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 vibrations of circular curved beams

2018 ◽  
Vol 211 ◽  
pp. 04006
Author(s):  
Ajinkya Baxy ◽  
Abhijit Sarkar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fem Simulation ◽  
Free Vibrations ◽  
Opening Angle ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Governing Equations ◽  
Simulation Results

The study of free vibrations of curved beams has relevance in engineering applications like modeling turbo machinery blades, propellers, arch design, etc. Vibration characteristics of structures are generally evaluated using the Finite Element Method. The governing equations for the curved beam using the inextensional theory are available in the literature. These equations are solved analytically for two different boundary conditions, namely (a) simplysupported, (b) cantilever. The results obtained for all the cases are compared against the FEM simulation results. It is found that the present solutions are in agreement with the FEM solutions up to an opening angle of 40°.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

Simple Modeling and Analysis for Crankshaft Three-Dimensional Vibrations, Part 1: Background and Application to Free Vibrations

1995 ◽  
Vol 117 (1) ◽  
pp. 70-79 ◽  
Author(s):  
H. Okamura ◽  
A. Shinno ◽  
T. Yamanaka ◽  
A. Suzuki ◽  
K. Sogabe
Keyword(s):  
Stiffness Matrix ◽  
Rectangular Cross Section ◽  
Dynamic Stiffness ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Dynamic Stiffness Matrix ◽  
Modeling And Analysis ◽  
Coupling Behavior ◽  
Film Stiffness

To simplify the analysis of the three-dimensional vibrations of automobile engine crankshafts under firing conditions, the crankshaft was idealized by a set of jointed structures consisting of simple round rods and simple beam blocks of rectangular cross-section. The front pulley, timing gear, and the fly-wheel were idealized by a set of masses and moments of inertia. The main journal bearings were idealized by a set of linear springs and dash-pots. For each constituent member, the dynamic stiffness matrix was derived (in closed form) from the transfer matrix. Then the dynamic stiffness matrix for the total crankshaft system was constructed, and the natural frequencies and mode shapes were calculated. The modeling and analysis procedures were applied to the analysis of free vibrations of four kinds of crankshafts: single cylinder, three-cylinder in-line, four-cylinder in-line, and V-six engines. The different coupling behavior of the three-dimensional vibrations in the planar-structure and the solid-structure crankshaft is discussed, and the influence of the bearing oil film stiffness on the crankshaft natural frequency is also analyzed.

scholarly journals Electrical analogs of curved beams and application to piezoelectric network damping

2021 ◽  
pp. 108128652110276
Author(s):  
Robin Darleux ◽  
Boris Lossouarn ◽  
Ivan Giorgio ◽  
Francesco dell’Isola ◽  
Jean-François Deü
Keyword(s):  
Finite Number ◽  
Analog Circuit ◽  
Mode Shapes ◽  
Curved Beam ◽  
Curved Beams ◽  
Lumped Element ◽  
Lumped Elements ◽  
Electric Analog ◽  
Frequency Coherence ◽  
Micro Structures

In this paper, the method of electric analog synthesis is applied to design a piezo-electro-mechanical arch able to show the capacity of multimodal damping. An electric-analog circuit is designed by using a finite number of lumped elements representing the equivalent of a curved beam. Spatial and frequency coherence conditions are proven to be verified for the modes to be damped: in fact, lumped-element circuit can damp only a finite number of vibration modes. Analogous boundary conditions are ensured, so that natural frequencies and mode shapes of both the curved beam and the analog circuit are equal. The instance considered here is the vibration mitigation of a piezo-electro-mechanical arch. Having a view towards prototypical applications, all simulations consider values of physically feasible passive circuital elements. It is believed that the present results may represent a step towards the design of multi-physics metamaterials based on micro-structures exploiting the principle of multimodal damping.

A weak form quadrature element method for nonlinear free vibrations of Timoshenko beams

2016 ◽  
Vol 33 (1) ◽  
pp. 274-287 ◽  
Author(s):  
Minmao Liao ◽  
Hongzhi Zhong
Keyword(s):  
Slenderness Ratio ◽  
Weak Form ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Radius Of Gyration ◽  
Element Formulation ◽  
Timoshenko Beams ◽  
Content Type ◽  
Quadrature Element Method ◽  
Element Method

Purpose – The purpose of this paper is to highlight the implementation of a recently developed weak form quadrature element method for nonlinear free vibrations of Timoshenko beams subjected to three different boundary conditions. Design/methodology/approach – The design of the paper is based on considering the geometrically nonlinear effects of axial strain, bending curvature, and shear strain. Then the quadrature element formulation of the beam is introduced. Findings – The efficiency of the method is demonstrated by a convergence study. Ratios of the nonlinear fundamental frequencies to the corresponding linear frequencies are extracted. Their variations with the ratio of amplitude to radius of gyration and the slenderness ratio are examined. The effects of the nonlinearity on higher order frequencies and mode shapes are also investigated. Originality/value – The computed results show fast convergence and compare well with available literature results.

