Vibration Analysis of a Circular Tunnel With Jointed Liners Embedded in an Elastic Medium Subjected to Seismic Waves

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Dong-Sheng Jeng ◽  
Jian-Fei Lu
Keyword(s):  
Elastic Medium ◽  
Seismic Waves ◽  
Differential Quadrature Method ◽  
Surrounding Medium ◽  
Beam Theory ◽  
Scattered Wave ◽  
Collocation Methods ◽  
Curved Beam ◽  
Curved Beams ◽  
Circular Tunnel

This paper presents a frequency domain analysis of a circular tunnel with piecewise liners subjected to seismic waves. In our model, the surrounding medium of the tunnel is considered as a linear elastic medium and described by the dynamic elasticity theory, while piecewise liners and connecting joints are treated as curved beams and described by a curved beam theory. Scattered wave field in the surrounding elastic medium are obtained by the wave function expansion approach. The governing equations for vibrations of a curved beam are discretized by the general differential quadrature method. We use domain decomposition methods to establish the global discrete dynamic equations for piecewise liners. Boundary least squares collocation methods, based on the continuity conditions of stresses and displacements between surrounding soil and the piecewise liners, are used to determine the response of the liners and the surrounding medium. Numerical results conclude that the presence of the joints significantly changes the distributions of the tunnel internal force, and dramatically increase shear forces and moment of the tunnel liners around joints.

An efficient GDQ model for vibration analysis of a multiwall carbon nanotube on Pasternak foundation with general boundary conditions

2011 ◽  
Vol 225 (7) ◽  
pp. 1730-1741 ◽  
Author(s):  
P Soltani ◽  
P Bahar ◽  
A Farshidianfar
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Elastic Medium ◽  
Differential Quadrature Method ◽  
Elastic Beam ◽  
Beam Theory ◽  
Multiwall Carbon Nanotube ◽  
Various Boundary Conditions ◽  
Aspect Ratios ◽  
Multiwall Carbon

In this article, the free transverse vibrational behaviour of a multiwall carbon nanotube (MWNT) surrounded by a Pasternak-type elastic medium has been determined using a very generalized model. The model has been made on the basis of Timoshenko elastic beam theory which allows the effects of shear deformation and rotary inertia and supports non-coaxial vibration of the adjacent layers of MWNT using interlayer van der Waals forces. The boundary conditions used in this simulation are such that not only standard and conventional kinds, but also all possible forms, of end conditions are applicable. A generalized differential quadrature method is utilized to solve the governing equations with assorted aspect ratios, various boundary conditions, and different foundation stiffnesses. This study shows that the resonant frequencies of MWNTs are strongly dependent on the stiffness of the elastic medium, aspect ratios, and number of walls in carbon nanotubes and, for short nanotubes, the boundary stiffness plays a significant role on the natural frequencies.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the analysis.

In Plane Radial Vibration of Uncracked and Cracked Circular Curved Beams Subjected to Moving Loads

2021 ◽  
pp. 2150146
Author(s):  
Jatin Poojary ◽  
Sankar Kumar Roy
Keyword(s):  
Dynamic Response ◽  
Moving Load ◽  
Real Life ◽  
Beam Theory ◽  
Point Of View ◽  
Curved Beam ◽  
Moving Loads ◽  
Curved Beams ◽  
Beam Elements ◽  
Curved Beam Element

The dynamic response of structures subjected to moving load is a subject of great importance from a practical point of view. In this work, the in-plane dynamic response of a cracked isotropic circular curved beam subjected to moving loads is investigated using the finite element method. The curved beam is modeled using curved beam elements, which is developed based on the Timoshenko beam theory. Furthermore, a cracked curved beam element is developed to incorporate the presence of cracks in the structure. The effect of moving load speed, depth, and the location of the crack on the dynamic response of the beam is investigated. The outcome of the work can be useful in the study of real-life moving load problems like bridges and railways and also in the field of condition monitoring using moving loads.

