• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.969-988
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• 2016

Vibration analysis of the beams on elastic foundation has gained the great interest of many researchers. In the literature, there are many studies that focus on the free vibration analysis of the beams on one or two parameter elastic foundations. On the other hand, there are no sufficient studies especially focus on the comparison of dynamic response including the bending moment and shear force of the beams resting on Winkler and two parameter foundations. In this study, dynamic response of the axially loaded Timoshenko beams resting on modified Vlasov type elastic soil was investigated by using the separation of variables method. Governing equations were obtained by assuming that the material had linear elastic behaviour and mass of the beam was distributed along its length. Numerical analysis were provided and presented in figures to find out the differences between the modified Vlasov model and conventional Winkler type foundation. Furthermore, the effect of shear deformation of elastic soil on the dynamic response of the beam was investigated.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.595-601
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• 2014

For analysis of the plates and membranes by numerical or analytical methods, the question of choice of the system of functions satisfying the different boundary conditions remains a major challenge to address. It is to this issue that is dedicated this work based on an approach of choice of combinations of trigonometric functions, which are shape functions of a bended beam with the boundary conditions corresponding to the plate support mode. To do this, the shape functions of beam vibrations for strength analysis of the rectangular plates by Kantorovich-Vlasov's method is considered. Using the properties of quasi-orthogonality of those functions allowed assessing to differential equation for every member of the series. Therefore it's proposed some new forms of integration of the beam functions, in order to simplify the problem.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.3
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• pp.306-320
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• 2010

Modern ultra-large container carriers can be exposed to the unprecedented springing excitation from ocean waves due to their relatively low torsional rigidity. Large deck opening on the deck of container carriers tends to cause warping distortion of hull structure under wave-induced excitation, eventually leading to the higher chance of resonance vibration between its torsional response and incoming waves. To handle this problem, a higher-order B-spline Rankine panel method and Vlasov-beam FE model was directly coupled in the time domain, and the coupled equation was solved by using an implicit iterative method. In order to capture the complicated behavior of thin-walled open section girder, a sophisticated beam-based finite element model was developed, which takes into account warping distortion and shear-on-wall effect. Then, the developed beam model was directly coupled with the time-domain Rankine panel method for hydrodynamic problem by using the fixed-point iteration method. The developed computational scheme was validated through the comparison with the frequency-domain solution on the container carrier model in linear springing regime.

• Steel and Composite Structures
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• v.36 no.6
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• pp.671-687
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• 2020

The aim of this research is to analyze buckling and bending behavior of a sandwich Reddy beam with porous core and composite face sheets reinforced by boron nitride nanotubes (BNNTs) and shape memory alloy (SMA) wires resting on Vlasov's foundation. To this end, first, displacement field's equations are written based on the higher-order shear deformation theory (HSDT). And also, to model the SMA wire properties, constitutive equation of Brinson is used. Then, by utilizing the principle of minimum potential energy, the governing equations are derived and also, Navier's analytical solution is applied to solve the governing equations of the sandwich beam. The effect of some important parameters such as SMA temperature, the volume fraction of SMA, the coefficient of porosity, different patterns of BNNTs and porous distributions on the behavior of buckling and bending of the sandwich beam are investigated. The obtained results show that when SMA wires are in martensite phase, the maximum deflection of the sandwich beam decreases and the critical buckling load increases significantly. Furthermore, the porosity coefficient plays an important role in the maximum deflection and the critical buckling load. It is concluded that increasing porosity coefficient, regardless of porous distribution, leads to an increase in the critical buckling load and a decrease in the maximum deflection of the sandwich beam.

