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Longitudinal and Transverse Vibrations

Values of load for the various types of beams and under various load conditions.

- Value of load for Cantilever beam with a point load at the free end
- Value of load for Cantilever beam with a uniformly distributed load
- Value of load for fixed beam with a central point load
- Value of load for fixed beam with a uniformly distributed load
- Value of load for fixed beam with an eccentric point load
- Value of load for simply supported beam with a central point load
- Value of load for simply supported beam with a uniformly distributed load
- Value of load for simply supported beam with an eccentric point load

Critical or Whirling Speed of a Shaft

- Additional deflection of centre of gravity of the rotor in terms of natural circular frequency
- Additional deflection of centre of gravity of the rotor in terms of whirling speed
- Additional deflection of centre of gravity of the rotor when the shaft starts rotating
- Centrifugal force acting radially outwards, causing the shaft to deflect
- Critical or Whirling speed in r.p.s
- Critical or Whirling speed in terms of static deflection
- Critical or whirling speed in terms of stiffness of shaft
- Force resisting the additional deflection of centre of gravity of the rotor
- Mass of the rotor in terms of centrifugal force
- Natural circular frequency of the shaft
- Static deflection of the shaft
- 2 More formulas!

Effect of Inertia of the Constraint in Longitudinal and Transverse Vibrations

Longitudinal vibration

- Length of the constraint for longitudinal vibration
- Longitudinal velocity of the free end for longitudinal vibration
- Natural frequency of longitudinal vibration
- Total kinetic energy possessed by the constraint for longitudinal vibration
- Total mass of the constraint for longitudinal vibration
- Velocity of the small element for longitudinal vibration

Frequency of Free Damped Vibrations

- Amplitude reduction factor
- Circular damped frequency (underdamping)
- Circular damped frequency in terms of natural frequency (underdamping)
- Condition for critical damping
- Critical damping coefficient
- Damping factor
- Damping factor(in terms of natural frequency)
- Displacement of the mass from the mean position (underdamping)
- Frequency constant for damped vibrations (underdamping)
- Frequency constant for damped vibrations if circular frequency is known(underdamping)
- Frequency of damped vibration (underdamping)
- 9 More formulas!

Frequency of Under Damped Forced Vibrations

- Complementary function
- Damping coefficient
- Deflection of the system under the static force
- External periodic disturbing force
- Maximum displacement or the amplitude of forced vibration
- Maximum displacement or the amplitude of forced vibration at resonance
- Maximum displacement or the amplitude of forced vibration in terms of natural frequency
- Maximum displacement or the amplitude of forced vibration when damping is negligible
- Particular integral
- Phase constant
- Static force
- 5 More formulas!

Natural Frequency of Free Longitudinal Vibrations

Equilibrium Method

- Acceleration of body in terms of stiffness of the constraint
- Angular velocity of free longitudinal vibrations
- Displacement of the body in terms of stiffness of the constraint
- Gravitational pull balanced by the spring force
- Length of the constraint
- Load attached to the free end of constraint
- Natural frequency of free longitudinal vibrations
- Natural frequency of free longitudinal vibrations if static deflection is known
- Natural frequency of free longitudinal vibrations if stiffness of constraint is known
- Natural frequency of free longitudinal vibrations if the time period is known
- Restoring force
- 6 More formulas!

Rayleigh’s Method

- Displacement of the body from the mean position
- Maximum displacement from mean position if displacement of the body from mean position is known
- Maximum displacement from mean position if maximum kinetic energy is known
- Maximum displacement from mean position if maximum potential energy is known
- Maximum displacement from mean position if maximum velocity at mean position is known
- Maximum displacement from mean position if velocity at mean position is known
- Maximum kinetic energy at mean position
- Maximum potential energy at mean position
- Maximum velocity at the mean position
- Natural circular frequency if displacement of the body is known
- Natural circular frequency if maximum velocity at mean position is known
- 7 More formulas!

Natural Frequency of Free Transverse Vibrations

- Acceleration of body in terms of stiffness of shaft
- Length of the shaft
- Load at the free end
- Moment of inertia of shaft in terms of static deflection
- Natural Frequency of free transverse vibrations
- Restoring force in terms of stiffness of shaft
- Static deflection in terms of moment of inertia of shaft
- Time period of free transverse vibrations

Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft

- Circular frequency due to uniformly distributed load
- Circular frequency in terms of static deflection
- Length of the shaft in terms of circular frequency
- Length of the shaft in terms of natural frequency
- Length of the shaft in terms of static deflection
- Maximum bending moment at a distance x from end A
- Moment of Inertia of shaft in terms of circular frequency
- Moment of Inertia of shaft in terms of natural frequency
- Moment of Inertia of shaft in terms of static deflection if load per unit length is known
- Natural frequency due to uniformly distributed load
- Natural frequency in terms of static deflection
- 7 More formulas!

