Unit-8
Mechanical Vibrations
Q 1) Explain difference between free vibration and forced vibration
A 1)
Free Vibrations Forced Vibrations
1 | Free vibrations are produced when a body is disturbed from its equilibrium position and released. | Forced vibrations are produced by an external periodic force. |
2 | Frequency of free vibrations depends on the body and is called its natural frequency. | The frequency of forced vibrations is equal to that of the external periodic force. |
Q 2) Describe Oscillating Motions?
A 2)
- The study of vibrations is concerned with the oscillating motion of elastic bodies and the force associated with them.
- All bodies possessing mass and elasticity are capable of vibrations.
- Most engineering machines and structures experience vibrations to some degree and their design generally requires consideration of their oscillatory motions.
- Oscillatory systems can be broadly characterized as linear or nonlinear.
Linear systems: The principle of superposition holds. Mathematical technique available for their analysis is well developed.
Nonlinear systems: The principle of superposition doesn't hold. The technique for the analysis of the nonlinear systems are under development (or less well known) and difficult to apply.
- All systems tend to become nonlinear with increasing amplitudes of oscillations.
- There are two general classes of vibrations– free and forced.
Q 3) Explain free vibrations
A 3)
Free vibration takes place when a system oscillates under the action of forces inherent in the system itself due to initial disturbance, and when the externally applied forces are absent.
The system under free vibration will vibrate at one or more of its natural frequencies, which are properties of the dynamical system, established by its mass and stiffness distribution.
Q 4) Explain Forced vibrations
A 4)
- The vibration that takes place under the excitation of external forces is called forced vibration.
- If excitation is harmonic, the system is forced to vibrate at excitation frequency. If the frequencies of excitation coincide with one of the natural frequencies of the system, a condition of resonance is encountered and dangerously large oscillations may result, which results in failure of major structures, i.e., bridges, buildings, or airplane wings etc.
- Thus calculation of natural frequencies is of major importance in the study of vibrations.
- Because of friction & other resistances vibrating systems are subjected to damping to some degree due to dissipation of energy.
- Damping has very little effect on natural frequency of the system, and hence the calculations for natural frequencies are generally made on the basis of no damping.
- Damping is of great importance in limiting the amplitude of oscillation at resonance.
Q 5) Explain Degrees of Freedom (d.o.f)
A 5)
- The number of independent co-ordinates required to describe the motion of a system is termed as degrees of freedom.
For example
Particle - 3 dof (positions)
Rigid body-6 dof (3-positions and 3-orientations)
Continuous elastic body - infinite dof (three positions to each particle of the body).
- If part of such continuous elastic bodies may be assumed to be rigid (or lumped) and the system may be considered to be dynamically equivalent to one having finite dof (or lumped mass systems).
- Large number of vibration problems can be analysed with sufficient accuracy by reducing the system to one having a few dof.
Q 6) Write Vibration measurement terminology
A 6)
Peak value: Indicates the maximum response of a vibrating part. It also places a limitation on the “rattle space” requirement.
Average value: Indicates a steady or static value (somewhat like the DC level of an electrical current) and it is defined as
Where x(t) is the displacement, and T is the time span (for example time period)
Q 7) Write Examples of resonance?
A 7)
- Sympathetic vibrations of pendulums
- Resonance in machine parts
- Resonance in a stretched string and sound box of musical instruments and sonometer
- Resonance in air column and tuning fork
- Resonance in a bridge
- Resonance in radio and TV receivers
Q.8. Define damped vibrations
A. 8
The vibrations of a body whose amplitude goes on reducing over every cycle of vibrations are known as damped vibrations. This is due to the fact that a certain amount of energy possessed by the vibrating body is always dissipated in overcoming frictional resistance to the motion.
Q 9) What is dry friction damper?
