Dinamik titreşim sönümleyicilerdeki katmanlı kiriş tipi yapıların titreşim analizi = Vibration analysis of layered beam type structures in dynamic vibration absorbers

Abstract

Bu tez çalışmasında, katmanlı-kiriş-tipi dinamik titreşim sönümleyicilerin titreşim sönümleme davranışları araştırılmıştır. Katmanlı kiriş yapısının ve uç kütlenin dönme ataletinin, dinamik titreşim sönümleyicisi (DTS)'nin verimliliği üzerindeki etkileri analitik ve deneysel olarak incelenmiştir. Katmanlı-kiriş tipi DTS'nin matematiksel modeli oluşturulurken, kiriş boyunun kiriş kalınlığına oranı (L/h)>10 olduğu için Euler-Bernoulli kiriş teorisine göre kabuller yapılmış ve Hamilton prensibi kullanılarak hareket denklemi elde edilmiştir. Uç kütlenin dönme ataleti, D'alambert Prensibi kullanılarak hareket denklemlerine dahil edilmiştir. Ayrıca, katmanlı kirişlerin eşdeğer eğilme rijitliği de elde edilerek hareket denklemine dahil edilmiştir. Son olarak, elde edilen sınır koşulları hareket denklemine dahil edilerek katmanlı-kiriş tipi DTS'nin frekans denklemi elde edilmiş ve bu frekans denklemi çözülerek DTS'ye ait doğal frekanslar elde edilmiştir. Bu şekilde DTS'lerin sönümleme yaptığı frekans aralığı / frekanslar analitik olarak belirlenmiştir. DTS'lerin doğal frekansları farklı kütle oranları, katman malzemeleri, bağlantı noktası ile uç kütlenin ağırlık merkezi arasındaki mesafeler ve diğer ilgili faktörler dahil olmak üzere fiziksel ve geometrik parametrelerin farklı kombinasyonları için hesaplanmıştır. Ayrıca, uç kütlenin dönme ataletinin, çeşitli kiriş katmanı malzemelerinin, kiriş katmanlarının sayısının ve değişen kütle oranlarının DTS'nin doğal frekansları üzerindeki etkileri de sunulmuştur. Elde edilen bulgular, uç kütlenin dönme ataletindeki artışın DTS'nin düşük frekansları üzerinde daha önemli bir etkisi olduğunu göstermiştir. Ayrıca beklenildiği gibi katman kalınlığının arttırılmasının DTS'nin frekanslarını arttırdığını göstermektedir. Analitik ve deneysel sonuçları elde edilen DTS'lerin, titreşim sönümleme verimliliklerinin araştırılması amacıyla, elde edilen DTS'ler, kütle-yaydan oluşan ana bir sisteme eklenmiştir. Ana sisteme eklenen DTS'ler, modal sarsıcının bağlı olduğu bir tabla üzerine yerleştirilerek, sisteme belirli genlik ve frekanslarda zorlayıcı kuvvet uygulanmıştır. Uygulanan kuvvet harmonik sinüs fonksiyonu olarak ayarlanmıştır. DTS eklenmemiş ve DTS eklenmiş sistemde meydana gelen genlikler elde edilmiştir. DTS ekli yapıya ait titreşim genlikleri, sarsıcı zeminine, ana kütle üzerine ve DTS uç kütlesine ivmeölçerler bağlanarak elde edilmiştir. Böylelikle uç kütlenin dönme ataletinin, farklı katman malzemelerinin, kiriş katmanlarının sayısının ve değişen kütle oranlarının DTS'nin titreşim sönümleme verimliliği üzerindeki etkileri deneysel olarak elde edilmiştir. Çalışmanın sonuçları, katmanlı kirişli yapıların enerji toplayıcıları, mikromekanik sensörler ve kiriş tipi dinamik titreşim sönümleyiciler dahil olmak üzere birçok mühendislik yapılarının tasarımına katkıda bulunacaktır.

