Oktay Demirdağ - Academia.edu (original) (raw)

Papers by Oktay Demirdağ

This study presents elastically supported Timoshenko column with attached masses for free vibrati... more This study presents elastically supported Timoshenko column with attached masses for free vibration analysis using fuzzy neural network. Neuro fuzzy frequency estimation (NFEE) models were developed to compute vibration frequencies using fuzzy logic toolbox of software Matlab 7.0. Gaussian membership functions and adaptive neuro fuzzy inference system (ANFIS) were used in NFFE model. Hybrid learning rule was applied for quantifying output variables in NFFE model. Frequency values of column with 1, 5 and 10 attached masses were computed. Training sets for NFFE models used transfer matrix method (TMM). During testing of NFFE model, good agreement was observed with results obtained using TMM as reduction in computation effort.

Selcuk University Journal of Engineering, Science and Technology, Feb 3, 2005

ABSTRACT This paper deals with the free vibration of Timoshenko columns with attached masses havi... more ABSTRACT This paper deals with the free vibration of Timoshenko columns with attached masses having rotary inertia. The support of the model is elastically restrained against rotation. The concept of fixity factor is used to define the stiffness of the elastic connection relative to that of the column. The governing equation of the column elements is solved by applying the separation of variables method in the transfer matrix method (TMM) algorithm. The same problems are solved, also, by finite element method (FEM) algorithm in which the matrices in equation of motion are obtained for Timoshenko column, and the results are compared with the ones of TMM. The comparison graphs are presented in numerical analysis to show the effectiveness of the considered methods, and it is resulted that FEM gives closer results to TMM.

Journal of Scientific & Industrial Research, 2009

... masses using fuzzy neural network Oktay Demirdag* and Yetis Sazi Murat Pamukkale University, ... more ... masses using fuzzy neural network Oktay Demirdag* and Yetis Sazi Murat Pamukkale University, Civil Engineering Department, Engineering Faculty, 20070 Kinikli, Denizli, Turkey Received 24 March 2008; revised 22 January 2009; accepted 27 January 2009 ...

Ordu üniversitesi bilim ve teknoloji dergisi, Jun 1, 2012

In this study, equation of motion for free vibration of both ends simply supported Timoshenko bea... more In this study, equation of motion for free vibration of both ends simply supported Timoshenko beam resting on two different elastic foundation are obtained considering P- effects. The eigenvalues being the fundamental frequencies of Timoshenko beam on elastic foundation and the frequency factors related to these eigenvalues are calculated using two different methods. Free vibration equation of Timoshenko beam is solved by using respectively differential transform method (DTM) and transfer matrix method (TMM), respectively. Frequency factor values obtained by both methods depending on the beam length ratios at two different foundation regions, the modulus of subgrade reactions and the axial load ratios are presented in the tables.

DOAJ (DOAJ: Directory of Open Access Journals), Mar 1, 2005

Cercevelerin dinamik analizinde hesap kolayligi acisindan, cercevelerin zemine baglandigi noktala... more Cercevelerin dinamik analizinde hesap kolayligi acisindan, cercevelerin zemine baglandigi noktalarin mafsalliveya tam ankastre oldugu, kat kutlelerinin kat seviyelerinde topaklandigi, kolonlarin yayili kutlesinin vedeformasyonunun ihmal edildigi kabullerine sik rastlanmaktadir. Ancak uygulamada cogu kez cercevelerinzemine baglandigi noktalar, zeminin elastik davranisi nedeni ile bir miktar donebilmektedir. Bu durumdacercevenin zemine baglandigi noktaya donmeye karsi elastik yay yerlestirilerek yari-rijit mesnet davranisimodellenebilir. Bu calismada, zemine yari-rijit bagli tek serbestlik dereceli (TSD) sistemlerin serbest titresimanalizi kolonlarin yayili kutlesi ve P-δ etkisi dikkate alinarak yapilmis ve acisal frekanslari elde edilmistir. Kolontabanindaki donme yay sabitindeki ve eksenel kuvvet degerindeki degisimin acisal frekans degerleri uzerindekietkileri tablo ve grafiklerle sunulmustur.

