Viskoelastik Mazlemelerin Karekterizasyonu ve Viskoelastik Malzemeli Yapıların Modellenmesi

Abstract

Çoğu zaman arzu edilmeyen titreşim, makina mühendislerinin başlıca problemlerinden biridir. Makinaların düzgün çalışması, kullanıcıya ve çevreye konfor sağlaması için genellikle makinalardan kaynaklanan titreşim ve gürültünün ortadan kaldırılması arzu edilmektedir. Ancak çoğu zaman titreşimleri ortadan tamamen kaldırmak mümkün olmamakta, rezonans genliklerini azaltabilmek için sönüm malzemeleri sıkça kullanılmaktadır. Sönüm malzemeleri çeşitli mekanik ve fiziksel özelliklere sahip olabilir. Doğru uygulama ve kullanım şartları için sönüm malzemelerinin özelliklerinin iyi bilinmesine ve tasarım yapılırken incelenecek modellere iyi şekilde yansıtılmasına ihtiyaç duyulmaktadır. Bu tez çalışmasında çeşitli sönüm malzemelerinin farklı yapısal uygulamalar üzerindeki etkisi incelenmiştir. İlk olarak tezin amacı özetlenmiş ve literatürde var olan çalışmalar hakkında bilgi verilmiştir. İkinci sırada titreşim hareketi ve sönüme dair teorik bilgiler, daha sonra sönüm özelliği yüksek viskoelastik malzemelerin dinamik davranışı hakkında bilgiler sunulmuştur. Devamında tek serbestlik dereceli sistemlerde titreşim parametrelerinin nasıl belirlendiği açıklanmıştır. Analiz metodları olan Yarı-güç, Daire uydurma ve Çizgi uydurma yöntemleri açıklanmış, daha sonra sönüm malzemesi özelliklerini belirlemek için sıkça kullanılan bir yöntem olan Oberst kiriş yöntemi anlatılmış, dikkat edilmesi gereken tedbirler ve malzeme özelliklerine dair hesaplamalar verilmiştir. İki farklı sönüm malzemesinin karakterizasyonuna yönelik olarak çalışmalar yapılmış, tek tarafı sönüm malzemeli çubuk, çift tarafı sönüm malzemeli çubuk ve iki metal çubuk arasına sönüm malzemesi konularak oluşturulan numuneler için çeşitli frekans çözünürlüklerinde ölçümler yapılmıştır. Daha sonra bu ölçümlerden üç farklı analiz yöntemiyle elde edilen değerler sonuç olarak verilmiştir. Buna ek olarak, sönüm parametrelerinin değerlerini belirlerken frekans çözünürlüğünün etkisi, modal analiz yönteminin etkisi ve manyetik tahrik altındaki uzunluğun etkisi incelenmiştir. Numuneler için en uygun değerler seçilerek, sönüm malzemelerinin özellikleri hesaplanmıştır. Daha sonra bu malzemelere sahip yapıların sonlu elemanlar yardımıyla modellenmesi yapılmıştır. Öncelikle Oberst test düzeneğinde test edilen yapılar modellenerek eldeki deney sonuçlarıyla karşılaştırılmıştır. Sonrasında, biraz daha karmaşık geometriye sahip L şeklinde plakalar üzerine sönüm malzemesi yapıştırılarak elde edilen yapılar için Modal Test yapılmış, elde edilen sonuçlar sonlu elemanlar ile oluşturulan model sonuçlarıyla mukayese edilmiştir. Son olarak bu tez çalışması sonucunda ulaşılan sonuçlar bulgular değerlendirilmiş tezin çıkarımlarından bahsedilmiştir. Gelecekte yapılabilecek çalışmalar hakkında öneriler sunulmuştur.

