• Architectural research
• /
• v.18 no.2
• /
• pp.65-74
• /
• 2016

Free vibration analysis of plates and shells is carried out by using isogeometric approach. For this purpose, an isogeometric shell element based on Reissner-Mindlin (RM) shell theory is developed. Non-uniform rational B-spline surface (NURBS) definition is introduced to represent the geometry of shell and it is also used to derive all terms required in the isogeometric element formulation. New anchor positions are proposed to calculate the shell normal vector. Gauss integration rule is used for the formation of stiffness and mass matrices. The proposed shell element is then used to examine vibrational behaviours of plate and shell structures. From numerical results, it is found to be that reliable natural frequencies and associated mode shapes can be predicted by the present isogeometric RM shell element.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2003.10a
• /
• pp.29-36
• /
• 2003

This paper deals with the free vibration analysis of horizontally circular mea beams with variable cross sectional width on elastic foundations. Taking into account the effects of rotatory inertia and shear deformation differential equations governing the free vibrations of such beams are derived, in which the Whlkler foundation model is considered as the elastic foundation. The variable width of beam is chosen as the linear equation. The differential equations are solved numerically to calculate natural frequencies. In numerical examples, the curved beam with the hinged-hinged, hinged-clamped, clamped-hinged and damped-clamped end constraints are considered The parametric studies are conducted and the lowest four frequency parameters are reported in figures as the non-dimensional forms.

• Advances in nano research
• /
• v.7 no.2
• /
• pp.99-108
• /
• 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.

• Steel and Composite Structures
• /
• v.46 no.5
• /
• pp.637-647
• /
• 2023

Nonlinear free vibration and stability responses of a carbon nanotube reinforced composite beam under temperature rising are investigated in this paper. The material of the beam is considered as a polymeric matrix by reinforced the single-walled carbon nanotubes according to different distributions with temperature-dependent physical properties. With using the Hamilton's principle, the governing nonlinear partial differential equation is derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The critical buckling temperatures, the nonlinear natural frequencies and the nonlinear free response of the system is obtained. The effect of different patterns of reinforcement on the critical buckling temperature, nonlinear natural frequency, nonlinear free response and phase plane trajectory of the carbon nanotube reinforced composite beam investigated with temperature-dependent physical property.

• Coupled systems mechanics
• /
• v.12 no.5
• /
• pp.461-479
• /
• 2023

The paper deals with the finite element modelling of the free vibration and structural behavior of a particular four-floor reinforced concrete structure subjected to static equivalent seismic loads and supported by a shallow foundation system called SNSF (Spider Net System Footing). The two FE models are a simple 2D Matlab model and a detailed 3D model based on solid elastic elements using Altairworks (Hypermesh and Optistruct). Both models can simulate the soil structure interaction. We concentrate on the behavior of a representative cell involving two columns on five levels. The influence of the boundary conditions on the external vertical planes of the domain are duly studied. The Matlab model appears relevant for a primary estimation of frequencies and stiffness of the whole structure under vertical and lateral loads.

• Advances in concrete construction
• /
• v.13 no.3
• /
• pp.255-264
• /
• 2022

Vibration is expected to occur in microtubules as tubular heterodimers. They oscillate like electric dipoles. Several research studies have estimated a frequency of vibration using the orthotropic model, a beam or rod like models and shell models, considering the surface forces. The effects of body forces on the dynamics of the microtubules were not yet taken into account. This study seeks to capture the body force effects on the vibration modes generated and on the corresponding frequency for microtubules. An orthotropic elastic shell model for the structural details of microtubules is used for the analysis. The tests are conducted out for microtubules, exposed to electro-magnetic and gravitational forces, the transverse vibration, radial mode vibration, and axial mode of vibration have accomplished. We therefore, evaluate and compare microtubules' frequencies with prior results of vibration frequency without the effects of body force.

• Steel and Composite Structures
• /
• v.24 no.1
• /
• pp.65-77
• /
• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2005.03a
• /
• pp.1148-1158
• /
• 2005

This work reports results of our study on the dynamic responses of the buried pipelines both along the axial and the transverse directions under various boundary end conditions. We have considered three cases, i.e., the free ends, the fixed ends, and the fixed-free ends. We have studied the seismic responses of the buried pipelines with the various boundary end conditions both along the axial and the transverse direction. We have considered three cases, i.e., the free ends, the fixed ends, and the fixed-free ends for the axial direction, and three more cases including the guided ends, the simply supported ends, and the supported-guided ends for the transverse direction. The buried pipelines are modeled as beams on elastic foundation while the seismic waves as a ground displacement in the form of a sinusoidal wave. The natural frequency and its mode, and the effect of parameters have been interpreted in terms of free vibration. The natural frequency varies most significantly by the soil stiffness and the length of the buried pipelines in the case of free vibration, which increases with increasing soil stiffness and decreases with increasing length of the buried pipeline. Such a behavior appears most prominently along the axial rather than the transverse direction of the buried pipelines. The resulting frequencies and the mode shapes obtained from the free vibration for the various boundary end conditions of the pipelines have been utilized to derive the mathematical formulae for the displacements and the strains along the axial direction, and the displacements and the bending strains along the transverse direction in case of the forced vibration. The negligibly small difference of 6.2% between our result and that of Ogawa et. al. (2001) for the axial strain with a one second period confirms the accuracy of our approach in this study.

• Steel and Composite Structures
• /
• v.35 no.5
• /
• pp.659-670
• /
• 2020

This paper proposes the use of a porous core between layers of laminated composite plates to examine its effect on the natural frequencies of the resulted porous laminated composite sandwich plate (PLCSP) resting on a two-parameter elastic foundation. Moreover, it has been suggested that the dispersion of porosity has two different functionally graded (FG) patterns which are compared with a uniformly dispersed (UD) profile to find their best vibrational efficiency in the proposed PLCSPs. In FG patterns, two types of dispersions, including symmetric (FG-S) and asymmetric (FG-A) patterns have been considered. To derive the governing Eigen value equation of such structures, the first order shear deformation theory (FSDT) of plates has been employed. Accordingly, a finite element method (FEM) is developed to solve the derived Eigen value equation. Using the mentioned theory and method, the effects of porosity parameters, fiber orientation of laminated composite, geometrical dimensions, boundary conditions and elastic foundation on the natural frequencies of the proposed PLCSPs have been studied. It is observed that embedding porosity in core layer leads to a significant improvement in the natural frequencies of PLCSPs. Moreover, the natural frequencies of PLCSPs with FG porous core are higher than those with UD porous core.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1998.04a
• /
• pp.381-385
• /
• 1998

Vibration-resistant rubbers, whose elastic and shear behaviors are similar to viscoelastic materials, are used to make brace-typed dampers to reduce the building vibration. Experimental study is carried out to find the vibration characteristics of the dampers installed in the building model. The natural frequencies and modal damping ratios are obtained from the free vibration test and Fourier analysis. Analytical model of the modal strain energy method are used to find the viscoelastic characteristics of the brace-typed dampers from the experimental results. Finally shaking table test is performed to find the response behavior of the building model under earthquake loading. The present experimental study shows that the brace-typed dampers have the behavior of viscoelastic dampers, which increase the modal damping ratios and viscoelastic characteristics.