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Makina temellerinde deprem etkisi

Makina temellerinde deprem etkisi

##### Dosyalar

##### Tarih

1995

##### Yazarlar

Altun, Selim

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Makina temellerinin tasarım ve projelendirilmesinde statik yüklerin yanında dinamik yüklerin de gözönüne alınması gerekmektedir. Sistemin statik yüklere göre dayanımının yanında, dinamik yüklerin oluşturduğu titreşim frekansları ve genliklerin belirli sınırlar içinde tutulması temel amaçtır. Makina - temel sistemi genel olarak simetrik olarak tasarlanır. Mevcut yabancı yayınlarda da genellikle simetrik sistemlerin inceleme ve araştırılması yapılmıştır. Yine aynı yayınlarda bu sistemler üzerine deprem etkisinin pek fazla incelenmediği görülmüştür. Bu çalışmada simetrik blok tipi makina - temel - mesnetler sisteminin hem rijit bağlı hem de makina ile temel arasında yay olması halinde serbest ve zorlanmış titreşimleri incelenerek bu sistemler üzerine depremin etkisi araştırılmıştır. Ayrıca konunun daha iyi anlaşılabilmesi için sayısal uygulamalar yapılmıştır. Uygulamalarda Erzincan 1992 depremi verileri kullanılarak sisteme depremin etkisi incelenmiştir.

The most important principle of the design of a machine foundation is certainly to take into consideration the dynamic loads together with static loads. The machine foundation has to be designed in a way that it should have an adequate strength to resist to the static and dynamic loads of the system. These loads produced by machine constitute the additional inertial force. During the design of machine foundation, there are two most important aims. First is to assure that the amplitudes of the foundation for forced vibrations dont pass over the permissible limits and, second is to assure the required difference between the frequency of the operating machine and the natural frequency for the free vibration. The different elastic support members can be used to assure this condition. In the present literature related to the design of the machine - foundation - supports system is generally assumed to be symmetric with respect to two planes which are perpendicular each other in plane. In this case, the total weight of the system W passes through the centroid of the base plane and through the elastic center of elements of the support. However, the effect of the earthquake on these systems can be seen not to investigate sufficiently in the most literature. The subject of this study is the investigation of the free and forced vibrations of the massive machine - foundation - supports system with damping which is symmetric with respect to two plane that are perpendicular each other in plane. In addition, the effects of the earthquake on these systems are investigated. In present study, a symmetric case is considered and the general equations of motion of the system are written and, free and forced vibration are examined. The system has, in general, six degrees of freedom and, therefore, six natural frequencies (one corresponding to each mode of vibrations). Three of them are translations along the three principal axes (x, y and z ) and the other three are rotations about the three axes. The following assumptions related to the system used in derivation of the governing equations of the problem. 1- The centroid of the base plane and the elastic center of elements of the support coincides. 2- The supporting elements of the system are on the same horizontal plane and they are of distance s from the gravitational center. 3- The material is linear elastic and, translations and rotations are very small and they can be neglected. 4- The ground motion takes place along the horizontal axes and affects the supports at the same time and intensity. 5- The elements of supports of the system are independent from each other and without mass and, are linear elastic. 6- In the case that the effects of the earthquake are considered, rotations are neglected to obtain a solution. A symmetric system is shown in following figure. The following notations are used in figure and equations. M : The mass of the system, S : The center of gravity of the system, Kx,Ky,Kz : The stiffness influence coefficients of the support elements. (translations along the three principal axes x, y and z respectively), X : The circular natural frequency of the system, © : The circular frequency of the machine, cx,cy,cz : The damping coefficients of the support elements. (translations along the three principal axes x, y and z respectively) s : Distance between the gravity center of the system S and the elastic center, x,y,z Translation of the gravity center of the system along the principal axes x, y and z respectively, ?x»+¥»$ y»Tz Rotations of the gravity center of the system about the principal axes x, y and z respectively. ¥? Machine Foundation 7ZKS ^V0^ I V02/: fc/2: So y/A\ >x ? Rotation Spring HWH &/4 :k ?y/4 C^ Ki/4 MAM ^?c y/2. y'4 Foundation Machine =v "y/2 Ks/4 ^ Kx/4 h/WM ? K I A. y/4 The general equations of motion are written by using d'Alembert's Principle. When the system is completely symmetric and only couple plane is considered, there are three equations of motion. One is the equations of motion of translation along vertical axis. The others are the coupled equations of horizontal translations and rocking motion. After the forward in section 1., information about theory of vibration and structural dynamics is outlined in section 2. Furthermore, determination of stiffness, damping parameters and mass is given in this section. Free and forced vibrations of support motion with or without damping are investigated. In section 3., design of the machine foundations is outlined. The types of machine and machine foundation are presented in this section. Information about the methods of design of the machine foundation is given. Furthermore permissible amplitude limits for machine foundation are presented. In section 4., the general equation of motion for the massive machine - foundation -supports system with damping having the complete symmetry are obtained. Using assumption, positive direction of motions and forces and determination of spring and damping forces of supports are given before obtaining the general equation. In section 5., the massive machine - foundation - supports system with damping having the complete symmetry is investigated in only couple x - z plane and, the natural frequencies and the amplitudes of the forced vibrations of the system are obtained. " half space theory " is used when solving the equation of motion of the system. When the system is symmetric and there are only the translational springs between the machine and foundation in one direction, the equation of motion for massive machine - foundation - supports system with damping are obtained in section 6. It is assume that the springs between the machine and the foundation permit only the translation at the direction of the x - axis. The natural frequencies for free vibrations and the amplitudes of the forced vibrations of such a system are noted. In section 7., the effects of the earthquake on the machine - foundation - supports system mentioned in section 4 - 5 are examined. It is assume to be subjected to the earthquake - excitation along the direction of the x - axis. In this case, expressions of amplitudes are obtained. Furthermore, information about Erzincan 1992 Earthquake is outlined. At the numerical solutions, the rigid machine foundation system and the springs between the machine and foundation and the effects of the earthquake ground motion excitation on two type machine foundation system are shown. In the earthquake excitation case, the numerical integration are used in order to solve the equation of motion. Furthermore, the effect of the variations of stiffness influence coefficients on amplitudes of the machine - foundation system are shown.