DOAJ (DOAJ: Directory of Open Access Journals), Mar 1, 2005

Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı noktala... more Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı noktaların mafsallı veya tam ankastre olduğu, kat kütlelerinin kat seviyelerinde topaklandığı, kolonların yayılı kütlesinin ve deformasyonunun ihmal edildiği kabullerine sık rastlanmaktadır. Ancak uygulamada çoğu kez çerçevelerin zemine bağlandığı noktalar, zeminin elastik davranışı nedeni ile bir miktar dönebilmektedir. Bu durumda çerçevenin zemine bağlandığı noktaya dönmeye karşı elastik yay yerleştirilerek yarı-rijit mesnet davranışı modellenebilir. Bu çalışmada, zemine yarı-rijit bağlı tek serbestlik dereceli (TSD) sistemlerin serbest titreşim analizi kolonların yayılı kütlesi ve P-δ etkisi dikkate alınarak yapılmış ve açısal frekansları elde edilmiştir. Kolon tabanındaki dönme yay sabitindeki ve eksenel kuvvet değerindeki değişimin açısal frekans değerleri üzerindeki etkileri tablo ve grafiklerle sunulmuştur.

In advanced wastewater treatment plants (AWWTP), the recovery of phosphorus (P) has become a rece... more In advanced wastewater treatment plants (AWWTP), the recovery of phosphorus (P) has become a recent focus of the wastewater engineering industry. The potential economic savings behind improved sludge management and the control of struvite encrustation in AWWTP are two of the primary driving forces behind this. Process control of phosphorus (struvite) recovery systems has only been partially successful because: (1) key control variables have yet to be identified and (2) there is no adequate performance evaluation model that is applicable to struvite recovery technologies. In process control, two different types of modeling are most commonly seen: mechanistic and ''black-box'' style models. In recent years, varying models have been developed to try to predict the formation of struvite in both sludge digestion process lines and P-recovery technologies designed for struvite removal. All of these are strictly mechanistic models, based on either the chemical equilibrium of the system or the associated kinetic parameters, with varying degrees of complexity. Artificial neural networks (ANN), as a type of black-box modeling, have seen limited application in wastewater treatment with regards to phosphate recovery. The analysis of several historical daily operational databases evaluated the predictive ability of two mechanistic and one ANN models. It was determined that the newly developed ANN model was not site specific and had the highest predictive ability of the three. This would be beneficial for the development of an automated control system for struvite removal package treatment processes.

Research on Engineering Structures & Materials, 2016

To cite this article Demirdag O, Yildirim B. Comparing transfer matrix method and ANFIS in free v... more To cite this article Demirdag O, Yildirim B. Comparing transfer matrix method and ANFIS in free vibration analysis of Timoshenko columns with attachments.

The main purpose of this study is to obtain dimensionless differential equation of motion for fre... more The main purpose of this study is to obtain dimensionless differential equation of motion for free vibration of the axially vibrating beams, to solve this dimensionless vibration problem for different boundary conditions and to obtain the natural frequencies for the first five modes. The dimensionless differential equation of motion of the beam is obtained and solved to obtain the frequency equation. An I-profile beam is chosen for the numerical analysis. The natural frequencies of the first five modes are obtained for the I-beam modeled as a fixed beam, a cantilever beam and a free beam. The frequency values are listed in the tables.

Abstract— In this study dimensionless free axial vibration analysis of an elastically supported b... more Abstract— In this study dimensionless free axial vibration analysis of an elastically supported beam is made. The supports are modeled by elastic translational springs. The frequency values for the first three vibration modes of the beam are obtained for various values of spring constants and presented in the tables. Three I-profile beams are chosen for the numerical analysis. The frequency values for the spring constants of zero and infinity are also compared, respectively, with the ones of free, fixed and cantilever beams and nearly the exact values are obtained with negligible error percentages.

Structural Engineering and Mechanics, 2007

Spectral analysis of semi-rigid supported single storey frames modeled as Timoshenko column with ... more Spectral analysis of semi-rigid supported single storey frames modeled as Timoshenko column with attached mass is studied for earthquake response including rotatory inertia of the columns. The earthquake response of the single storey frames is evaluated by Newmark-β method where generalized equation of motion is derived by substituting energy relations of the model into Langrange's equation. Response spectrum analysis of the model subjected to Izmit earthquake is made by Newmark-β method for period values of 0 to 3 seconds using a computer program. Langrange's equation and kinetic, potential, load energies of the model are analyzed using transformation and boundary conditions. Results show that displacement, velocity, acceleration response spectrum of semi-rigid supported single storey frames are 10000, 100000 and 10000000 (t/m, tm/rad) respectively