scholarly journals Analysis of a Frame-Shear Wall Concrete Structure by Using Base Isolation and Evaluation of Structure-Soil Interaction

2017 ◽  
Vol 7 (6) ◽  
pp. 2282-2287
Author(s):  
H. I. Polat
Keyword(s):  
Cross Sections ◽  
Base Isolation ◽  
Shear Wall ◽  
Structure Design ◽  
Mode Shapes ◽  
Earthquake Response ◽  
Response Analysis ◽  
Seismic Load ◽  
Isolation System ◽  
Base Isolation System

A base isolation system is a type of earthquake-resistant structure design approach based on the principle of reducing a structure’s earthquake response rather than increasing the structure’s earthquake resistance capacity. Seismic base isolated structures have the ability to make large displacements relative to the level of insulation elements. This means that a large structure performs very small displacements between floors during an earthquake and exhibits a rigid body behavior. At this point, the earthquake forces acting on the structure decrease along with the floors. In this article a school building composed of frame-shear wall is resolved primarily with the traditional fixed base structure system, mode shapes are found and periods are obtained. For earthquake response analysis, earthquake loads are distributed to the floors using the equivalent seismic load method and structural elements experiencing capacity problems are found. Then, using the earthquake record, larger failure of cross sections and capacity problems are obtained compared to the first method. In the second stage, the same structure is dissolved again by placing the lead core rubber base isolators between the base and the vertical structural members. The periods of structures under earthquake load have increased significantly by utilizing base isolation, as a result of that spectral accelerations decreased. Thus, large decreases in the shear forces acting to the structure are determined and failures of cross sections are removed.

scholarly journals Analysis of the effect of the secondary moment on curved beams of full cross section

2021 ◽  
Vol 14 (2) ◽  
Author(s):  
Thiago Cunha da Silva ◽  
Emil de Souza Sánchez Filho
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Structural Model ◽  
Paper Analysis ◽  
Opening Angle ◽  
Curved Beam ◽  
Curved Beams ◽  
Straight Beam ◽  
Full Cross Section

abstract This paper analysis the effect of the secondary moment on curved beams using the equivalent nodal loads method. A case study was carried out applying the equivalent nodal loads method to a two-span prestressed curved beam, using a curved finite element as the structural model, analyzing the effect of the secondary moment for each case and comparing it with its equivalent in straight beam. It was found that the stiffness parameters E I and G J influence the secondary moment. The results demonstrates that the beam opening angle reduces the effect of secondary moment, and that the greater the angle, the greater is the reduction that occurs in its secondary moment compared to its equivalent straight beam.

A novel modal calculation method of 1-D phononic crystal band gap

2015 ◽  
Vol 11 (1) ◽  
pp. 16-22
Author(s):  
Lei Li ◽  
Qing Liu
Keyword(s):  
Band Gap ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Mode Shapes ◽  
Response Analysis ◽  
Content Type ◽  
Existence Conditions ◽  
Harmonic Response Analysis ◽  
Modal Method

Purpose – The purpose of this paper is to propose a modal method to calculate the band gaps of one-dimensional (1D) phononic crystals. Design/methodology/approach – The phononic crystals have modes with exponential form envelope in the band gaps, however, outside the band gaps the modes are of amplitude modulation periodic form. Thus the start and end frequencies of band gaps can be determined from the existence conditions of periodic modes. So, the band gaps calculation of 1D phononic crystal is transformed into the existence discussion of periodic solution of mode shapes equation. The results are verified by finite element harmonic response analysis. Findings – At the start and end frequencies of the band gap, the mode equation have solution with period of lattice constant. Originality/value – Compared with the traditional theoretical methods, the proposed modal method has a clearer principle and easier calculation.

scholarly journals An investigation into the free vibrations of carbon nanotubes using analytical and finite element methods

2021 ◽  
Author(s):  
Ishan Ali Khan
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Nonlinear Eigenvalue Problem ◽  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Wide Range ◽  
Walled Cnts

Since their discovery, immense attention has been given to carbon nanotubes (CNTs), due to their exceptional thermal, electronic and mechanical properties and, therefore, the wide range of applications in which they are, or can be potentially, employed. Hence, it is important that all the properties of carbon nanotubes are studied extensively. This thesis studies the vibrational frequencies of double-walled and triple-walled CNTs, with and without an elastic medium surrounding them, by using Finite Element Method (FEM) and Dynamic Stiffness Matrix (DSM) formulations, considering them as Euler-Bernoulli beams coupled with van der Waals interaction forces. For FEM modelling, the linear eigenvalue problem is obtained using Galerkin weighted residual approach. The natural frequencies and mode shapes are derived from eigenvalues and eigenvectors, respectively. For DSM formulation of double-walled CNTs, a nonlinear eigenvalue problem is obtained by enforcing displacement and load end conditions to the exact solution of single equation achieved by combining the coupled governing equations. The natural frequencies are obtained using Wittrick-Williams algorithm. FEM formulation is also applied to both double and triple-walled CNTs modelled as nonlocal Euler-Bernoulli beam. The natural frequencies obtained for all the cases, are in agreement with the values provided in literature.

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