Types of Free Vibrations with Weightless Constraint

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Questions and Answers

What type of vibrations occur when the particles of the shaft move parallel to the axis of the shaft?

Torsional vibrations

Radial vibrations

Longitudinal vibrations (correct)

Transverse vibrations

In which type of vibrations does the shaft experience bending stresses?

Lateral vibrations

Transverse vibrations (correct)

Torsional vibrations

Longitudinal vibrations

What type of stresses are induced in the shaft during torsional vibrations?

Torsional shear stresses (correct)

Radial stresses

Bending stresses

Tensile and compressive stresses

When the particles of the shaft move in a circle about the axis of the shaft, what type of vibrations occur?

Torsional vibrations Signup and view all the answers

Which type of vibrations involve the shaft being elongated and shortened alternately?

Longitudinal vibrations Signup and view all the answers

What happens to the shaft during transverse vibrations?

It is straightened and bent alternately Signup and view all the answers

What is the term used to describe the speed at which the shaft runs so that the additional deflection of the shaft from the axis of rotation becomes infinite?

Whirling speed Signup and view all the answers

What causes the bending of the shaft with mountings such as gears or pulleys?

Centrifugal force Signup and view all the answers

When does the additional deflection y of the shaft from the axis of rotation become infinite?

$n = c$ Signup and view all the answers

What is the unit of critical or whirling speed?

Revolutions per second Signup and view all the answers

Which parameter determines both the value of eccentricity and the speed at which the shaft rotates?

Mass of rotor Signup and view all the answers

What happens to the shaft deflection if the circular frequency n is greater than the critical speed c?

Negative deflection Signup and view all the answers

In a two-rotor system, when do torsional vibrations occur?

The two rotors move in opposite directions with different frequencies Signup and view all the answers

What point can be safely assumed as the fixed end of a shaft in a three-rotor system?

"Nodal" point Signup and view all the answers

What does C represent in a three-rotor system's natural frequency equation?

"Modulus" of rigidity Signup and view all the answers

'The shaft behaves like a spring.' What resists the deflection of the shaft?

"Stiffness" Signup and view all the answers

Study Notes

Types of Vibrations in Shafts

Longitudinal vibrations occur when shaft particles move parallel to the axis.
Bending vibrations cause the shaft to experience bending stresses.
Torsional vibrations induce shear stresses in the shaft.

Circular and Alternating Vibrations

Circular vibrations arise when shaft particles move in a circle about the axis of rotation.
Axial vibrations involve the shaft being elongated and shortened alternately.

Effects of Transverse Vibrations

During transverse vibrations, the shaft undergoes lateral oscillations, affecting its stability and performance.

Critical Speed and Eccentricity

Critical or whirling speed is the term for the speed at which additional deflection from the axis of rotation becomes infinite.
Eccentricity and the speed of rotation are determined by the same parameter, affecting the shaft's dynamic behavior.

Deflection Dynamics

When the circular frequency (n) exceeds the critical speed (c), the shaft deflection increases significantly.
Torsional vibrations in a two-rotor system occur when there is a relative motion between rotors.

Fixed Points and Natural Frequency

In a three-rotor system, one end of the shaft can usually be assumed as fixed.
In the natural frequency equation of a three-rotor system, C typically represents a constant related to system parameters.

Resistance to Shaft Deflection

The resistance to deflection in a shaft is analogous to a spring's behavior, indicating elasticity and return to the original position.

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Description

Explore the three important types of free vibrations: Longitudinal, Transverse, and Torsional vibrations. Learn about vibrations in weightless constraints such as springs or shafts carrying heavy discs.