Absract: In practice, concrete is mixed at a wide range of temperatures and also remains in servi... more Absract: In practice, concrete is mixed at a wide range of temperatures and also remains in service at different temperatures. There are some special problems involved in concreting in hot weather, arising both from a higher temperature of the concrete and, in many cases, from an increased rate of evaporation from the fresh mix. These problems concern the mixing, placing and curing of the concrete. Hot-weather concreting is not so much an unusual or a specialized process; rather, it requires taking certain recognized measures to minimize or control the effect of high ambient temperature, high temperature of the concrete, low relative humidity, high wind velocity, and high solar radiation. What is required on each construction project where any one or more of the above conditions exist is to develop appropriate techniques and procedures and to follow them rigorously.

Advanced Composites Letters

International Journal of Mechanical Sciences, 2008

... embedded in soil. Doyle and Pavlovic [18] solved the partial differential equation for free v... more ... embedded in soil. Doyle and Pavlovic [18] solved the partial differential equation for free vibration of beams partially attached to elastic foundation using separation of variable method and neglecting shear effect. Catal [19] and ...

Abstract— In this study dimensionless free axial vibration analysis of beam with tip masses is ma... more Abstract— In this study dimensionless free axial vibration analysis of beam with tip masses is made. The tip masses are modeled by concentrated masses at both ends of the beam. The frequency values for the first three vibration modes of the beam are obtained for various values of concentrated masses and presented in the tables. Three I-profile beams are chosen for the numerical analysis. The frequency values for the concentrated masses of zero and infinity are also compared, respectively, with the ones of free, fixed and cantilever beams and nearly the exact values are obtained with negligible error percentages.

fbe.dumlupinar.edu.tr

ÖZET Çerçevelerin dinamik analizinde sıkça kullanılan kabullerden birisi hareket denklemini kat h... more ÖZET Çerçevelerin dinamik analizinde sıkça kullanılan kabullerden birisi hareket denklemini kat hizasında topaklanmış kütleye göre yazmak ve kolonları rijitlik elemanı olarak modellemektir. Ancak gerçekte, kolonlar yayılı kütleye ve rijitliğe sahiptir ve çerçevelerin zeminle bağlantı noktaları, pratikte, dinamik yük sırasında zeminin elastik davranışına bağlı olarak bir miktar dönebilmekte ve ötelenebilmektedir. Bu durumda, çerçevelerin mesnetlerinde dönmeye ve ötelenmeye karşı elastik yaylar kullanılarak, elastik mesnet davranışı modellenebilir. Bu çalışmada, elastik mesnetli Timoshenko kolonu olarak modellenen tek katlı çerçevelerin serbest titreşimi kolonların dönme ataleti de dikkate alınarak incelenmiş ve farklı yay sabitleri için doğal frekanslar elde edilmiştir.

Selçuk Üniversitesi Mühendislik, Bilim ve Teknoloji Dergisi, Feb 3, 2005

ÖZET: Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı n... more ÖZET: Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı noktaların tam ankastre olduğu, kat kütlelerinin kat seviyelerinde topaklandığı, kolonların yayılı kütlesinin ve kayma deformasyonunun ihmal edildiği kabullerine sık rastlanmaktadır. Ancak uygulamada çoğu kez çerçevelerin zemine bağlandığı noktalar, zeminin elastik davranışı nedeni ile bir miktar dönebilmekte ve ötelenebilmektedir. Bu durumda çerçevenin zemine bağlandığı noktaya dönmeye ve ötelenmeye karşı elastik yaylar yerleştirilerek yarı-rijit mesnet davranışı modellenebilir. Bu çalışmada, zemine yarı-rijit bağlı tek katlı çerçevelerin serbest titreşim analizi kolonların yayılı kütlesi ve kayma deformasyonu dikkate alınarak yapılmış ve açısal frekansları elde edilmiştir. Kolon tabanındaki ötelenme ve dönme yay sabiti değerlerindeki artışın frekans değerlerinde meydana getirdiği artma ve kolon üst serbest ucundaki toplu kütlenin ve dönme ataletinin değerlerindeki artışın frekanslarda meydana getirdiği azalma grafiklerle sunulmuştur.