Engineering structures are exposed to various dynamic forces, depending on their place of use. Some of these forces may be wind and earthquakes affecting buildings, unbalanced forces that may occur in an internal combustion engine, or centrifugal forces due to the unbalanced mass in a rotating shaft. When structures and machines are exposed to a harmonic type of external force, unwanted vibrations occur in the structural elements. In particular, as a result of the coincidence of the frequency of the force acting on the structure and the natural frequency of the structure, a phenomenon known as resonance occurs, and the vibration amplitudes of the structure increase to maximum levels. As a result, the structure may be damaged in a short time, and undesirable results may occur. In order to avoid these negative consequences, reduce the vibrations of the structure, and ensure that the structures can perform its functions safely, researchers and engineers have been working on vibration analysis and vibration control of structures for years. In order to dampen the vibrations of structures, the idea of adding an additional system tuned to the frequency of the force acting on the structure was put forward, and the concept of a dynamic vibration absorber (DVA) emerged. A dynamic vibration absorber, also known as a tuned mass damper, is a mechanical device added to the structure to reduce the vibration of the structure. Traditional DVAs consist of a secondary mass-spring and damping element added to the main structure and are frequently used in passive vibration damping applications. A DVA tuned to the resonance frequency of the structure protects the structure against forces that may affect the structure at the resonance frequency. A DVA tuned to the frequency at which the vibration of the structure is desired to be suppressed absorbs the energy coming from the structure and reduces the vibrations of the structure at that frequency. The vibration-damping performance of a DVA generally depends on three parameters. These are the ratio of the DVA mass to the main system mass, the frequency ratio between the DVA and the main mass, and the DVA damping ratio. For a good DVA design, these three parameters must be chosen well. With the rapid development of science and technology, new structures, materials, and technologies have become popular and applied to DVAs. Various types of DVA have emerged and studies have been conducted on the usability of continuous systems such as DVA. In this thesis study, the usability of beam-type structures, which are continuous systems, as DVA was investigated. The vibration-damping behavior of multilayer beam-type DVAs was studied. The effects of the layered beam structure and the rotational inertia of the end masses on the efficiency of the DVA were investigated analytically and experimentally. This thesis study consists of 5 chapters. In the introduction section (Part 1), descriptive information about DVAs is given and the working principle of DVA is tried to be explained. The usage areas of DVAs in engineering structures are explained and their application areas are shown. A comprehensive literature review has been made and the studies on DVAs so far are presented in a systematic order and according to subject areas. At the end of the literature review, studies on the use of beam-type structures as DVA were mentioned. At the end of the introduction section, the purpose and importance of the thesis study are stated and the innovative aspect of the study is emphasized. In the second part of the thesis, mathematical modeling of the considered system and the DVA added to the system was made. First of all, theoretical information about forced vibrations in undamped and damped systems is given. Then, information about the mathematical modeling of DVAs is given. An explanation was made about the use of beam-type structures as DVA and the equations of motion of the beams were obtained. While creating the mathematical model of the layered beam type DVA, since the ratio of the beam length to the beam thickness (L/h) is >10, assumptions were made according to the Euler-Bernoulli beam theory, and the equation of motion was obtained using the Hamilton principle. In obtaining the equation of motion, the rotational inertia of the end mass was included in the equations of motion using the D'alambert Principle. Additionally, the equivalent bending stiffness of the layered beams was obtained and included in the equation of motion. By including the boundary conditions of the system in the equation of motion, the frequency equation of the multi-layered-beam type DVA was obtained, and by solving this frequency equation, the natural frequencies of the DVA were obtained. In this way, the frequency range/frequencies that DVAs dampen were determined analytically. In the third chapter of the thesis, information about experimental studies is given. First of all, the concepts of modal analysis and experimental modal analysis are explained and the basic theoretical concepts in vibration analysis are explained. Information about the equipment required to obtain the modal parameters (natural frequencies, mode shapes, and damping ratios) of a structure is given and the points to be considered in vibration measurement are emphasized. Then, information is given about the beam materials and end masses from which the layered beam DVAs are formed, and the way of creating the layered beam DVAs is explained. Information is given about the experimental setup established to measure the natural frequencies of the obtained multi-layered beam DVAs, and the features of the equipment used during vibration measurement are explained. Then, the forced vibration experimental setup created to measure the vibration-damping performance of DVAs is explained in detail. DVAs added to the main system were placed on a table to which the modal shaker was connected, and coercive force was applied to the system at certain amplitudes and frequencies. The applied force was set as a harmonic sine function. The amplitudes occurring in the system without DVA and with DVA were obtained. Vibration amplitudes of the DVA-attached structure were obtained by connecting accelerometers to the main mass ground, the main mass, and the DVA end mass. Thus, the effect of the rotational inertia of the tip mass, different layer materials, the number of beam layers, and varying mass ratios on the vibration-damping efficiency of DVA has been experimentally obtained. At the end of the section, information is given about the compression test and the test device used to measure the spring constant in the system. In the 4th chapter of the thesis, the analytical and experimental findings are given and explained. The natural frequencies of DVAs have been calculated analytically for different combinations of physical and geometric parameters, including different mass ratios, layer materials, distances between the junction and the center of the tip mass, and other relevant factors. Additionally, the effects of the rotational inertia of the tip mass, various beam layer materials, the number of beam layers, and varying mass ratios on the natural frequencies of the DVA are also presented. The findings showed that the increase in the rotational inertia of the tip mass has a more significant effect on the lower frequencies of the DVA. It also shows that, as expected, increasing the layer thickness increases the frequencies of DVA. In the 5th chapter of the thesis, the conclusions that can be drawn from the study are included; various suggestions have been made to guide future studies. The results of the study will contribute to the design of many engineering structures, including energy harvesters of layered beam structures, micromechanical sensors, and beam-type DVAs.