# TMR4182 - Marine Dynamics

### Examination arrangement

Examination arrangement: Portfolio assessment

Evaluation Weighting Duration Grade deviation Examination aids
Exercises 20/100
School exam 80/100 4 hours C

### Course content

Free and forced vibration of single degree of freedom systems and small multi-DOF systems. Formulation of the equation of motion for simple systems. Eigenvalue and eigenvector calculations for MDOF systems. Vibration isolation. Rigid body motion - resilient mounting and floating body in waves, including coupled motions. Eigenfrequency-calculation of beams, wires, and rods using the differential equation energy method. Modelling of continuous systems using generalized co-ordinates. Calculation of forced response in time and frequency domain, modal superposition. Numerical time-domain integration methods. Irregular waves and wave spectra, short-term and long-term statistics of waves. Stochastic analysis of structural responses, including fatigue calculation and extreme response estimation.

### Learning outcome

At the end of the course, the student will be able to:

- formulate the equations of motion for simple SDOF and MDOF systems

- explain how stiffness, damping and inertia forces will influence response for varying load frequency for SDOF systems, and provide examples of sources of stiffness, damping, inertia, and external loads in the marine environment

- apply frequency-domain methods, Laplace transforms, state-space formulation, Runge-Kutta’s method, or constant average acceleration to find the dynamic response of SDOF systems subjected to different kinds of forcing

- explain the concepts of natural frequencies, mode shapes, and orthogonal eigenmodes for MDOF systems

- apply frequency-domain methods to find the response of 2DOF systems to harmonic forcing

- establish and solve the differential equations for free vibration of beams, tensioned strings, and rods in axial or torsional vibration

- transfer simple continuous systems to single degree of freedom systems by use of generalized coordinates, and understand the limitations in accuracy when using approximate mode shapes

- apply modal analysis to find the response of continuous systems

- account for that a rigid body is a model of stiff body whose motions are fully described by 6 DOFs that follow from a generalized version of Newton’s second law

- understand the relation between reality and linear potential flow theory, and formulate the linearized boundary value problem (BVP) for a rigid body floating in waves

- derive the linear, coupled 6DOF equations of motion for a rigid body floating in waves, and explain the physical meaning of the different terms (added mass, damping, restoring and wave excitation)

- account for limitations and application areas of the Morison equation, both for the inertia term and the viscous term

- explain physically and mathematically how irregular waves are described using the wave spectrum for both long-crested and short-crested waves.

- explain the main properties of standard wave spectra (Pierson-Moskowitz type spectra, JONSWAP spectrum) including standard directional spectra

- define and explain the meaning of the spectral moments and wave parameters such as significant wave height, spectral peak period, mean zero-crossing period etc.

- explain the physical meaning of a stationary narrow- band Gaussian wave process and to apply the Rayleigh distribution to calculate short term statistics of waves including the statistics of the largest wave heights

- explain the meaning of long term statistics based on using the Rayleigh distribution together with joint frequency tables/scatter diagrams; also how scatter diagrams are used to determine e.g Hm0, Tp corresponding to a return period of 100 years.

- find transfer functions for simple systems and use these to describe stochastic response for fatigue analysis and extreme response estimation based on short term and long term statistics.

### Learning methods and activities

Lectures and exercises, including laboratory and computational problem sets. A given number of exercises must be accepted to be allowed to meet for the final written exam.

• Exercises

### Further on evaluation

Portfolio assessment is the basis for the grade in the course. The portfolio includes a digital exam (80%) and graded exercises (20%). The results for the parts are given in %-scores, while the entire portfolio is assigned a letter grade. 10 exercises must be approved in order to take the exam.  Lectures are in English. If there is a re-sit examination, the examination form may change to oral. For a re-take of an examination, all assessments during the course must be re-taken.

### Specific conditions

Compulsory activities from previous semester may be approved by the department.

### Required previous knowledge

Basic courses on fluid dynamics, structural mechanics, mathematics (second order differential equations), physics and mathematical statistics.

### Course materials

Marine dynamics coursepack

More on the course

No

Facts

Version: 1
Credits:  7.5 SP
Study level: Third-year courses, level III

Coursework

Term no.: 1
Teaching semester:  AUTUMN 2021

Language of instruction: English

Location: Trondheim

Subject area(s)
• Technological subjects
Contact information
Course coordinator: Lecturer(s):

Department of Marine Technology

# Examination

#### Examination arrangement: Portfolio assessment

Term Status code Evaluation Weighting Examination aids Date Time Digital exam
Autumn ORD School exam 80/100 2021-12-06 15:00
Autumn ORD Exercises 20/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

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