Post on 23-Nov-2015
Development of an Optimal Floating Breakwater Using Numerical Computation Method
Sistem Pengendalian (4)Marine System EngineeringNaval Architecture DepartmentEngineering Faculty, Hasanuddin UniversityFaisal MAHMUDDIN
f.mahmuddin@gmail.comThank you very much Prof. Kashiwagi for the chance.Good morning everyone and thank you very much also for coming to my presentation.Today I will present my dissertation which is about DesignI guess everyone has seen or knows about floating breakwater which can be seen in these photos.
1Inverse Laplace TransformReferensi : Invers Transformasi Laplace, Febrizal MT Even though the analysis was verified using hydrodynamical relations shown in the previous slide, it is also important to conduct experiment to further confirmed the analysis.Besides to check the numerical results, the experiment could also tell us how different the numerical results to measured results since the anaylis is based on potential flow.2Definisi Inverse Laplace Transform3
Pecahan Partial4
Aturan Pecahan Partial5
Contoh (1)6
Contoh (2)7
Contoh (3)8
Contoh (3)9
Sistem Penyimpanan Cairan (1)10
Aturan Cover Up11
Contoh (1)12
Contoh (3)13
Tugas14
Jawaban Tugas15
Transformasi LaplaceEven though the analysis was verified using hydrodynamical relations shown in the previous slide, it is also important to conduct experiment to further confirmed the analysis.Besides to check the numerical results, the experiment could also tell us how different the numerical results to measured results since the anaylis is based on potential flow.16Aplikasi Transformasi Laplace17Persamaan differensial atau model matematis dapat digunakan untuk merepresentasikan semua atau sebagian sistem kontrolUntuk mengetahui response dari sebuah sistem, persamaan differensialnya harus diselesaikan Karena waktu biasanya merupakan variabel bebas maka solusi biasanya terdiri atas solusi steady state dan transienMetode matematika klasik biasanya menciptakan solusi yang rumit untuk persamaan differensial linear diatas orde satuTransformasi Laplace dapat digunakan untuk menyederhanakan persamaan dan menentukan solusi dalam dua bentuk yang dibutuhkanSolusi yang didapatkan kemudian diinverse ke bentuk aslinya
17Untuk Apa Transformasi18Transformasi digunakan untuk mentransformasi masalah kepada sebuah masalah yang lebih mudah diselesaikan kemudian menggunakan inverse dari transformasi tersebut untuk menyelesaikan masalah aslinya
Time Domain VS Frekuensi Domain19
t adalah variabel realf(t) adalah fungsi real
Time Domain
s adl variabel komplex
F(s) adl fungsi dengan nilai komplex
Frequency Domain
LLaplace TransformL-1InverseLaplace TransformTR. Laplace untuk Penyelesaian ODE20Differential Equation
Laplace TransformAlgebraic Equation
Solution of theAlgebraic Equation Inverse Laplace transformSolution of the Differential Equation
Definisi Transformasi Laplace21
Sufficient conditions for existence of the Laplace transform Contoh Fungsi Orde Pangkat22
Contoh (1)23unit step
Contoh (2)24Shifted Step
Integral by Parts25
Contoh (3)26Ramp
Contoh (4)27Exponential Function
Contoh (5)28
sine Function Contoh (6)29cosine Function
Properti Transformasi Laplace30Addition
Properties of Laplace TransformMultiplication by exponential
Properties of Laplace TransformExamples Multiplication by exponential
Useful Identities
Examplesin Function
Examplecosine Function
Laplace TransformInverse Laplace TransformProperties of Laplace TransformMultiplication by time
Properties of Laplace Transform
Properties of Laplace TransformIntegration
Properties of Laplace TransformDelay
Properties of Laplace Transform
Slope =ALProperties of Laplace Transform4Slope =ALLSlope =A__A LSlope =AL=