• Advances in nano research
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• 제7권2호
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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.

• 한국농공학회:학술대회논문집
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• 한국농공학회 1999년도 Proceedings of the 1999 Annual Conference The Korean Society of Agricutural Engineers
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• pp.206-211
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• 1999

The purpose of this study is to investigate the natural frequencies and mode shapes of beam-columns on the non-homogeneous foundaion. The beam model is based on the classical Bernoulli-Euler beam theory. The linear foundation modulus is chosen as the non-homogeneous foundation in this study . The differentidal equation goeverning free vibrations of such beam-columns subjected to axial load is derived and solved numerically for calculting the natural frquencies and mode shapes. In numerical fivekinds of end constraint are considered, and the lowest four natural frquencies and corresponding mode shape are obtained as the non-dimensional forms.

• Structural Engineering and Mechanics
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• 제40권2호
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• pp.279-295
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• 2011

A solution of space curved bars with generalized Winkler soil found by means of Transfer Matrix Method is presented. Distributed, concentrated loads and imposed strains are applied to the beam as well as rigid or elastic boundaries are considered at the ends. The proposed approach gives the analytical and numerical exact solution for circular beams and rings, loaded in the plane or perpendicular to it. A well-approximated solution can be found for general space curved bars with complex geometry. Elastic foundation is characterized by six parameters of stiffness in different directions: three for rectilinear springs and three for rotational springs. The beam has axial, shear, bending and torsional stiffness. Numerical examples are given in order to solve practical cases of straight and curved foundations. The presented method can be applied to a wide range of problems, including the study of tanks, shells and complex foundation systems. The particular case of box girder distortion can also be studied through the beam on elastic foundation (BEF) analogy.

• Computers and Concrete
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• 제27권2호
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• pp.85-97
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• 2021

In this study, the effect of steel fiber utilization, boundary conditions, different beam cross-section, and length parameter are investigated on the free vibration behavior of fiber reinforced self-compacting concrete beam on elastic foundation. In the analysis of the beam model recommended by Euler-Bernoulli, a method utilizing Stokes transformations and Fourier Sine series were used. For this purpose, in addition to the control beam containing no fiber, three SCC beam elements were prepared by utilization of steel fiber as 0.6% by volume. The time-dependent fresh properties and some mechanical properties of self-compacting concrete mixtures were investigated. In the modelled beam, four different beam specimens produced with 0.6% by volume of steel fiber reinforced and pure (containing no fiber) SCC were analyzed depending on different boundary conditions, different beam cross-sections, and lengths. For this aim, the effect of elasticity of the foundation, cross-sectional dimensions, beam length, boundary conditions, and steel fiber on natural frequency and frequency parameters were investigated. As a result, it was observed that there is a noticeable effect of fiber reinforcement on the dynamic behavior of the modelled beam.

• Structural Engineering and Mechanics
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• 제30권1호
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• pp.21-36
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• 2008

The static response of a finite beam resting on a tensionless Pasternak foundation and subjected to a concentrated vertical load is assessed in this study. The concentrated vertical load may be applied at the center of the beam, or it may be offset from the center. The tensionless character of the foundation results in the creation of lift-off regions between the beam and the foundation. An analytical/ numerical solution is obtained from the governing equations of the contact and lift-off regions to determine the extent of the contact region. Although there is no nonlinear term in the equations, the problem shows a nonlinear character since the contact region is not known in advance. Due to that nonlinearity, the essentials of the problem (the coordinates of the lift-off points) are calculated numerically using the Newton-Raphson technique. The numerical results are presented in figures to illustrate the behaviours of the free-free and pinned-pinned beams under symmetric or asymmetric loading. The figures illustrate the effects of the shear foundation parameter and the symmetric and asymmetric loading options on the variation of the contact lengths and the displacement of the beam.

• 한국정밀공학회지
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• 제21권11호
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• pp.179-185
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• 2004

The effect of viscous damping on stability of beam resting on an elastic foundation subjected to a dry friction force is analytically studied. The beam resting on an elastic foundation subjected to dry friction force is modeled for simplicity into a beam resting on Kelvin-Voigt type foundation subjected to distributed follower load. In particular, the effects of four boundary conditions (clamped-free, clamped-pinned, pinned-pinned, clamped-clamped) on the system stability are considered. The critical value and instability type of columns on the elastic foundation subjected to a distributed follower load is investigated by means of finite element method for four boundary conditions. The elastic foundation modulus, viscous damping coefficient and boundary conditions affect greatly both the instability type and critical load. Also, the increase of damping coefficient raises the critical flutter load (stabilizing effect) but reduces the critical divergence load (destabilizing effect).

• Advances in aircraft and spacecraft science
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• 제5권6호
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• Advances in nano research
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• 제15권5호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.1060-1065
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• 2002

In this paper, the numerical analysis of beam rest ing on hyperbolic Winkler elastic foundation by differential transformation is performed. Accordig to the change of parameter of hyperbolic Winkler elastic foundation, beam deformation is computed when the boundary conditions are clamped-clamped, pined-pined and clamped-free.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문초록집
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• pp.402.2-402
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• 2002

In this paper, the numerical analysis of beam resting on hyperbolic Winkler elastic foundation by differential transformation is performed. Accordig to the change of parameter of hyperbolic Winkler elastic foundation, beam deformation is computed when the boundary conditions are clamped-clamped, pined-pined and clamped-free.