AEROFRACTURELASTICITY ANALYSIS ON UNIDIRECTIONAL COMPOSITE PLATE BY MEANS OF FINITE ELEMENT METHOD AND DOUBLET LATTICE METHOD THESIS Submitted as a partial fulfillment for the degree of Magister Teknik from Institut Teknologi Bandung Written by FAISAL AKMAL RAMADHAN NIM: 23623009 (Master’s Program in Aerospace Engineering) INSTITUT TEKNOLOGI BANDUNG JUNI 2024 ii ABSTRACT AEROFRACTURELASTICITY ANALYSIS ON UNIDIRECTIONAL COMPOSITE PLATE BY MEANS OF FINITE ELEMENT METHOD AND DOUBLET LATTICE METHOD Written by Faisal Akmal Ramadhan NIM: 23623009 (Master’s Program in Aerospace Engineering) In the recent decades, composite materials have become key element to construct advanced structure, i.e., aircraft structure. The present work is aimed to provide insight on how fiber orientation and crack existence in dynamic characteristics and aeroelastic instability. A plate-like wing made of unidirectional composite is investigated. Different fiber orientations and configuration with various crack lengths and locations are observed. Modal analyses to obtain the dynamic characteristics, i.e., mode shapes and natural frequencies, are conducted by means of Finite Element Method (FEM). The Modal Assurance Criteria (MAC) is used to quantitatively evaluate the similarity of the mode shapes for different fiber orientations. In addition, the aeroleastic analysis conducted through the implementation of P-K Method. The dynamic characteristics represented with the MAC results depict that the order of the first six vibration modes, i.e., bending and torsion modes, does not altered by the change of orientation. However, the fiber orientation does affect the value of natural frequencies. Furthermore, the existence of crack could reduce the natural frequencies significantly. Based on the MAC evaluation, as the crack length increases, the order of the mode shapes changes and the natural frequency of a particular mode decreases. For the fundamental modes, first bending and torsion, the natural frequencies decrease by as much as 20% as the crack located near the root. For higher order modes, i.e., second and third bending, the natural frequencies decrease the most when the crack located near the antinode of the respective mode. Based on these results, there is very likely that coupling of two or more modes occur as the frequencies become closer. This argument fortified with the results obtained from the aeroelastic analysis. The change of fiber orientation affects the value of divergence and critical flutter speed. There are several orientations that experienced increase or decrease relative to the undamaged model. Furthermore, similar to the dynamic characteristics results, the variation of crack location does not affect the divergence nor flutter speed whereas the crack length does. Keyword: Composite; Dynamic Characteristics; Aeroelastic Analysis, Flutter, Mode Shape; Natural Frequency; Finite Element Method (FEM); Modal Assurance Criterion (MAC) iii ABSTRAK ANALISIS AEROFRAKTURELASTISITAS PADA PELAT KOMPOSIT SEARAH MENGGUNAKAN METODE ELEMEN HINGGA DAN METODE DOUBLET LATTICE Oleh Faisal Akmal Ramadhan NIM: 23623009 (Program Studi Teknik Dirgantara) Dalam beberapa dekade terakhir, komposit menjadi elemen penting dalam struktur yang kompleks, seperti struktur pesawat terbang. Penelitian ini bertujuan untuk memperoleh pemahaman bagaimana orientasi serat dan retak mempengaruhi karakteristik dinamik dan ketidakstabilan aeroelastik. Sebuah sayap berbentuk pelat yang terbuat dari komposit searah dianalisis. Berbagai orientasi serat dan konfigurasi dengan berbagai panjang dan lokasi retak diamati. Analisis modal untuk memperoleh karakteristik dinamik, yaitu modus getar dan frekuensi alami, dilakukan dengan menggunakan Metode Elemen Hingga (MEH). Modal Assurance Criterion (MAC) digunakan untuk