observed in the peak pressure due to the limitations of the Euler equation and the sampling rate of the measurement system. Using the estimation method, the pressure fields during wave-in-deck loading were determined in the study, with an analysis of the mechanism of impact and negative pressure occurrence.

• Advances in nano research
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• v.12 no.2
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• pp.139-150
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• 2022

This paper presents sets of explicit analytical equations that compute the static displacements of nanobeams by adopting the nonlocal elasticity theory of Eringen within the framework of Euler Bernoulli and Timoshenko beam theories. Castigliano's theorem is applied to an equivalent Virtual Local Beam (VLB) made up of linear elastic material to compute the displacements. The first derivative of the complementary energy of the VLB with respect to a virtual point load provides displacements. The displacements of the VLB are assumed equal to those of the nonlocal beam if nonlocal effects are superposed as additional stress resultants on the VLB. The illustrative equations of displacements are relevant to a few types of loadings combined with a few common boundary conditions. Several equations of displacements, thus derived, matched precisely in similar cases with the equations obtained by other analytical methods found in the literature. Furthermore, magnitudes of maximum displacements are also in excellent agreement with those computed by other numerical methods. These validated the superposition of nonlocal effects on the VLB and the accuracy of the derived equations.

• Journal of Korean Society of Steel Construction
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• v.19 no.1
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• pp.129-137
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• 2007

In this study, the elastic out-of-plane buckling load and the effective length factor of X-bracing systems were studied. Points of the intersection of diagonals were modeled as a rigid connection or a pinned connection depending on the connection method of diagonals. The boundary condition of the intersection influences the buckling load of X-bracing systems. For each boundary condition of the intersection, effective out-of-plane length factors of X-bracing systems were derived as a function of the length ratio of tension and compression diagonals $L_P$/$L_T$, the applied force ratio of tension and compression diagonals T/P, and the Euler buckling load ratio of tension and compression diagonals $P_{ET}$/$P_{EP}$. The proposed effective out-of-plane length factors of X-bracing systems were compared with the results of previous researchers and those of the finite element analysis and their properties were verified. Finally, the effects of the boundary condition of the intersection on the out-of-plane buckling load of X-bracing systems were investigated.

• Smart Structures and Systems
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• v.22 no.6
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• pp.689-697
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• 2018

This paper presents a model of the elastic curve for rectangular beams with straight haunches under uniformly distributed load and moments in the ends considering the bending and shear deformations (Timoshenko Theory) to obtain the deflections and rotations on the beam, which is the main part of this research. The traditional model of the elastic curve for rectangular beams under uniformly distributed load considers only the bending deformations (Euler-Bernoulli Theory). Also, a comparison is made between the proposed and traditional model of simply supported beams with respect to the rotations in two supports and the maximum deflection of the beam. Also, another comparison is made for beams fixed at both ends with respect to the moments and reactions in the support A, and the maximum deflection of the beam. Results show that the proposed model is greater for simply supported beams in the maximum deflection and the traditional model is greater for beams fixed at both ends in the maximum deflection. Then, the proposed model is more appropriate and safe with respect the traditional model for structural analysis, because the shear forces and bending moments are present in any type of structure and the bending and shear deformations appear.

• Journal of Advanced Marine Engineering and Technology
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• v.14 no.4
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• pp.46-56
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• 1990

Stress analysis of axi-symetric body with non-symetric loading and non-symetric given displacements is investigated in this paper using the finite element method. As the non-symetric load and non-symetric given displacements of axi-symetric body are generally periodic functions of angle .theta., the nodal forces and nodal displacements can be expanded in cosine and sine series, that is, Fourier series. Furthermore, using Euler's formula, the cosine and sine series can be converted into exponential series and it is prooved that the related calculus become more clear. Substituting the nodal displacements expanded in Fourier series into the strain components of cylindrical coordinates system, the element strains are expressed in series form and by the principal of virtual work, the element stiffness martix and element load vector are obtained for each order. It is also showed that if the non-symetric loads are even or odd functions of angle ${\theta}$ the stiffness matrix and load vector of the system are composed with only real numbers and relatively small capacity fo computer memory is enough for calculation.