Trakya Üniversitesi Fen Bilimleri Dergisi, Aug 5, 2016

This study presents elastically supported Timoshenko column with attached masses for free vibrati... more This study presents elastically supported Timoshenko column with attached masses for free vibration analysis using fuzzy neural network. Neuro fuzzy frequency estimation (NFEE) models were developed to compute vibration frequencies using fuzzy logic toolbox of software Matlab 7.0. Gaussian membership functions and adaptive neuro fuzzy inference system (ANFIS) were used in NFFE model. Hybrid learning rule was applied for quantifying output variables in NFFE model. Frequency values of column with 1, 5 and 10 attached masses were computed. Training sets for NFFE models used transfer matrix method (TMM). During testing of NFFE model, good agreement was observed with results obtained using TMM as reduction in computation effort.

Selcuk University Journal of Engineering, Science and Technology, Feb 3, 2005

ABSTRACT This paper deals with the free vibration of Timoshenko columns with attached masses havi... more ABSTRACT This paper deals with the free vibration of Timoshenko columns with attached masses having rotary inertia. The support of the model is elastically restrained against rotation. The concept of fixity factor is used to define the stiffness of the elastic connection relative to that of the column. The governing equation of the column elements is solved by applying the separation of variables method in the transfer matrix method (TMM) algorithm. The same problems are solved, also, by finite element method (FEM) algorithm in which the matrices in equation of motion are obtained for Timoshenko column, and the results are compared with the ones of TMM. The comparison graphs are presented in numerical analysis to show the effectiveness of the considered methods, and it is resulted that FEM gives closer results to TMM.

Journal of Scientific & Industrial Research, 2009

... masses using fuzzy neural network Oktay Demirdag* and Yetis Sazi Murat Pamukkale University, ... more ... masses using fuzzy neural network Oktay Demirdag* and Yetis Sazi Murat Pamukkale University, Civil Engineering Department, Engineering Faculty, 20070 Kinikli, Denizli, Turkey Received 24 March 2008; revised 22 January 2009; accepted 27 January 2009 ...

Ordu üniversitesi bilim ve teknoloji dergisi, Jun 1, 2012

In this study, equation of motion for free vibration of both ends simply supported Timoshenko bea... more In this study, equation of motion for free vibration of both ends simply supported Timoshenko beam resting on two different elastic foundation are obtained considering P- effects. The eigenvalues being the fundamental frequencies of Timoshenko beam on elastic foundation and the frequency factors related to these eigenvalues are calculated using two different methods. Free vibration equation of Timoshenko beam is solved by using respectively differential transform method (DTM) and transfer matrix method (TMM), respectively. Frequency factor values obtained by both methods depending on the beam length ratios at two different foundation regions, the modulus of subgrade reactions and the axial load ratios are presented in the tables.

DOAJ (DOAJ: Directory of Open Access Journals), Mar 1, 2005

Cercevelerin dinamik analizinde hesap kolayligi acisindan, cercevelerin zemine baglandigi noktala... more Cercevelerin dinamik analizinde hesap kolayligi acisindan, cercevelerin zemine baglandigi noktalarin mafsalliveya tam ankastre oldugu, kat kutlelerinin kat seviyelerinde topaklandigi, kolonlarin yayili kutlesinin vedeformasyonunun ihmal edildigi kabullerine sik rastlanmaktadir. Ancak uygulamada cogu kez cercevelerinzemine baglandigi noktalar, zeminin elastik davranisi nedeni ile bir miktar donebilmektedir. Bu durumdacercevenin zemine baglandigi noktaya donmeye karsi elastik yay yerlestirilerek yari-rijit mesnet davranisimodellenebilir. Bu calismada, zemine yari-rijit bagli tek serbestlik dereceli (TSD) sistemlerin serbest titresimanalizi kolonlarin yayili kutlesi ve P-δ etkisi dikkate alinarak yapilmis ve acisal frekanslari elde edilmistir. Kolontabanindaki donme yay sabitindeki ve eksenel kuvvet degerindeki degisimin acisal frekans degerleri uzerindekietkileri tablo ve grafiklerle sunulmustur.