Vibration, which is unwanted oscillations in many applications, is one of the main problems for mechanical engineering. For quiet and comfortable operations of many machines, it is desirable to eliminate vibrations. However, it is not quite possible to avoid the structural vibrations completely even though damping treatments are used to reduce structure-borne vibrations in many applications. Different damping materials have different mechanical and physical properties. It is essential that appropriate material should be chosen for individual applications for maximum benefit. For many damping applications, viscoelastic materials are used in practice. Yet, determination of the elastic and damping properties of these materials is quite difficult in the sense that the identified results may contain high degree of uncertainty. One of the aims of the this thesis is to identify material properties with a high level of accuracy. It is also aimed to model structures with viscoelastic materials so as to estimate the dynamic behavior of such structures. First, a literature survey is given about published work on the characterization of viscoelastic materials as well as composites that have viscoelastic materials. After that, the theoretical background for basic mechanical vibration is given. The single degree of freedom system, which is the simplest vibration model, is considered and the theoretical formulations for free- and forced-vibrations of undamped and damped (viscous and hysteretic) systems are summarized. Then, some information about the behaviors of viscoelastic materials are presented. The models which are used for the representation of the characters of damping materials are summarized, including the models called Standard Linear Model and Generalized Standard Model. As explained, one of the best ways of describing the elastic and damping properties of viscoelastic materials is the use of the complex modulus approach. Hysteresis loops, energy dissipation, the relation between moduli, and the relation between harmonic and transient response are described. Furthermore, the effects of environmental factors such as temperature, frequency, cyclic dynamic strain, static preloading, etc. on damping materials are explained. Estimation of the properties of viscoelastic materials is one of the main subjects of this thesis and the classical method named as Oberst Beam Method is used for this purpose. The characterization of viscoelastic materials using the Oberst Beam Method based on non-contact excitation and response measurements is revisited in this study. At the beginning of the third chapter, specimen preparations including bare beams, one side damped (free-layered) beams, both side damped (free-layered), and sandwich (constrained layered) beams are explained. Precautions are given and formulations that are used for determining material properties are presented. After that, analysis methods including half-power, circle-fit and line-fit methods are summarized. Experiments are then run for the characterization of two types of viscoelastic materials using random excitation within a frequency range up to 2.0 kHz. The length of test samples is selected as suggested by relevant standards. The length of the beam section exposed to the electromagnetic field is selected based on the recommendations presented in previous studies. The most appropriate test parameters, such as windowing, averaging, minimizing electromagnetic effects, etc, are chosen so as to minimize the noise level in the signal and to get the most reliable measurements. In order to determine other signal processing parameters such as frequency resolution, the method of system identification, and the effect of the specimen length in magnetic excitation, a large number of FRFs are measured using several samples under various conditions. For the first damping material, a steel beam, two 'identical' one-sided (free-layered) damped beams, a both-sided (free-layered) damped beam and a few sandwiched (constrained-layered) beams are tested. For the second damping material, a one-sided beam and two sandwiched beams are tested. The FRF measurements are conducted at several frequency resolutions. The so called half-power, circle-fit, and line-fit methods are used to extract the modal parameters from measured FRFs. Once the suitable frequency resolution and analyzing method are chosen, the effects of magnetic excitation are determined. Three sets of FRF measurements at each frequency resolution are conducted for each test sample. The individual sets of FRFs are analyzed using the aforementioned three methods. The effect of frequency resolution is found to be very critical when damping levels are to be identified. Therefore, the effects of frequency resolution and the modal analysis method on identified modal loss factors are investigated in detail. Overall, the average values of the modal loss factors of a bare (steel) beam, one-sided damped beam, a both-sided damped beam and sandwiched beam are determined by analysing the measured FRFs using three modal analysis methods for several frequency resolution values. It is noted that, in general, higher loss factors are obtained when the frequency resolution values are higher (coarser). It is also found that the stiffening effect of magnetic excitation affects the natural frequencies, however it does not change the modal loss factors. The natural frequencies increase as the length in magnetic excitation increases. It is also noted that the adverse effect of magnetic excitation decreases as the mode number increases. After the investigations for making reliable FRF measurements, optimum parameters are selected and the natural frequencies and modal loss factors determined from measured FRFs of the beams are used for identification of the material properties. Young's modulus and damping levels (loss factors) of the damping materials corresponding to the individual vibration modes are then extracted from free-layered specimens. In a similar way, shear modulus and damping levels of the damping materials are extracted from the constrained layered specimens. It is found that obtaining the material properties using free-layered specimens is relatively easier and more reliable than doing so for constrained layered specimens. The last part of the thesis, chapter 5, deals with modeling and analyzing structures with viscoelastic materials. The finite element (FE) approach is used for this purpose, and as software, FINES and ABAQUS programs are used. Firstly, models for specimens tested in Oberst Beam Method are developed. For representing more complex structures, various L-shapes plates including bare plate, free layered patch plate and constrained layered patch plate are modelled using FINES and ABAQUS. For validation of the FE results, L-shaped plates are also created and modal tests are performed on them with a modal hammer and accelerometer in order to get experimental modal parameters. Once modal test results are obtained, comparisons are made between FE and experimental results. It is seen that there is a good correlation between FE and test results for bare and free-layered specimens. However, the correlation for the constrained layered case is found to be poor. Finally, results are discussed and some conclusions are made. Also, some suggestions are made for future studies.