Judul: FRP Compiling Materials and Their Combustion  Waste at UD Wahyu Asih Fiberglass Kebumen, Central Java
Abstrak: The increased use of FRP materials ultimately raises new problems related to the waste produced. One of the shipyards conducts open burning to destroy FRP waste, namely UD Wahyu Asih Fiberglass. The combustion process produces thick and thick black smoke and a strong smell like residue. The combustion does not destroy the fiberglass material to the end but still produces waste in the form of a kind of solid ash from the combustion. This condition shows that fiberglass waste cannot be destroyed through combustion. To be able to destroy FRP waste until it runs out, it is necessary to first study the composition or chemical elements contained in FRP shipbuilding materials. Therefore, the purpose of this study is to describe the type of material and the content of chemical elements and their properties contained in FRP shipbuilding materials at UD Wahyu Asih Fiberglass Shipyard, and calculate the ash content produced from each gram of burned FRP ship material. Data were collected by observation, literature study, and laboratory tests, which were then analyzed descriptively. The results showed that the materials used in making FRP ships include CSM300, WR600, WR800, yukalac 235 series resin, mepoxe catalyst, aerosil, miracle gloss, talc, cobalt napthanate, pigments, and gelcoat. Chemical elements found in FRP materials are hydrogen, sodium, magnesium, calcium, silicon, carbon, oxygen, and cobalt. The amount of ash obtained from the remaining combustion of FRP ship waste is 15.97% per gram of material., Peningkatan penggunaan bahan FRP pada akhirnya menimbulkan permasalahan baru terkait dengan limbah yang dihasilkan. Salah satu galangan melakukan pembakaran secara terbuka untuk memusnahkan limbah FRP, yaitu UD Wahyu Asih Fiberglass. Proses pembakaran tersebut menghasilkan asap hitam pekat dan tebal serta bau yang menyengat seperti bau residu. Pembakaran tersebut tidak memusnahkan material fiberglass hingga habis, akan tetapi masih menghasilkan limbah berupa semacam abu padat sisa pembakaran. Kondisi ini menunjukkan bahwa limbah fiberglass tidak dapat musnah melalui pembakaran. Untuk dapat memusnahkan limbah FRP hingga habis, maka perlu dikaji terlebih dahulu komposisi/unsur kimia yang terkandung di dalam material pembuat kapal FRP. Oleh karena itu, tujuan penelitian ini adalah mendeskripsikan jenis material dan kandungan unsur kimia serta sifatnya yang terkandung dalam material pembuat kapal FRP di Galangan UD Wahyu Asih Fiberglass, dan menghitung kadar abu yang dihasilkan dari setiap gram material kapal FRP yang dibakar. Data dikumpulkan dengan metode observasi, studi literatur, dan uji laboratorium, yang selanjutnya dianalisis secara deskriptif. Hasil penelitian menunjukkan bahwa material yang digunakan dalam membuat kapal FRP meliputi CSM300, WR600, WR800, resin yukalac 235 series, katalis mepoxe, aerosil, miracle gloss, talc, cobalt napthanate, pigmen, dan gelcoat. Unsur kimia yang terdapat pada material FRP adalah hidrogen, natrium, magnesium, kalsium, silikon, karbon, oksigen, dan kobalt. Jumlah abu yang didapatkan dari sisa pembakaran limbah kapal FRP adalah 15,97% per gram material.
Keyword: limbah, fiberglass, FRP, kadar abu, residu

Judul: Strength of FRP Hull Construction of Small Shipyard UD  Wahyu Asih Fiberglass, Kebumen-Central Java
Abstrak: Galangan kapal rakyat UD Wahyu Asih Fiberglass sudah banyak memproduksi kapal FRP. Namun, pembuatan kapal tersebut tidak mengikuti ketentuan yang ditetapkan oleh Biro Klasifikasi Indonesia (BKI) dan hanya berdasarkan pengetahuan otodidak dari pemilik usaha. Selain itu, galangan kapal ini belum dapat membuktikan kekuatan konstruksi lambung kapal FRP yang dibuatnya secara ilmiah. Tujuan penelitian ini adalah untuk mendeskripsikan proses pembuatan konstruksi kapal dan material yang digunakan serta mendapatkan nilai kekuatan uji tarik, uji tekan, dan modulus elastisitas untuk konstruksi lambung kapal FRP. Data dikumpulkan dengan studi literatur, observasi lapang, pembuatan spesimen, serta pengujian kekuatan konstruksi (uji tarik, uji tekan, dan modulus elastisitas), dilanjutkan dengan analisis deskriptif komparatif. Hasil penelitian menunjukkan bahwa material yang digunakan dalam membuat kapal FRP meliputi resin yukalac 235, gelcoat yukalac g-123 t-ex, CSM300, WR600, WR800, katalis mepoxe, cobalt napthanate, pyrogenic silica, talc, pewarna matapel unipol, miracle gloss, minyak tanah, ivory rubbing compound, dan kit (compound). Adapun proses pembuatan kapal FRP meliputi proses pembuatan laminasi dan proses finishing dengan menggunakan metode hand lay up. Meskipun kekuatan tarik sudah memenuhi nilai minimum yang ditetapkan oleh BKI, namun kekuatan tekan dan modulus elastisitas belum memenuhi nilai minimum yang ditetapkan oleh BKI., Small shipyards UD Wahyu Asih Fiberglass have produced many FRP boats. However, the construction of these boats doesn't follow the regulations set by the Indonesian Classification Bureau (BKI) and is only based on the owner's self-taught knowledge. Additionally, these shipyards haven't been able to scientifically prove the structural strength of their FRP boat hulls. The aim of this research is to describe the process of constructing a boat and the materials used as well as to obtain the values of tensile strength, compressive strength, and modulus of elasticity for FRP boat hull construction. Data was collected through literature studies, field observations, specimen making, and construction strength testing (tensile test, compressive test, and modulus of elasticity), followed by descriptive comparative analysis. The materials used in making FRP boats include yukalac 235 resin, yukalac g-123 t-ex gelcoat, CSM300, WR600, WR800, mepoxe catalyst, cobalt napthanate, pyrogenic silica, talc, matapel unipol dye, miracle gloss, kerosene, ivory rubbing compound, and kit (compound). The process of making FRP boats includes the laminated structures and finishing processes using the hand lay-up method. Although the tensile strength meets the minimum values set by BKI, the compressive strength and elastic modulus don't yet meet the minimum values set by BKI.
Keyword: manufacturing process, tensile and compressive strength, UD Wahyu Asih Fiberglass, material, modulus of elasticity

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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