A 9)
The dry-friction damper consists of a shock-absorbing mass with a flexible link with the frame, dry friction shoes coupled to the mass, and an expansion spring to provide the necessary amount of dry friction. The damper is designed to reduce normal pressure on the contact surfaces when there is a change in direction of the absorbing mass by incorporating an inertia mass which has a flexible link with the shoes. During oscillation in a system, inertia mass undergoes various accelerations and the greater the acceleration on the inertia mass the smaller is the effort with which shoes are pressed against the friction surfaces. With a sufficiently rigid link the acceleration of the inertia mass is virtually equal to the acceleration of the absorbing mass which means that with maximum acceleration of the absorbing mass the dry friction force will be the least.
Q 10) What is meant by logarithmic decrement?
A 10)
Logarithmic decrement method is used to measure damping in time domain In this method, the free vibration displacement amplitude history of a system to an impulse is measured and recorded. Logarithmic decrement is the natural logarithmic value of the ratio of two adjacent peak values of displacement in free decay vibration.
Q 11) Define the flexibility and stiffness influence coefficients.
A 11)
Flexibility: It is defining as the design that can adapt any change when any external change occurs. Stiffness influence coefficients: It is defined as when the system is unconstrained the stiffness matrix is positive semi definite hence a constant is used to show the stiffness of system is knows as stiffness influence coefficient denoted as ‘K’.
Q 12) What is Rayleigh’s Principle?
A 12)
Rayleigh principle: It is stated that the distribution of the potential and kinetic energies of conservation, elastic system in the fundamental mode of vibration is such that the frequency is minimum.
Q 13) How many natural frequencies does a continuous system have?
A 13)
A continuous system which is under a vibration have only one natural frequency which create the resonance if the frequency of system matches with natural frequency.
Q 14) What is the difference between a vibration absorber and a vibration isolator?
A 14)
Difference between a vibration absorber and a vibration isolator:
A vibration absorber is a device that can absorb the vibration and make it’s intensity low while an isolator is device that can keep apart the vibration between two surface or system in contact in which one is vibrate continuously.
Unit-8
Mechanical Vibrations
Q 1) Explain difference between free vibration and forced vibration
A 1)
Free Vibrations Forced Vibrations
1 | Free vibrations are produced when a body is disturbed from its equilibrium position and released. | Forced vibrations are produced by an external periodic force. |
2 | Frequency of free vibrations depends on the body and is called its natural frequency. | The frequency of forced vibrations is equal to that of the external periodic force. |
Q 2) Describe Oscillating Motions?
A 2)
- The study of vibrations is concerned with the oscillating motion of elastic bodies and the force associated with them.
- All bodies possessing mass and elasticity are capable of vibrations.
- Most engineering machines and structures experience vibrations to some degree and their design generally requires consideration of their oscillatory motions.
- Oscillatory systems can be broadly characterized as linear or nonlinear.
Linear systems: The principle of superposition holds. Mathematical technique available for their analysis is well developed.
Nonlinear systems: The principle of superposition doesn't hold. The technique for the analysis of the nonlinear systems are under development (or less well known) and difficult to apply.
- All systems tend to become nonlinear with increasing amplitudes of oscillations.
- There are two general classes of vibrations– free and forced.
Q 3) Explain free vibrations
A 3)
Free vibration takes place when a system oscillates under the action of forces inherent in the system itself due to initial disturbance, and when the externally applied forces are absent.
The system under free vibration will vibrate at one or more of its natural frequencies, which are properties of the dynamical system, established by its mass and stiffness distribution.
Q 4) Explain Forced vibrations
A 4)
- The vibration that takes place under the excitation of external forces is called forced vibration.
- If excitation is harmonic, the system is forced to vibrate at excitation frequency. If the frequencies of excitation coincide with one of the natural frequencies of the system, a condition of resonance is encountered and dangerously large oscillations may result, which results in failure of major structures, i.e., bridges, buildings, or airplane wings etc.
- Thus calculation of natural frequencies is of major importance in the study of vibrations.