mengevaluasi secara kuantitatif kesamaan bentuk modus getar untuk berbagai orientasi serat. Selain itu, analisis aeroelastik dilakukan melalui penerapan Metode P-K. Karakteristik dinamik yang direpresentasikan dengan hasil MAC menunjukkan bahwa urutan enam mode getaran pertama, yaitu modus bending dan torsi, tidak berubah oleh perubahan orientasi. Namun, orientasi serat mempengaruhi nilai frekuensi natural. Selain itu, keberadaan retak dapat mengurangi frekuensi alami secara signifikan. Berdasarkan evaluasi MAC, seiring bertambahnya panjang retak, urutan modus getar berubah dan frekuensi alami suatu modus tertentu menurun. Untuk modus yang fundamental, yaitu bending pertama dan torsi, frekuensi alami menurun hingga 20% ketika retak berada di dekat pangkal sayap. Untuk modus orde lebih tinggi, yaitu bending kedua dan ketiga, frekuensi alami menurun paling banyak ketika retak berada di dekat antinode dari modus tersebut. Berdasarkan hasil ini, sangat mungkin terjadi percampuran dua atau lebih modus ketika frekuensi menjadi lebih dekat. Argumen ini diperkuat dengan hasil yang diperoleh dari analisis aeroelastik. Perubahan orientasi serat mempengaruhi nilai kecepatan divergence dan flutter. Ada beberapa orientasi yang mengalami peningkatan atau penurunan relatif terhadap model tanpa retak. Selain itu, serupa dengan hasil karakteristik dinamik, variasi lokasi retak tidak mempengaruhi kecepatan divergence maupun flutter, sementara panjang retak mempengaruhinya. Kata kunci: Komposit; Karakteristik Dinamik; Analisis Aeroelastik; Modus Getar; Frekuensi Alami; Finite Element Method (FEM); Modal Assurance Criterion (MAC) iv AEROFRACTURE ANALYSIS ON UNIDIRECTIONAL COMPOSITE PLATE BY MEANS OF FINITE ELEMENT METHOD AND DOUBLET LATTICE METHOD Written by Faisal Akmal Ramadhan NIM: 23623009 (Master’s Program in Aerospace Engineering) Institut Teknologi Bandung Approve Advisory Team Bandung,of June 2024 Advisor 1 ______________________ Dr. Djarot Widagdo (NIP 19700927 200604 1007) Advisor 2 ______________________ Prof. Dr. Ir. Leonardo Gunawan (NIP 19621111 198910 1001) Advisor 3 ______________________ Rianto Adhy Sasongko, S.T., M.Sc., Ph.D. (NIP 19740215 199903 1002) v THESIS USAGE GUIDLINES This master’s Thesis, while unpublished, is registered and available at the Library of Institut Teknologi Bandung and is open to the public under the condition that the copyright remains with the author, following the HaKI regulations applicable at Institut Teknologi Bandung. Bibliographic references are allowed to be recorded, but any quotations or summaries may only be made with the author's permission and must be accompanied by scientific standards for citing the source. Citations of this Thesis research can be written in Indonesian as follows: Ramadhan, F.A. (2024): Analisis Aerofraktur pada Pelat Komposit Unidirectional Menggunakan Metode Elemen Hingga dan Doublet Lattice Method, Tesis Program Magister, Institut Teknologi Bandung. and in English as follows: Ramadhan, F.A. (2024): Aerofracture Analysis on Unidirectional Composite Plate by Means of Finite Element Method and Doublet Lattice Method, master’s Thesis, Institut Teknologi Bandung. Reproduction or publication of any part or the entire thesis must be authorized by the Dean of the Graduate School, Institut Teknologi Bandung. vi ACKNOWLEDGEMENT I am grateful to Allah for enabling me to complete my thesis and reach the end of my undergraduate studies at Institut Teknologi Bandung. Many individuals have supported me throughout this journey, and while it is impossible to name them all here, I would like to express my heartfelt thanks to my parents for encouraging me to pursue my passion for aerospace engineering, my younger siblings for reminding me of the importance of family, and my extended family for their unwavering support.