Consistent Treatment of Extensional Deformations for the Bending of Arches, Curved Beams and Rings

1977 ◽  
Vol 99 (1) ◽  
pp. 2-11 ◽  
Author(s):  
O. A. Fettahlioglu ◽  
J. Mayers
Keyword(s):  
Beam Theory ◽  
Dynamical Problem ◽  
Curved Beam ◽  
Curved Beams ◽  
Governing Equations ◽  
Closed Form Solutions ◽  
Circular Rings ◽  
Consistent Treatment ◽  
Discontinuity Conditions ◽  
Complete Solutions

A consistent treatment of the extensional deformations of thin circular rings subjected to general distributed and concentrated loadings is presented. Coupled Euler equations and consistent boundary condition combinations in terms of the radial and tangential midsurface displacements are obtained for the dynamical problem using Hamilton’s principle. Discontinuity conditions corresponding to discrete application of generalized forces are also provided. For static analysis, the governing equations are transformed into two uncoupled sixth-order differential equations in the radial and tangential displacements, respectively, and the complete solutions are obtained for general loading. Closed-form solutions for displacements and stress resultants are developed for illustrative and comparative purposes relative to specific full ring, curved beam, and arch examples. The results confirm that extensional deformations can play a significant role in the bending of thin curved beams, and arches and that such structures are more readily and consistently analyzed by the present treatise than by Winkler curved-beam theory with its potential for inconsistent approximations toward thinness and resulting possible violation of static equilibrium by the stress resultants calculated from the stress-displacement state.

Partial Plane Contact of an Elastic Curved Beam Pressed by a Flat Surface

2006 ◽  
Vol 129 (1) ◽  
pp. 60-64 ◽  
Author(s):  
Joseph M. Block ◽  
Leon M. Keer
Keyword(s):  
Mixed Boundary ◽  
Contact Region ◽  
Finite Thickness ◽  
Beam Theory ◽  
Fourier Series Expansion ◽  
Radius Of Curvature ◽  
Curved Beam ◽  
Curved Beams ◽  
Normal Contact ◽  
As Stress

The normal contact of a frictionless, elastic curved beam indented by a flat, rigid surface is solved using a Michell–Fourier series expansion, which satisfies the mixed boundary value problem resulting from partial contact. When the contact region is small compared to the radius of curvature of the beam, semi-analytical solutions are obtained by exploiting dual series equation techniques. The relation between the level of loading and the extent of contact, as well as stress on the surface, are found for plane strain. The elasticity results extend Hertz line contact to finite thickness, curved beams. As the beam becomes thin, beam theory type behavior is recovered. The results may have application to finite-thickness wavy surfaces, cylindrical structures, or pressurized seals.

Numerical solution for dynamic analysis of semicircular curved beams acted upon by moving loads

2014 ◽  
Vol 228 (13) ◽  
pp. 2314-2322 ◽  
Author(s):  
Ali Nikkhoo ◽  
Hassan Kananipour
Keyword(s):  
Numerical Solution ◽  
Differential Quadrature Method ◽  
Moving Load ◽  
Beam Theory ◽  
Differential Quadrature ◽  
Steel Bridge ◽  
Quadrature Method ◽  
Curved Beams ◽  
Various Boundary Conditions ◽  
Structural Problems

The present study proposes a dynamic numerical solution for deflections of curved beam structures. In order to extract characteristic equations of an arch under an in-plane constant moving load, an analysis procedure based on the Euler–Bernoulli beam theory considering polar system is conducted. A prismatic semicircular arch with uniform cross section, in various boundary conditions, is assumed. Radial and tangential displacements, as well as bending moments are obtained using differential quadrature method as a well-known numerical method. In addition to parametric studies, a curved steel bridge as an actual application is analyzed by the mentioned method. By using this differential quadrature technique, the function values and some partial derivatives are approximated by weighting coefficients. Convergence study is carried out to demonstrate the stability of the present method. In order to confirm the high level of accuracy of this approach, some comparisons are made between the results obtained by selected methods such as differential quadrature method, Galerkin method, and finite element method. The results show that in the structural problems with specific geometry, using differential quadrature method, which is independent of domain discretization, is proven to be efficient.

Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part I: Theory

1997 ◽  
Vol 64 (1) ◽  
pp. 50-58 ◽  
Author(s):  
Ruichong Zhang ◽  
Liyang Zhang ◽  
Masanobu Shinozuka
Keyword(s):  
Wave Field ◽  
Half Space ◽  
Seismic Waves ◽  
Scattered Wave ◽  
Inhomogeneous Layer ◽  
Dislocation Source ◽  
Seismic Dislocation ◽  
Body Forces ◽  
The Mean ◽  
Layered Half Space