- Because of friction & other resistances vibrating systems are subjected to damping to some degree due to dissipation of energy.
- Damping has very little effect on natural frequency of the system, and hence the calculations for natural frequencies are generally made on the basis of no damping.
- Damping is of great importance in limiting the amplitude of oscillation at resonance.
Q 5) Explain Degrees of Freedom (d.o.f)
A 5)
- The number of independent co-ordinates required to describe the motion of a system is termed as degrees of freedom.
For example
Particle - 3 dof (positions)
Rigid body-6 dof (3-positions and 3-orientations)
Continuous elastic body - infinite dof (three positions to each particle of the body).
- If part of such continuous elastic bodies may be assumed to be rigid (or lumped) and the system may be considered to be dynamically equivalent to one having finite dof (or lumped mass systems).
- Large number of vibration problems can be analysed with sufficient accuracy by reducing the system to one having a few dof.
Q 6) Write Vibration measurement terminology
A 6)
Peak value: Indicates the maximum response of a vibrating part. It also places a limitation on the “rattle space” requirement.
Average value: Indicates a steady or static value (somewhat like the DC level of an electrical current) and it is defined as
Where x(t) is the displacement, and T is the time span (for example time period)
Q 7) Write Examples of resonance?
A 7)
- Sympathetic vibrations of pendulums
- Resonance in machine parts
- Resonance in a stretched string and sound box of musical instruments and sonometer
- Resonance in air column and tuning fork
- Resonance in a bridge
- Resonance in radio and TV receivers
Q.8. Define damped vibrations
A. 8
The vibrations of a body whose amplitude goes on reducing over every cycle of vibrations are known as damped vibrations. This is due to the fact that a certain amount of energy possessed by the vibrating body is always dissipated in overcoming frictional resistance to the motion.
Q 9) What is dry friction damper?
A 9)
The dry-friction damper consists of a shock-absorbing mass with a flexible link with the frame, dry friction shoes coupled to the mass, and an expansion spring to provide the necessary amount of dry friction. The damper is designed to reduce normal pressure on the contact surfaces when there is a change in direction of the absorbing mass by incorporating an inertia mass which has a flexible link with the shoes. During oscillation in a system, inertia mass undergoes various accelerations and the greater the acceleration on the inertia mass the smaller is the effort with which shoes are pressed against the friction surfaces. With a sufficiently rigid link the acceleration of the inertia mass is virtually equal to the acceleration of the absorbing mass which means that with maximum acceleration of the absorbing mass the dry friction force will be the least.
Q 10) What is meant by logarithmic decrement?
A 10)
Logarithmic decrement method is used to measure damping in time domain In this method, the free vibration displacement amplitude history of a system to an impulse is measured and recorded. Logarithmic decrement is the natural logarithmic value of the ratio of two adjacent peak values of displacement in free decay vibration.
Q 11) Define the flexibility and stiffness influence coefficients.
A 11)
Flexibility: It is defining as the design that can adapt any change when any external change occurs. Stiffness influence coefficients: It is defined as when the system is unconstrained the stiffness matrix is positive semi definite hence a constant is used to show the stiffness of system is knows as stiffness influence coefficient denoted as ‘K’.
Q 12) What is Rayleigh’s Principle?
A 12)
Rayleigh principle: It is stated that the distribution of the potential and kinetic energies of conservation, elastic system in the fundamental mode of vibration is such that the frequency is minimum.
Q 13) How many natural frequencies does a continuous system have?
A 13)
A continuous system which is under a vibration have only one natural frequency which create the resonance if the frequency of system matches with natural frequency.
Q 14) What is the difference between a vibration absorber and a vibration isolator?
A 14)
Difference between a vibration absorber and a vibration isolator:
A vibration absorber is a device that can absorb the vibration and make it’s intensity low while an isolator is device that can keep apart the vibration between two surface or system in contact in which one is vibrate continuously.
