Magnification Factor given Transmissibility Ratio Calculator

✖Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.ⓘ Transmissibility Ratio [ε]			+10% -10%
✖Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.ⓘ Stiffness of Spring [k]			+10% -10%
✖Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.ⓘ Damping Coefficient [c]			+10% -10%
✖Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.ⓘ Angular Velocity [ω]			+10% -10%

✖Magnification Factor is the ratio of the amplitude of the vibrating body to the amplitude of the force causing the vibration.ⓘ Magnification Factor given Transmissibility Ratio [D]

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Magnification Factor given Transmissibility Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
D = (ε*k)/(sqrt(k^2+(c*ω)^2))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Magnification Factor - Magnification Factor is the ratio of the amplitude of the vibrating body to the amplitude of the force causing the vibration.
Transmissibility Ratio - Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.
Angular Velocity - (Measured in Radian per Second) - Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.

STEP 1: Convert Input(s) to Base Unit

Transmissibility Ratio: 19.20864 --> No Conversion Required
Stiffness of Spring: 60000 Newton per Meter --> 60000 Newton per Meter No Conversion Required
Damping Coefficient: 9000.022 Newton Second per Meter --> 9000.022 Newton Second per Meter No Conversion Required
Angular Velocity: 0.200022 Radian per Second --> 0.200022 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = (ε*k)/(sqrt(k^2+(c*ω)^2)) --> (19.20864*60000)/(sqrt(60000^2+(9000.022*0.200022)^2))

Evaluating ... ...

D = 19.2000000008453

STEP 3: Convert Result to Output's Unit

19.2000000008453 --> No Conversion Required

FINAL ANSWER

19.2000000008453 ≈ 19.2 <-- Magnification Factor

(Calculation completed in 00.006 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Vibration Isolation and Transmissibility » Magnification Factor given Transmissibility Ratio

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Vibration Isolation and Transmissibility Calculators

Maximum Displacement of Vibration using Force Transmitted

LaTeX Go Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))

Stiffness of Spring using Force Transmitted

LaTeX Go Stiffness of Spring = sqrt((Force Transmitted/Maximum Displacement)^2-(Damping Coefficient*Angular Velocity)^2)

Damping Coefficient using Force Transmitted

LaTeX Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity

Force Transmitted

LaTeX Go Force Transmitted = Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)

< Forced Vibration Calculators

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

LaTeX Go Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio

Angular Velocity of Vibration using Force Transmitted

LaTeX Go Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient

Damping Coefficient using Force Transmitted

LaTeX Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity

Applied Force given Transmissibility Ratio

LaTeX Go Applied Force = Force Transmitted/Transmissibility Ratio

Magnification Factor given Transmissibility Ratio Formula

LaTeX Go

Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
D = (ε*k)/(sqrt(k^2+(c*ω)^2))

What is meant by Vibration Isolation?

Vibration isolation is a commonly used technique for reducing or suppressing unwanted vibrations in structures and machines. With this technique, the device or system of interest is isolated from the source of vibration through insertion of a resilient member or isolator.

How to Calculate Magnification Factor given Transmissibility Ratio?

Magnification Factor given Transmissibility Ratio calculator uses Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)) to calculate the Magnification Factor, Magnification Factor given Transmissibility Ratio formula is defined as a dimensionless quantity that expresses the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave in a mechanical vibration system, providing a measure of the energy transmission through the system. Magnification Factor is denoted by D symbol.

How to calculate Magnification Factor given Transmissibility Ratio using this online calculator? To use this online calculator for Magnification Factor given Transmissibility Ratio, enter Transmissibility Ratio (ε), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω) and hit the calculate button. Here is how the Magnification Factor given Transmissibility Ratio calculation can be explained with given input values -> 19.2 = (19.20864*60000)/(sqrt(60000^2+(9000.022*0.200022)^2)).

FAQ

What is Magnification Factor given Transmissibility Ratio?

Magnification Factor given Transmissibility Ratio formula is defined as a dimensionless quantity that expresses the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave in a mechanical vibration system, providing a measure of the energy transmission through the system and is represented as D = (ε*k)/(sqrt(k^2+(c*ω)^2)) or Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)). Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis, Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched, Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss & Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.

How to calculate Magnification Factor given Transmissibility Ratio?

Magnification Factor given Transmissibility Ratio formula is defined as a dimensionless quantity that expresses the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave in a mechanical vibration system, providing a measure of the energy transmission through the system is calculated using Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)). To calculate Magnification Factor given Transmissibility Ratio, you need Transmissibility Ratio (ε), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω). With our tool, you need to enter the respective value for Transmissibility Ratio, Stiffness of Spring, Damping Coefficient & Angular Velocity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Magnification Factor?

In this formula, Magnification Factor uses Transmissibility Ratio, Stiffness of Spring, Damping Coefficient & Angular Velocity. We can use 2 other way(s) to calculate the same, which is/are as follows -

Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))
Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))

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