Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix

Soydas, Ozan
Sarıtaş, Afşin
In this analytical study, free vibration analyses of a 3d mixed formulation beam element are performed by adopting force-based consistent mass matrix that incorporates shear and rotary inertia effects. The force-based approach takes into account the actual distribution of mass of an element in the derivation of the mass matrix. Moreover, the force-based approach enables accurate determination of free vibration frequencies of members with varying geometry and material distribution without any need for specification of different displacement shape functions for each individual case. This phenomenon is justified by comparing free vibration frequencies of cantilever beams that have circular and rectangular cross-sections and various mass distribution configurations. Vibration frequencies of the mixed formulation element are compared with the frequencies obtained from closed-form solutions and finite element analyses. Fundamental frequency is computed with only one element per member span and higher order frequencies are determined with two or four elements with considerable accuracy by employing 3d mixed element and force-based consistent mass matrix.


Hybrid finite element for analysis of functionally graded beams
Sarıtaş, Afşin; Soydas, Ozan (2017-01-01)
A hybrid finite element model is presented, where stiffness and mass distributions over a beam with functionally graded material (FGM) are accurately modeled for both elastic and inelastic material responses. Von Mises and Drucker-Prager plasticity models are implemented for metallic and ceramic parts of FGM, respectively. Three-dimensional stress-strain relations are solved by a general closest point projection algorithm, and then condensed to the dimensions of the beam element. Numerical examples and veri...
Nonlinear fiber modeling of steel-concrete partially composite beams with channel shear connectors
Öztürk, Alper; Baran, Eray; Department of Civil Engineering (2017)
The purpose of this study is to develop a nonlinear fiber-based finite element model of steel-concrete composite beams. The model was developed in OpenSees utilizing the available finite element formulations and the readily available uniaxial material constitutive relations. The model employed beam elements for the steel beam and the concrete slab, while zero-length connector elements were used for the steel-concrete interface. The channel shear connector response used in numerical models was based on the p...
Induced current magnetic resonance electrical impedance tomography (ICMREIT) with low frequency switching of gradient fields
Eroğlu, Hasan Hüseyin; Eyüboğlu, Behçet Murat; Department of Electrical and Electronics Engineering (2017)
In this thesis, it is aimed to investigate induced current magnetic resonance electrical impedance tomography (ICMREIT) starting from modeling and analysis to experimental validation. Forward and inverse problems of ICMREIT are formulated. A magnetic resonance imaging (MRI) pulse sequence is proposed for the realization of ICMREIT using the slice selection (z) gradient coil of MRI scanners. Considering the proposed MRI pulse sequence, relationship between the low frequency (LF) MR phase and the secondary ma...
Optimum design of high-speed flexible robotic arms with dynamic behavior constraints
Oral, Süha (1997-10-01)
A methodology is presented for the optimum design of robotic arms under time-dependent stress and displacement constraints by using mathematical programming. Finite elements are used in the modeling of the flexible links. The design variables are the cross-sectional dimensions of the elements. The time dependence of the constraints is removed through the use of equivalent constraints based on the most critical constraints. It is shown that this approach yields a better design than using equivalent constrain...
Computational simulation and realization of three-dimensional metamaterials with various exotic properties
İbili, Hande; Ergül, Özgür Salih; Department of Electrical and Electronics Engineering (2019)
In this study, computational analysis and realization of three-dimensional metamaterial structures that induce negative and zero permittivity and/or permeability values in their host environment, as well as plasmonic nanoparticles that are used to design metamaterials at optical frequencies are presented. All these electromagnetic problems are challenging since effective material properties become negative/zero, while numerical solvers are commonly developed for ordinary positive parameters. In real life, t...
Citation Formats
O. Soydas and A. Sarıtaş, “Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix,” JOURNAL OF VIBRATION AND CONTROL, pp. 2635–2655, 2017, Accessed: 00, 2020. [Online]. Available: