Boş uzaydaki homojen olmayan insansı bünyeye sahip dielektrik cisimden elektromanyetik saçılma
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Dosyalar
Tarih
2023
Yazarlar
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Yayıncı
Bursa Teknik Üniversitesi, Lisansüstü Eğitim Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Günümüzde elektromanyetik saçılma problemleri savunma sanayii, tıp ve daha birçok alanda geniş yer bulmaktadır. Saçılma problemlerini temel alan genel mühendislik konuları kullanılmak üzere olan alanlardaki ihtiyaçlara göre geliştirilmiştir. Bu konuların çözümleri analitik ve sayısal yöntemler kullanılarak elde edilmektedir. Pratik problemlerin tam çözümü analitik yöntemler ile çoğu zaman elde edilememektedir. Bu yüzden bilgisayarların varlığının oluşturduğu kolaylık ile sayısal yöntemler değer kazanmıştır. Bu tez çalışmasında, düzlemsel dalgalar ile aydınlatılan boş uzayda yer alan bir homojen dielektrik cisimden saçılan elektrik alan değerlerinin hesaplanması amaçlanmıştır. Ancak uygulanılan yöntem kolaylıkla homojen olmayan cisimlerden saçılma problemlerine genişletilebilir. Maxwell denklemlerinden Lorentz koşulu altında dyadik Green fonksiyonları yardımıyla elektrik alan integral denklemi (EAİD) elde edilmiştir. Elde edilen elektrik alan integral denkleminde gözlem noktası kaynak noktası ile aynı olduğu durumda üçüncü derece tekillikler (hesaplanması zor noktalar) söz konusudur. Bu çalışmada Green fonksiyonlarından kaynaklanan tekilliklerin çözümü asal değer integralleri kullanılarak yapılmıştır. Asal değer integrali tanımının temel; kaynak noktasının bulunduğu alanın çok küçük hacim olarak ifade edilmesi ve integral sınırlarının bu hacme göre ifade edilmesi ile başlar. Çok küçük hacmin integral sınırları ile çözümlenmesi sonucunda asal değer integralinin çözümüne ulaşılır. Bu çözüm sonucunda ilgili hacmin ortaya çıkarttığı katkı ile oluşan yapının çözümü moment yöntemi (MoM) ile elde edilmiştir. Moment yöntemi ile ayrıklaştırılmış problem sayısal olarak çözüme uygun hale gelmiştir. Modellenen problem bir denklem sistemi oluşturur. Bu denklem sistemi MATLABTM ile kodlanarak çözülmüştür. Bu sayede insan hatalarından kaçınılmış ve sonuca en yaklaşık değerler elde edilmiştir. Çözüm için fiziksel problem küplere modellenmiş ve her küpün içindeki elektrik alanın sabit olduğu kabul edilmiştir. Saçıcı cisim olarak iki model oluşturulmuştur. Bu modeller insansı bir bünyeye benzetilmek üzere seçilmiş geometrik yapılardan ibarettir. İlk örnekte silindir bir blok üzerine yarıçapı silindirden daha küçük olacak şekilde küre, ikinci örnekte ise dikdörtgenler prizmasının üzerine teğet olacak şekilde ve prizmanın kısa kenarına eşit çapa sahip bir küre model olarak seçilmiştir. Her iki modelinde eşit cisim eksen boylarına sahip iken 100,300,500,700 MHz frekanslarda dalga iletilmiştir. İletilen bu dalgaların dielektrik cisimler üzerindeki etkileri incelenmiştir. Bir diğer uygulamada ise farklı cisim eksen boylarında sahip (35,44,50, 55 ve 100 santimetre) ve aynı dielektrik sabitinde modeller oluşturulmuştur. Bu modellerde ise aynı frekans değerlerine sahip dalgalar iletilmiştir. Bu uygulamada ise örneklenen dielektrik cismin farklı hacim/eksen boyu değerlerine sahip iken oluşacak elektrik alan değerleri arasındaki ilişki gözlemlenmiştir. Son olarak yapılan uygulamada ise aynı geometriye sahip ancak farklı dielektrik sabitine sahip cisimlere aynı frekans değerlerindeki dalgalar iletilmiş ancak farklı dielektrik sabiti değerleri uygulanmıştır. Bu son uygulamada ise dielektrik sabiti ve elektrik alan arasındaki oran gözlemlenmiştir. Elde edilen bu sonuçlar neticesinde; elektrik alan-frekans, elektrik alan-dielektrik cisim hacmi ve elektrik alan-dielektrik sabiti arasındaki ilişki incelenmiştir.