The most important principle of the design of a machine foundation is certainly to take into consideration the dynamic loads together with static loads. The machine foundation has to be designed in a way that it should have an adequate strength to resist to the static and dynamic loads of the system. These loads produced by machine constitute the additional inertial force. During the design of machine foundation, there are two most important aims. First is to assure that the amplitudes of the foundation for forced vibrations dont pass over the permissible limits and, second is to assure the required difference between the frequency of the operating machine and the natural frequency for the free vibration. The different elastic support members can be used to assure this condition. In the present literature related to the design of the machine - foundation - supports system is generally assumed to be symmetric with respect to two planes which are perpendicular each other in plane. In this case, the total weight of the system W passes through the centroid of the base plane and through the elastic center of elements of the support. However, the effect of the earthquake on these systems can be seen not to investigate sufficiently in the most literature. The subject of this study is the investigation of the free and forced vibrations of the massive machine - foundation - supports system with damping which is symmetric with respect to two plane that are perpendicular each other in plane. In addition, the effects of the earthquake on these systems are investigated. In present study, a symmetric case is considered and the general equations of motion of the system are written and, free and forced vibration are examined. The system has, in general, six degrees of freedom and, therefore, six natural frequencies (one corresponding to each mode of vibrations). Three of them are translations along the three principal axes (x, y and z ) and the other three are rotations about the three axes. The following assumptions related to the system used in derivation of the governing equations of the problem. 1- The centroid of the base plane and the elastic center of elements of the support coincides. 2- The supporting elements of the system are on the same horizontal plane and they are of distance s from the gravitational center. 3- The material is linear elastic and, translations and rotations are very small and they can be neglected. 4- The ground motion takes place along the horizontal axes and affects the supports at the same time and intensity. 5- The elements of supports of the system are independent from each other and without mass and, are linear elastic. 6- In the case that the effects of the earthquake are considered, rotations are neglected to obtain a solution. A symmetric system is shown in following figure. The following notations are used in figure and equations. M : The mass of the system, S : The center of gravity of the system, Kx,Ky,Kz : The stiffness influence coefficients of the support elements. (translations along the three principal axes x, y and z respectively), X : The circular natural frequency of the system, © : The circular frequency of the machine, cx,cy,cz : The damping coefficients of the support elements. (translations along the three principal axes x, y and z respectively) s : Distance between the gravity center of the system S and the elastic center, x,y,z Translation of the gravity center of the system along the principal axes x, y and z respectively, ?x»+¥»$ y»Tz Rotations of the gravity center of the system about the principal axes x, y and z respectively. ¥? Machine Foundation 7ZKS ^V0^ I V02/: fc/2: So y/A\ >x ? Rotation Spring HWH &/4 :k ?y/4 C^ Ki/4 MAM ^?c y/2. y'4 Foundation Machine =v "y/2 Ks/4 ^ Kx/4 h/WM ? K I A. y/4 The general equations of motion are written by using d'Alembert's Principle. When the system is completely symmetric and only couple plane is considered, there are three equations of motion. One is the equations of motion of translation along vertical axis. The others are the coupled equations of horizontal translations and rocking motion. After the forward in section 1., information about theory of vibration and structural dynamics is outlined in section 2. Furthermore, determination of stiffness, damping parameters and mass is given in this section. Free and forced vibrations of support motion with or without damping are investigated. In section 3., design of the machine foundations is outlined. The types of machine and machine foundation are presented in this section. Information about the methods of design of the machine foundation is given. Furthermore permissible amplitude limits for machine foundation are presented. In section 4., the general equation of motion for the massive machine - foundation -supports system with damping having the complete symmetry are obtained. Using assumption, positive direction of motions and forces and determination of spring and damping forces of supports are given before obtaining the general equation. In section 5., the massive machine - foundation - supports system with damping having the complete symmetry is investigated in only couple x - z plane and, the natural frequencies and the amplitudes of the forced vibrations of the system are obtained. " half space theory " is used when solving the equation of motion of the system. When the system is symmetric and there are only the translational springs between the machine and foundation in one direction, the equation of motion for massive machine - foundation - supports system with damping are obtained in section 6. It is assume that the springs between the machine and the foundation permit only the translation at the direction of the x - axis. The natural frequencies for free vibrations and the amplitudes of the forced vibrations of such a system are noted. In section 7., the effects of the earthquake on the machine - foundation - supports system mentioned in section 4 - 5 are examined. It is assume to be subjected to the earthquake - excitation along the direction of the x - axis. In this case, expressions of amplitudes are obtained. Furthermore, information about Erzincan 1992 Earthquake is outlined. At the numerical solutions, the rigid machine foundation system and the springs between the machine and foundation and the effects of the earthquake ground motion excitation on two type machine foundation system are shown. In the earthquake excitation case, the numerical integration are used in order to solve the equation of motion. Furthermore, the effect of the variations of stiffness influence coefficients on amplitudes of the machine - foundation system are shown.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1995

##### Anahtar kelimeler

Deprem analizi,
Makineler,
Titreşim,
Earthquake analysis,
Machinery,
Vibration