Seismic waves in a layered half-space with lateral inhomogeneities, generated by a buried seismic dislocation source, are investigated in these two consecutive papers. In the first paper, the problem is formulated and a corresponding approach to solve the problem is provided. Specifically, the elastic parameters in the laterally inhomogeneous layer, such as P and S wave speeds and density, are separated by the mean and the deviation parts. The mean part is constant while the deviation part, which is much smaller compared to the mean part, is a function of lateral coordinates. Using the first-order perturbation approach, it is shown that the total wave field may be obtained as a superposition of the mean wave field and the scattered wave field. The mean wave field is obtainable as a response solution for a perfectly layered half-space (without lateral inhomogeneities) subjected to a buried seismic dislocation source. The scattered wave field is obtained as a response solution for the same layered half-space as used in the mean wave field, but is subjected to the equivalent fictitious distributed body forces that mathematically replace the lateral inhomogeneities. These fictitious body forces have the same effects as the existence of lateral inhomogeneities and can be evaluated as a function of the inhomogeneity parameters and the mean wave fleld. The explicit expressions for the responses in both the mean and the scattered wave fields are derived with the aid of the integral transform approach and wave propagation analysis.

scholarly journals Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

2021 ◽  
Author(s):  
Tuoya Sun ◽  
Junhong Guo ◽  
E. Pan
Keyword(s):  
Elastic Medium ◽  
Vibration Frequency ◽  
Surrounding Medium ◽  
Nonlocal Parameter ◽  
Buckling Load ◽  
Width Ratio ◽  
Two Dimensional ◽  
Coating Materials ◽  
Decagonal Quasicrystal ◽  
Critical Buckling Load

AbstractA mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

Earthquake response of linear-elastic arch-frames using exact curved beam formulations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Baran Bozyigit
Keyword(s):  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Opening Angle ◽  
Earthquake Response ◽  
Response Analysis ◽  
Curved Beam ◽  
Curved Beams ◽  
Base Shear ◽  
Content Type

PurposeThis study aims to obtain earthquake responses of linear-elastic multi-span arch-frames by using exact curved beam formulations. For this purpose, the dynamic stiffness method (DSM) which uses exact mode shapes is applied to a three-span arch-frame considering axial extensibility, shear deformation and rotational inertia for both columns and curved beams. Using exact free vibration properties obtained from the DSM approach, the arch-frame model is simplified into an equivalent single degree of freedom (SDOF) system to perform earthquake response analysis.Design/methodology/approachThe dynamic stiffness formulations of curved beams for free vibrations are validated by using the experimental data in the literature. The free vibrations of the arch-frame model are investigated for various span lengths, opening angle and column dimensions to observe their effects on the dynamic behaviour. The calculated natural frequencies via the DSM are presented in comparison with the results of the finite element method (FEM). The mode shapes are presented. The earthquake responses are calculated from the modal equation by using Runge-Kutta algorithm.FindingsThe displacement, base shear, acceleration and internal force time-histories that are obtained from the proposed approach are compared to the results of the finite element approach where a very good agreement is observed. For various span length, opening angle and column dimension values, the displacement and base shear time-histories of the arch-frame are presented. The results show that the proposed approach can be used as an effective tool to calculate earthquake responses of frame structures having curved beam elements.Originality/valueThe earthquake response of arch-frames consisting of curved beams and straight columns using exact formulations is obtained for the first time according to the best of the author’s knowledge. The DSM, which uses exact mode shapes and provides accurate free vibration analysis results considering each structural members as one element, is applied. The complicated structural system is simplified into an equivalent SDOF system using exact mode shapes obtained from the DSM and earthquake responses are calculated by solving the modal equation. The proposed approach is an important alternative to classical FEM for earthquake response analysis of frame structures having curved members.

scholarly journals Free Vibration Analysis of Single Walled Carbon Nanotube with Exponentially Varying Stiffness

2018 ◽  
Vol 5 (1) ◽  
pp. 201-212 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Free Vibration ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Scaling Parameters ◽  
Governing Differential Equation ◽  
Theory Application ◽  
Walled Carbon Nanotubes

Abstract In this paper, Differential Quadrature Method (DQM) is applied to investigate free vibration of Single Walled Carbon Nanotubes (SWCNTs) with exponentially varying stiffness based on non-local Euler-Bernoulli beam theory. Application of DQ method in the governing differential equation converts the problem to a generalized eigenvalue problem and its solution gives frequency parameters. Convergence of the results show that DQM solutions converge fast. In this article, a detailed investigation has been reported and MATLAB code has been developed to analyze the numerical results for different scaling parameters as well as for four types of boundary conditions. Present results are compared with other available results and are found to be in good agreement.

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