Today, electromagnetic scattering problems have a wide place in the defense industry, medicine and many other fields. General engineering topics based on scattering problems are developed according to the needs of the fields to be used. The solutions of these issues are obtained by using analytical and numerical methods. The exact solution of practical problems cannot be obtained with analytical methods most of the time. For this reason, numerical methods have gained value with the convenience created by the existence of computers. In this thesis, it is aimed to calculate the electric field values scattered from a homogeneous dielectric body in the empty space illuminated by planar waves. However, the applied method can be easily extended to scattering problems from inhomogeneous bodies. The electric field integral equation (EAID) was obtained from Maxwell's equations with the help of dyadic Green's functions under the Lorentz condition. In the obtained electric field integral equation, when the observation point is the same as the source point, there are third-degree singularities (points that are difficult to calculate). In this study, the solution of singularities arising from Green's functions is done by using prime value integrals. The basics of the definition of the prime value integral; It starts with expressing the area where the welding point is located as a very small volume and expressing the integral limits according to this volume. As a result of solving the very small volume with the integral limits, the solution of the prime value integral is reached. As a result of this solution, the solution of the structure formed by the contribution of the relevant volume was obtained by the moment method (MoM). The discretized problem with the moment method has become numerically suitable for solution. The modeled problem creates a system of equations. This system of equations was solved by coding with MATLABTM. In this way, human errors were avoided and the most approximate values were obtained. For the solution, the physical problem is modeled into cubes and the electric field inside each cube is assumed to be constant. Two models were created as the scattering body. These models consist of geometrical structures chosen to be likened to a humanoid body. In the first example, a sphere with a radius smaller than the cylinder was chosen on a cylinder block, and in the second example, a sphere with a diameter equal to the short side of the prism and tangential to the rectangular prism was chosen as the model. While both models have equal body axis lengths, waves were transmitted at frequencies of 100,300,500,700 MHz. The effects of these transmitted waves on dielectric bodies were investigated. In another application, models with different body axis lengths (35,44,50, 55 and 100 centimeters) and the same dielectric constant were created. In these models, waves with the same frequency values are transmitted. In this application, the relationship between the electric field values that will occur while the sampled dielectric body has different volume/axis length values has been observed. In the last application, waves with the same frequency values were transmitted to the objects with the same geometry but different dielectric constant, but different dielectric constant values were applied. In this last application, the ratio between the dielectric constant and the electric field has been observed. As a result of these results obtained; The relationship between electric field-frequency, electric field-dielectric body volume and electric field-dielectric constant was investigated.
Today, electromagnetic scattering problems have a wide place in the defense industry, medicine and many other fields. General engineering topics based on scattering problems are developed according to the needs of the fields to be used. The solutions of these issues are obtained by using analytical and numerical methods. The exact solution of practical problems cannot be obtained with analytical methods most of the time. For this reason, numerical methods have gained value with the convenience created by the existence of computers. In this thesis, it is aimed to calculate the electric field values scattered from a homogeneous dielectric body in the empty space illuminated by planar waves. However, the applied method can be easily extended to scattering problems from inhomogeneous bodies. The electric field integral equation (EAID) was obtained from Maxwell's equations with the help of dyadic Green's functions under the Lorentz condition. In the obtained electric field integral equation, when the observation point is the same as the source point, there are third-degree singularities (points that are difficult to calculate). In this study, the solution of singularities arising from Green's functions is done by using prime value integrals. The basics of the definition of the prime value integral; It starts with expressing the area where the welding point is located as a very small volume and expressing the integral limits according to this volume. As a result of solving the very small volume with the integral limits, the solution of the prime value integral is reached. As a result of this solution, the solution of the structure formed by the contribution of the relevant volume was obtained by the moment method (MoM). The discretized problem with the moment method has become numerically suitable for solution. The modeled problem creates a system of equations. This system of equations was solved by coding with MATLABTM. In this way, human errors were avoided and the most approximate values were obtained. For the solution, the physical problem is modeled into cubes and the electric field inside each cube is assumed to be constant. Two models were created as the scattering body. These models consist of geometrical structures chosen to be likened to a humanoid body. In the first example, a sphere with a radius smaller than the cylinder was chosen on a cylinder block, and in the second example, a sphere with a diameter equal to the short side of the prism and tangential to the rectangular prism was chosen as the model. While both models have equal body axis lengths, waves were transmitted at frequencies of 100,300,500,700 MHz. The effects of these transmitted waves on dielectric bodies were investigated. In another application, models with different body axis lengths (35,44,50, 55 and 100 centimeters) and the same dielectric constant were created. In these models, waves with the same frequency values are transmitted. In this application, the relationship between the electric field values that will occur while the sampled dielectric body has different volume/axis length values has been observed. In the last application, waves with the same frequency values were transmitted to the objects with the same geometry but different dielectric constant, but different dielectric constant values were applied. In this last application, the ratio between the dielectric constant and the electric field has been observed. As a result of these results obtained; The relationship between electric field-frequency, electric field-dielectric body volume and electric field-dielectric constant was investigated.
Açıklama
Anahtar Kelimeler
Electromagnetic fields, Elektromanyetik dalgalar, Electromagnetic waves, Elektromanyetik saçılma, Electromagnetic scattering, Elektromanyetik alanlar
