Fonksiyonel derecelenmiş malzeme ve değişken kesitli silindirik ve silindirik olmayan viskoelastik helisel çubukların dinamik analizi
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Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Adana Alparslan Türkeş Bilim Ve Teknoloji Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tezde değişken kesit ve fonksiyonel derecelenmiş malzemeye sahip silindirik ve silindirik olmayan viskoelastik helisel çubukların dinamik davranışı incelenmiştir. Helisel çubukların davranışını idare eden denklemler elde edilirken Timoshenko kiriş teorisi kullanılmıştır. Elde edilen diferansiyel denklemlerde eksenel ve kayma deformasyonları dikkate alınmıştır. Laplace uzayında sistemin dinamik davranışını idare eden adi diferansiyel denklemler taşıma matrisi yöntemi kullanılarak çözülmüştür. Viskoelastik çözümlerde, elastik-viskoelastik analojisi kullanılarak elastik malzeme sabitleri Laplace uzayındaki kompleks karşılıkları ile değiştirilmiştir. Kelvin tipi viskoelastik model kullanılmıştır. Laplace uzayında elde edilen sonuçlar Durbin'in sayısal ters Laplace dönüşümü yardımıyla zaman uzayına dönüştürülmüştür. Silindirik ve silindirik olmayan helisel çubuklarda, kesit değişim parametresi, malzeme değişim parametresi, helis sarım sayısı, helis yükselme açısı ve sönüm oranının dinamik davranışa etkileri araştırılmıştır. Önerilen yöntemle elde edilen sonuçlar ile literatür ve sonlu elemanlar yöntemine dayalı ANSYS programından elde edilen sonuçların uyumlu olduğu görülmüştür.
In this thesis, dynamic behaviour of cylindrical and non-cylindrical viscoelastic helical rods with functionally graded material and variable cross-section was investigated. The differential equations governing the dynamic behaviour of the helical rods were derived by the Timoshenko beam theory. Axial and shear deformations were taken into consideration in the obtained differential equations. Ordinary differential equations were then solved in the Laplace domain by the transfer matrix method. For the viscoelastic solutions, elastic constants were replaced with their viscoelastic counterparts in Laplace domain by using the correspondence principle. Kelvin viscoelastic model was used for the solutions. Obtained results were transferred from Laplace domain to the time domain by the Modified Durbin's numerical inverse Laplace transform algorithm. The effects of section variation, material variation, active number of turns, helix pitch angle, helix radius ratio and damping ratio on the dynamic behaviour of cylindrical and non-cylindrical helical rods were investigated. It can be seen that obtained results with proposed model are in good agreement with the ones available in the literature and the ones acquired from finite element based program ANSYS.
In this thesis, dynamic behaviour of cylindrical and non-cylindrical viscoelastic helical rods with functionally graded material and variable cross-section was investigated. The differential equations governing the dynamic behaviour of the helical rods were derived by the Timoshenko beam theory. Axial and shear deformations were taken into consideration in the obtained differential equations. Ordinary differential equations were then solved in the Laplace domain by the transfer matrix method. For the viscoelastic solutions, elastic constants were replaced with their viscoelastic counterparts in Laplace domain by using the correspondence principle. Kelvin viscoelastic model was used for the solutions. Obtained results were transferred from Laplace domain to the time domain by the Modified Durbin's numerical inverse Laplace transform algorithm. The effects of section variation, material variation, active number of turns, helix pitch angle, helix radius ratio and damping ratio on the dynamic behaviour of cylindrical and non-cylindrical helical rods were investigated. It can be seen that obtained results with proposed model are in good agreement with the ones available in the literature and the ones acquired from finite element based program ANSYS.
Açıklama
Lisansüstü Eğitim Enstitüsü, İnşaat Mühendisliği Ana Bilim Dalı
Anahtar Kelimeler
İnşaat Mühendisliği, Civil Engineering