DOAJ (DOAJ: Directory of Open Access Journals), Mar 1, 2005

Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı noktala... more Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı noktaların mafsallı veya tam ankastre olduğu, kat kütlelerinin kat seviyelerinde topaklandığı, kolonların yayılı kütlesinin ve deformasyonunun ihmal edildiği kabullerine sık rastlanmaktadır. Ancak uygulamada çoğu kez çerçevelerin zemine bağlandığı noktalar, zeminin elastik davranışı nedeni ile bir miktar dönebilmektedir. Bu durumda çerçevenin zemine bağlandığı noktaya dönmeye karşı elastik yay yerleştirilerek yarı-rijit mesnet davranışı modellenebilir. Bu çalışmada, zemine yarı-rijit bağlı tek serbestlik dereceli (TSD) sistemlerin serbest titreşim analizi kolonların yayılı kütlesi ve P-δ etkisi dikkate alınarak yapılmış ve açısal frekansları elde edilmiştir. Kolon tabanındaki dönme yay sabitindeki ve eksenel kuvvet değerindeki değişimin açısal frekans değerleri üzerindeki etkileri tablo ve grafiklerle sunulmuştur.

In advanced wastewater treatment plants (AWWTP), the recovery of phosphorus (P) has become a rece... more In advanced wastewater treatment plants (AWWTP), the recovery of phosphorus (P) has become a recent focus of the wastewater engineering industry. The potential economic savings behind improved sludge management and the control of struvite encrustation in AWWTP are two of the primary driving forces behind this. Process control of phosphorus (struvite) recovery systems has only been partially successful because: (1) key control variables have yet to be identified and (2) there is no adequate performance evaluation model that is applicable to struvite recovery technologies. In process control, two different types of modeling are most commonly seen: mechanistic and ''black-box'' style models. In recent years, varying models have been developed to try to predict the formation of struvite in both sludge digestion process lines and P-recovery technologies designed for struvite removal. All of these are strictly mechanistic models, based on either the chemical equilibrium of the system or the associated kinetic parameters, with varying degrees of complexity. Artificial neural networks (ANN), as a type of black-box modeling, have seen limited application in wastewater treatment with regards to phosphate recovery. The analysis of several historical daily operational databases evaluated the predictive ability of two mechanistic and one ANN models. It was determined that the newly developed ANN model was not site specific and had the highest predictive ability of the three. This would be beneficial for the development of an automated control system for struvite removal package treatment processes.

Research on Engineering Structures & Materials, 2016

To cite this article Demirdag O, Yildirim B. Comparing transfer matrix method and ANFIS in free v... more To cite this article Demirdag O, Yildirim B. Comparing transfer matrix method and ANFIS in free vibration analysis of Timoshenko columns with attachments.

The main purpose of this study is to obtain dimensionless differential equation of motion for fre... more The main purpose of this study is to obtain dimensionless differential equation of motion for free vibration of the axially vibrating beams, to solve this dimensionless vibration problem for different boundary conditions and to obtain the natural frequencies for the first five modes. The dimensionless differential equation of motion of the beam is obtained and solved to obtain the frequency equation. An I-profile beam is chosen for the numerical analysis. The natural frequencies of the first five modes are obtained for the I-beam modeled as a fixed beam, a cantilever beam and a free beam. The frequency values are listed in the tables.

Abstract— In this study dimensionless free axial vibration analysis of an elastically supported b... more Abstract— In this study dimensionless free axial vibration analysis of an elastically supported beam is made. The supports are modeled by elastic translational springs. The frequency values for the first three vibration modes of the beam are obtained for various values of spring constants and presented in the tables. Three I-profile beams are chosen for the numerical analysis. The frequency values for the spring constants of zero and infinity are also compared, respectively, with the ones of free, fixed and cantilever beams and nearly the exact values are obtained with negligible error percentages.

Structural Engineering and Mechanics, 2007

Spectral analysis of semi-rigid supported single storey frames modeled as Timoshenko column with ... more Spectral analysis of semi-rigid supported single storey frames modeled as Timoshenko column with attached mass is studied for earthquake response including rotatory inertia of the columns. The earthquake response of the single storey frames is evaluated by Newmark-β method where generalized equation of motion is derived by substituting energy relations of the model into Langrange's equation. Response spectrum analysis of the model subjected to Izmit earthquake is made by Newmark-β method for period values of 0 to 3 seconds using a computer program. Langrange's equation and kinetic, potential, load energies of the model are analyzed using transformation and boundary conditions. Results show that displacement, velocity, acceleration response spectrum of semi-rigid supported single storey frames are 10000, 100000 and 10000000 (t/m, tm/rad) respectively

