Owing to their flexibility, the components of structures and machinery are capable of relative motion when subjected to internal or external forces. If such motion is oscillatory in nature, the motion is referred to as vibration. Although applications exist where vibration performs a useful function, vibration in ships is undesirable as it tends to accelerate the wearing of parts such as bearings and gears, create excessive noise and transmit significant forces and/or motion to accommodation, working and recreation spaces as well as to other equipment.

Humans may be exposed to vibrations transmitted to the whole body or to particular parts of the body, such as the head or limbs. Designers should primarily be concerned with vibrations transmitted to the body through supporting surfaces such as the buttocks or feet. Research shows that mechanical vibration interferes with work quality and productivity, safety, health, comfort, and causes motion sickness. The literature also shows that vibration may modify crewmember perception (e.g., reading text and instruments, depth perception), influence task control movements (e.g., tactile sense, head/hand movements, manual tracking) and lead to impairment of speech. These factors may result in increased crewmember reaction/response times and possibility of human error.

There are many different sources of vibration in ships, such as propeller and stern wake, main engine and other machinery, wave loads and environmental effects. Due to the complexity of these sources of excitation and of the structural configuration of ships, harmful vibration problems still occur even though vibration prediction techniques have developed rapidly and are well established through the use of Finite Element Method software. Continuing research activities have shown that carrying out vibration control is a tend as well as requirement for ships and offshore structures. Also in many other engineering branches it is well known that the proper vibration control in the design process is necessary a safe and satisfactory working and living environment as well as to avoid abnormal wear and tear on the machinery and structures.

Since vibration and noise disturb the surrounding medium, their levels should be low also from reason, particularly in submarines. The appropriately reduced acoustic emission and electromagnetic signature of submarines decrease a vessel’s susceptibility to naval influence mines and the probability of being detected by underwater and airborne surveillance system.

A vibration design prognosis, based on Finite Element Models of the full ship, is normally carried out early in the design stage. However, there are some areas and new

Developments where not only experience and sophisticated but also appropriate knowledge of vibration theory is required. The contents of the following pages may be regarded only as initial chapters in treatise on vibration theory which includes also such topics not touched upon here as nonlinear vibration, random vibration, numerical calculation methods, measurement techniques, etc. It is hoped that the present textbook will inspire the reader to further studies in this field.

1. INTRODUCTION

2. VIBRATION AS DYNAMIC PROCESS

   1. Newton’s laws of motion

   2. Plane motion of rigid bodies

   3. Rotation of a rigid body about a fixed point

   4. Equations of motion of a rigid body

   5. Second – order ordinary differential equations with constant coefficients

      1. Homogeneous equations

      2. Nonhomogeneous equations

      3. Initial conditions and complete solution

Review questions

3. FUNDAMENTALS OF VIBRATION

   1. Basic concepts of vibration

   2. Classification of vibration

   3. Parameters of vibration

   4. Vibration analysis procedure

Review questions

4. FREE VIBRATION OF UNDAMPED SINGLE DEGREE OF FREEDOM SYSTEMS

   1. Simple harmonic oscillation

   2. Free vibration of an undamped torsional system

   3. Energy methods

   4. Stability conditions

Review questions

5. FREE VIBRATION OF DAMPED SINGLE DEGREE OF FREEDOM SYSTEMS

   1. Free vibration with viscous damping

   2. Torsional system with viscous damping

   3. Free vibration with Coulomb damping

   4. Torsional system with Coulomb damping

Review questions

6. FORCED VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEMS

   1. Harmonically excited vibration of an undamped system

   2. Harmonically excited vibration of an damped system

      1. Response of a damped system under harmonic force

      2. Response of a damped system under rotating unbalance

      3. Whirling of rotating shafts

      4. Response of a viscously damped system under the harmonic motion of the base

      5. Vibration isolation

      6. Forced vibration of a system whit Coulomb damping

   3. Self – excited and flow – induced vibrations

   4. Response under a nonperiodic force

Review questions

7. VIBRATION OF MULTIDEGREE OF FREEDOM SYSTEMS

   1. Two degree of freedom systems

      1. Equations of motion for forced vibration

      2. Free vibration of an undamped system

      3. Response of an undamped system under harmonic force

   2. Mulitdegree of freedom systems

      1. Equations of motion

      2. Eigenvalue problem

      3. Harmonically excited vibration of undamped system

      4. Forced vibration of undamped system using modal analysis

      5. Forced vibration of viscously damped system

   3. Analogy between mechanical and electric systems

Review questions

8. VIBRATION OF CONTINUOUS SYSTEMS

   1. Modeling of vibrating systems

   2. Longitudinal vibration of a rod

   3. Torsional vibration of a shaft or rod

   4. Lateral vibrations of beams

Review questions

9. VIBRATION IN SHIPS

   1. Explanatory notes

      1. Effects of vibration

      2. Environmental factors

   2. Main excitation sources

      1. Wave – induced vibration

      2. Propeller – induced vibration

      3. Vibration of piston engines

      4. Shafting vibration

   3. Vibration criteria

Review questions

10. CONCLUDING REMARKS

References

APPENDIX