Natural Frequency of Free Transverse Vibrations of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load

- Bending moment at a distance x from end A
- Circular frequency in terms of static deflection(Shaft fixed, uniformly distributed load)
- Length of shaft in terms of natural circular frequency(Shaft fixed, uniformly distributed load)
- Length of shaft in terms of natural frequency(Shaft fixed, uniformly distributed load)
- Length of shaft in terms of static deflection(Shaft fixed, uniformly distributed load)
- Load in terms of natural circular frequency(Shaft fixed, uniformly distributed load)
- Load in terms of natural frequency(Shaft fixed, uniformly distributed load)
- load in terms of static deflection(Shaft fixed, uniformly distributed load)
- M.I of shaft in terms of natural circular frequency(Shaft fixed, uniformly distributed load)
- M.I of shaft in terms of natural frequency(Shaft fixed, uniformly distributed load)
- M.I of shaft in terms of static deflection(Shaft fixed, uniformly distributed load)
- 7 More formulas!

Values of length of beam for the various types of beams and under various load conditions

- Length of beam for cantilever beam with a point load at the free end
- Length of beam for cantilever beam with a uniformly distributed load
- Length of beam for fixed beam with a central point load
- Length of beam for fixed beam with a uniformly distributed load
- Length of beam for fixed beam with an eccentric point load
- Length of beam for simply supported beam with a central point load
- Length of beam for Simply supported beam with a uniformly distributed load
- Length of beam for simply supported beam with an eccentric point load

Values of static deflection for the various types of beams and under various load conditions

- Static deflection for cantilever beam with a point load at free end
- Static deflection for cantilever beam with a uniformly distributed load
- Static deflection for fixed beam with a central point load
- Static deflection for fixed beam with a uniformly distributed point load
- Static deflection for fixed beam with an eccentric point load
- Static deflection for simply supported beam with an eccentric point load
- Static deflection for simply supported beam with central point load
- Static deflection for simply supported beam with uniformly distributed load

Vibration Isolation and Transmissibility

- Angular velocity of vibration in terms of force transmitted
- Applied force if transmissibility ratio and maximum displacement of vibration is given
- Applied force if transmissibility ratio is known
- Damping coefficient in terms of force transmitted
- Force transmitted
- Magnification factor if transmissibility ratio is given
- Magnification factor in terms of transmissibility ratio if natural circular frequency is known
- Maximum displacement of vibration if Transmissibility ratio is known
- Maximum displacement of vibration in terms of force transmitted
- Natural circular frequency in terms of transmissibility ratio
- Stiffness of spring in terms of force transmitted
- 8 More formulas!

Torsional Vibrations

Effect of Inertia of the Constraint on Torsional Vibrations

- Angular velocity of free end if kinetic energy of constraint is known
- Angular velocity of the element
- Kinetic energy possessed by the element
- Mass moment of inertia of the element
- Natural frequency of torsional vibration due to effect of inertia of constraint
- Torsional stiffness of shaft due to effect of constraint on torsional vibrations
- Total kinetic energy of the constraint
- Total mass moment of inertia of constraint if kinetic energy of constraint is known

Free Torsional Vibrations of Rotor Systems

Free Torsional Vibrations of a Two Rotor System

- Distance of node from rotor A, for torsional vibration of a two rotor system
- Distance of node from rotor B, for torsional vibration of a two rotor system
- Mass moment of inertia of rotor A, for torsional vibration of a two rotor system
- Mass moment of inertia of rotor B, for torsional vibration of a two rotor system
- Natural frequency of free torsional vibration for rotor A of a two rotor system
- Natural frequency of free torsional vibration for rotor B of a two rotor system

Natural Frequency of Free Torsional Vibrations

- Accelerating force
- Angular displacement of the shaft from mean position
- Angular velocity of the shaft
- Moment of inertia of the disc in terms of angular velocity
- Moment of Inertia of the disc in terms of natural frequency of vibration
- Moment of inertia of the disc in terms of time period of vibration
- Natural frequency of vibration
- Restoring force for free torsional vibrations
- Time period for the vibrations
- Torsional stiffness of the shaft
- Torsional stiffness of the shaft in terms of angular velocity
- 3 More formulas!

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