Unit 4 Forced Vibration
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This document discusses forced vibration, which occurs when a body vibrates under the influence of an external force. There are three types of external excitation forces: periodic, impulsive, and random. For a spring mass system undergoing harmonic disturbances, the amplitude and maximum amplitude of forced vibration are given by formulas involving the excited force, phase lag, and angular velocity. Phase lag and magnification factor are also discussed. Forced vibration due to unbalance and support motion are described. Transmissibility and vibration isolation are then defined and different types are explained.
Unit 4 Forced Vibration
- 1. Unit IV FORCED VIBRATION DYNAMICS OF MACHINES FORCED VIBRATION DOM - B.K.P 1 B.K.Parrthipan, M.E., M.B.A., (Ph.D)., Assistant Professor / Mechanical Engineering Kamaraj College of Engineering and Technology.
- 2. Forced Vibration When the body vibrates under the influence of external force, then the body is said to be under forced vibration. Example:Example: 1. Ringing of electrical bell 2. Vibrations of air compressors
- 3. Types of External Excitation Three types of external forces applied are (i) Periodic forces (ii) Impulsive type of forces, and (iii) Random forces
- 4. Harmonic Disturbances (Spring mass system) The amplitude of the forced vibration is given by Fo is the excited force and ᵩis the phase lag
- 5. Harmonic Disturbances (Spring mass system) The maximum amplitude of the forced vibration is given by ω is the angular velocity of the excited force or applied force.
- 6. Harmonic Disturbances (Spring mass system) The amplitude of the forced vibration is given by ᵩFo is the excited force and ᵩis the phase lag The maximum amplitude of the forced vibration is given by
- 7. 1. Phase Lag φ As the displacement takes place after applying force, the displacement vector lags the force vector by some angle φ. This angle is known Harmonic Disturbances (Spring mass system) vector by some angle φ. This angle is known as phase lag. Mathematically, where r is the frequency ratio
- 8. Harmonic Disturbances (Spring mass system) 2. Magnification factor or Dynamic Magnifier The ratio of maximum displacement of the forced vibration (Xmax) to the static deflection (X ) due to static force and it is denoted by(Xo) due to static force and it is denoted by M.F.
- 9. Harmonic Disturbances (Spring mass system) It is clear that the magnification factor depends up on (i) The ratio of circular frequencies and (ii) The damping factor
- 10. 1. Frequency response curve A curve drawn between magnification factor and frequency ratio is known as frequency response curve. Harmonic Disturbances – Characteristics Curve response curve.
- 11. 2. Phase - frequency response curve A curve drawn between phase angle and frequency ratio is known as phase frequency response curve. Harmonic Disturbances – Characteristics Curve response curve.
- 12. Disturbance caused by unbalance Almost in all rotating and reciprocating machinery like an electric motor, a turbine, an IC engine, etc have some amount of unbalanced force left in them even afterunbalanced force left in them even after correcting their unbalance on precision balancing machines. This unbalance produces the exciting force in a machine.
- 13. Disturbance caused by unbalance The amplitude of the forced vibration is given by mu - unbalanced mass, and e - eccentricitymu - unbalanced mass, and e - eccentricity The maximum amplitude of the forced vibration is given by
- 14. Phase Lag φ As the displacement takes place after applying force, the displacement vector lags the force vector by some angle φ. This angle is known as phase lag. Disturbance caused by unbalance as phase lag. Mathematically, where r is the frequency ratio
- 15. Forced Vibration due to the excitation of the support (Support Motion) • Absolute amplitude The amplitude of the forced vibration is given by where Y is the amplitude
- 16. Forced Vibration due to the excitation of the support (Support Motion) • Relative amplitude In many cases, it is useful to know the response of the system relative to a moving system. The steady state relative amplitude of the forcedThe steady state relative amplitude of the forced vibration is given by where z is the relative motion of the mass with respect to support
- 17. Transmissibility • Transmissibility is a measure of the effectiveness of the vibration isolating material. • Types 1. Force Transmissibility1. Force Transmissibility 2. Motion Transmissibility
- 18. Force Transmissibility • Force Transmissibility is defined as the ratio of the force transmitted (FT) to the force applied on the system (FO). • This ratio is also known as isolating factor.• This ratio is also known as isolating factor. • It is denoted by epsilon.
- 20. Motion Transmissibility • Motion transmissibility is defined as the ratio of absolute amplitude of the mass (FT) to the base (or support) base excitation amplitute (Y). • This ratio is also known as Amplitude• This ratio is also known as Amplitude Transmissibility. • It is denoted by ϵA
- 21. Vibration Isolation • The process of reducing the vibrations of machines and hence reducing the transmitted force to the foundation using vibration isolating materials is called as vibrationisolating materials is called as vibration isolation. • The materials used for vibration isolation are (i) Rubber (ii) Cork and (iii) Metallic Springs
- 22. Types of Isolation 1. Isolation of forces Vibrations produced in unbalanced machines should be isolated from the foundations so that the adjoining structure is not set into vibrations. This type of isolation is known as force isolation. 2. Isolation of motions The unbalanced machines are isolated from their foundations so that there should not be any damage either to the machine or the foundations. This type of isolation is known as motion isolation.