• Advances in nano research
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• v.15 no.5
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• pp.423-439
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• 2023

The aim of this paper is to investigate the free vibration behavior of the micro sandwich beam composing of five layers such as functionally graded (FG) porous core, nanocomposite reinforced by carbon nanotubes (CNTs) and piezomagnetic/piezoelectric layers subjected to magneto electrical potential resting on silica aerogel foundation. The effect of foundation has been taken into account using Vlasov model in addition to rigid base assumption. For this purpose, an iterative technique is applied. The material properties of the FG porous core and FG nanocomposite layers are considered to vary throughout the thickness direction of the beams. Based on the Timoshenko beam theory and Hamilton's principle, the governing equations of motion for the micro sandwich beam are obtained. The Navier's type solution is utilized to obtain analytical solutions to simply supported micro sandwich beam. Results are verified with corresponding literatures. In the following, a study is carried out to find the effects of the porosity coefficient, porous distribution, volume fraction of CNT, the thickness of silica aerogel foundation, temperature and moisture, geometric parameters, electric and magnetic potentials on the vibration of the micro sandwich beam. The results are helpful for the design and applications of micro magneto electro mechanical systems.

• Journal of Korean Society of Steel Construction
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• v.18 no.3
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• pp.349-359
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• 2006

This paper presents a new block stiffness matrix for the analysis an orthogonal Cartesian coordinate system. The displacement fields are defined using the first order shear deformable beam theory. The longitudinal displacement can be expressed as the sum of the projected plane deformation of the cross-section due to Timoshenko's beam theory and axial warping deformation due to modified Vlasov's thin-waled beam theory. The derived element takes into account flexural shear deformation and torsional warping deformation. Three different types of beam elements, namely, the two-noded, three-noded, and four-noded beam elements, are developed. The quadratic and cubic elements are found to be very efficient for the flexural analysis of laminated composite beams. The versatility and accuracy of the new element are demonstrated by comparing the numerical results available in the literature.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.23-31
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• 2017

In the study, dynamic behavior of laminated orthotropic beams on elastic foundation is investigated. Consistent model presented here combines the finite element solution of the system with SAP2000 software and the calculation of soil parameters with MATLAB software using Modified Vlasov Model type elastic foundation. For this purpose, a computing tool is coded in MATLAB which employs Open Application Programming Interface (OAPI) feature of SAP2000 to provide two-way data flow during execution. Firstly, an example is taken from the literature to demonstrate the accuracy of the consistent FEM-Vlasov Model. Subsequently, the effects of boundary conditions, subsoil depth, elasticity modulus of subsoil, slenderness ratio, velocity of moving load and lamination scheme on the behavior of laminated orthotropic beams on elastic foundation are investigated on a new numerical example. It can be concluded that it is really convenient to use OAPI feature of SAP2000 to model this complex behavior of laminated orthotropic beams on elastic foundation under moving load.

• Steel and Composite Structures
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• v.3 no.1
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• pp.65-73
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• 2003

A higher level of engineering standard in the field of construction, is the use of prestressing in building structures. The concept of prestressing steel structures has only recently been widely considered, despite a long and successful history of prestressing concrete members. Several analytical studies of prestressed steel girders were reported in literatures, but much of the work was not studied with reference to the optimal design and behaviour of the prestressed steel plate girder. A plate girder prestressed eccentrically, will behave as a beam-column, which is subjected to axial compression and bending moment which will cause the beam to buckle out. The study of buckling of the prestressed steel plate girder is necessary for stability criteria. This paper deals with the stability of prestressed steel plate girder using concept of "Vlasov's Circle of Stability" under eccentric prestressing force.

• Structural Engineering and Mechanics
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• v.32 no.3
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• pp.447-457
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• 2009

A general analytical method for computing the joint stiffness from the sectional properties of the members that form the joint is derived using Vlasov's thin-walled beam theory. The analytical model of box T-joint under out-of-plane loading is investigated and validated using shell finite element results and experimental data. The analytical model of the T-joint is implemented in a beam finite element model using a revolute joint element. The out-of-plane displacement computed using the beam-joint model is compared with the corresponding shell element model. The results show close correlation between the beam revolute joint model and shell element model.

• Steel and Composite Structures
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• v.16 no.3
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• pp.233-252
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• 2014

In this paper a computer program is developed for the determination of geometrical and material properties of composite thin-walled beams with arbitrary open cross-section and any arbitrary laminate stacking sequence. Theory of thin-walled composite beams is based on assumptions consistent with the Vlasov's beam theory and classical lamination theory. The program is written in Fortran 77. Some numerical examples are given, with complete information about input and output.