Absract: In practice, concrete is mixed at a wide range of temperatures and also remains in servi... more Absract: In practice, concrete is mixed at a wide range of temperatures and also remains in service at different temperatures. There are some special problems involved in concreting in hot weather, arising both from a higher temperature of the concrete and, in many cases, from an increased rate of evaporation from the fresh mix. These problems concern the mixing, placing and curing of the concrete. Hot-weather concreting is not so much an unusual or a specialized process; rather, it requires taking certain recognized measures to minimize or control the effect of high ambient temperature, high temperature of the concrete, low relative humidity, high wind velocity, and high solar radiation. What is required on each construction project where any one or more of the above conditions exist is to develop appropriate techniques and procedures and to follow them rigorously.

Advanced Composites Letters

International Journal of Mechanical Sciences, 2008

... embedded in soil. Doyle and Pavlovic [18] solved the partial differential equation for free v... more ... embedded in soil. Doyle and Pavlovic [18] solved the partial differential equation for free vibration of beams partially attached to elastic foundation using separation of variable method and neglecting shear effect. Catal [19] and ...

Abstract— In this study dimensionless free axial vibration analysis of beam with tip masses is ma... more Abstract— In this study dimensionless free axial vibration analysis of beam with tip masses is made. The tip masses are modeled by concentrated masses at both ends of the beam. The frequency values for the first three vibration modes of the beam are obtained for various values of concentrated masses and presented in the tables. Three I-profile beams are chosen for the numerical analysis. The frequency values for the concentrated masses of zero and infinity are also compared, respectively, with the ones of free, fixed and cantilever beams and nearly the exact values are obtained with negligible error percentages.

fbe.dumlupinar.edu.tr

ÖZET Çerçevelerin dinamik analizinde sıkça kullanılan kabullerden birisi hareket denklemini kat h... more ÖZET Çerçevelerin dinamik analizinde sıkça kullanılan kabullerden birisi hareket denklemini kat hizasında topaklanmış kütleye göre yazmak ve kolonları rijitlik elemanı olarak modellemektir. Ancak gerçekte, kolonlar yayılı kütleye ve rijitliğe sahiptir ve çerçevelerin zeminle bağlantı noktaları, pratikte, dinamik yük sırasında zeminin elastik davranışına bağlı olarak bir miktar dönebilmekte ve ötelenebilmektedir. Bu durumda, çerçevelerin mesnetlerinde dönmeye ve ötelenmeye karşı elastik yaylar kullanılarak, elastik mesnet davranışı modellenebilir. Bu çalışmada, elastik mesnetli Timoshenko kolonu olarak modellenen tek katlı çerçevelerin serbest titreşimi kolonların dönme ataleti de dikkate alınarak incelenmiş ve farklı yay sabitleri için doğal frekanslar elde edilmiştir.

Selçuk Üniversitesi Mühendislik, Bilim ve Teknoloji Dergisi, Feb 3, 2005

ÖZET: Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı n... more ÖZET: Çerçevelerin dinamik analizinde hesap kolaylığı açısından, çerçevelerin zemine bağlandığı noktaların tam ankastre olduğu, kat kütlelerinin kat seviyelerinde topaklandığı, kolonların yayılı kütlesinin ve kayma deformasyonunun ihmal edildiği kabullerine sık rastlanmaktadır. Ancak uygulamada çoğu kez çerçevelerin zemine bağlandığı noktalar, zeminin elastik davranışı nedeni ile bir miktar dönebilmekte ve ötelenebilmektedir. Bu durumda çerçevenin zemine bağlandığı noktaya dönmeye ve ötelenmeye karşı elastik yaylar yerleştirilerek yarı-rijit mesnet davranışı modellenebilir. Bu çalışmada, zemine yarı-rijit bağlı tek katlı çerçevelerin serbest titreşim analizi kolonların yayılı kütlesi ve kayma deformasyonu dikkate alınarak yapılmış ve açısal frekansları elde edilmiştir. Kolon tabanındaki ötelenme ve dönme yay sabiti değerlerindeki artışın frekans değerlerinde meydana getirdiği artma ve kolon üst serbest ucundaki toplu kütlenin ve dönme ataletinin değerlerindeki artışın frekanslarda meydana getirdiği azalma grafiklerle sunulmuştur.

Trakya Üniversitesi Fen Bilimleri Dergisi, Aug 5, 2016