Dynamic stiffness formulations for harmonic response of infilled frames

Bozyigit, Baran,Yesilcea, Yusuf 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.68 No.2

In this paper, harmonic responses of infilled multi-storey frames are obtained by using a single variable shear deformation theory (SVSDT) and dynamic stiffness formulations. Two different planar frame models are used which are fully infilled and soft storey. The infill walls are modeled by using equivalent diagonal strut approach. Firstly, free vibration analyses of bare frame and infilled frames are performed. The calculated natural frequencies are tabulated with finite element solution results. Then, harmonic response curves (HRCs) of frame models are plotted for different infill wall thickness values. All of the results are presented comparatively with Timoshenko beam theory results to reveal the effectiveness of SVSDT which considers the parabolic shear stress distribution along the frame member cross-sections.

Investigation of natural frequencies of multi-bay and multi-storey frames using a single variable shear deformation theory

Bozyigit, Baran,Yesilce, Yusuf Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.1

This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

Free vibration and harmonic response of cracked frames using a single variable shear deformation theory

Baran Bozyigit,Yusuf Yesilce,Magd Abdel Wahab 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.74 No.1

The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.

Dynamic stiffness formulations for harmonic response of infilled frames

Baran Bozyigit,Yusuf Yesilce 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.68 No.2

In this paper, harmonic responses of infilled multi-storey frames are obtained by using a single variable shear deformation theory (SVSDT) and dynamic stiffness formulations. Two different planar frame models are used which are fully infilled and soft storey. The infill walls are modeled by using equivalent diagonal strut approach. Firstly, free vibration analyses of bare frame and infilled frames are performed. The calculated natural frequencies are tabulated with finite element solution results. Then, harmonic response curves (HRCs) of frame models are plotted for different infill wall thickness values. All of the results are presented comparatively with Timoshenko beam theory results to reveal the effectiveness of SVSDT which considers the parabolic shear stress distribution along the frame member cross-sections.

Investigation of natural frequencies of multi-bay and multi-storey frames using a single variable shear deformation theory

Baran Bozyigit,Yusuf Yesilce 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.1

This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures

Baran Bozyigit,Yusuf Yesilce,Magd Abdel Wahab 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.73 No.2

This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.

Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam

Baran Bozyigit,Yusuf Yesilce 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.58 No.5

In this study, the free vibration analysis of axially moving beams is investigated according to Reddy-Bickford beam theory (RBT) by using dynamic stiffness method (DSM) and differential transform method (DTM). First of all, the governing differential equations of motion in free vibration are derived by using Hamilton’s principle. The nondimensionalised multiplication factors for axial speed and axial tensile force are used to investigate their effects on natural frequencies. The natural frequencies are calculated by solving differential equations using analytical method (ANM). After the ANM solution, the governing equations of motion of axially moving Reddy-Bickford beams are solved by using DTM which is based on Finite Taylor Series. Besides DTM, DSM is used to obtain natural frequencies of moving Reddy-Bickford beams. DSM solution is performed via Wittrick-Williams algorithm. For different boundary conditions, the first three natural frequencies that calculated by using DTM and DSM are tabulated in tables and are compared with the results of ANM where a very good proximity is observed. The first three mode shapes and normalised bending moment diagrams are presented in figures.

Differential transform method and Adomian decomposition method for free vibration analysis of fluid conveying Timoshenko pipeline

Baran Bozyigit,Yusuf Yesilce,Seval Catal 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.62 No.1

The free vibration analysis of fluid conveying Timoshenko pipeline with different boundary conditions using Differential Transform Method (DTM) and Adomian Decomposition Method (ADM) has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical fluid velocity of the pipelines on different supports are analyzed based on Timoshenko model by using DTM and ADM in this study. At first, the governing differential equations of motion of fluid conveying Timoshenko pipeline in free vibration are derived. Parameter for the nondimensionalized multiplication factor for the fluid velocity is incorporated into the equations of motion in order to investigate its effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, the efficient and easy mathematical techniques called DTM and ADM are used to solve the governing differential equations of the motion, respectively. The calculated natural frequencies of fluid conveying Timoshenko pipelines with various combinations of boundary conditions using DTM and ADM are tabulated in several tables and figures and are compared with the results of Analytical Method (ANM) where a very good agreement is observed. Finally, the critical fluid velocities are calculated for different boundary conditions and the first five mode shapes are presented in graphs.