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Transmissibility Ratio Formula

GoTransmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Formula

GoTransmissibility Ratio given Natural Circular Frequency and Magnification Factor Formula

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Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis. Check FAQs

ε = \frac{K \cdot \sqrt{k^{2} + {(c \cdot ω)}^{2}}}{F a}

ε - Transmissibility Ratio?K - Maximum Displacement?k - Stiffness of Spring?c - Damping Coefficient?ω - Angular Velocity?F_a - Applied Force?

Transmissibility Ratio Example

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Here is how the Transmissibility Ratio equation looks like with Values.

Here is how the Transmissibility Ratio equation looks like with Units.

Here is how the Transmissibility Ratio equation looks like.

19.2086 = \frac{0.8 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{2500}

19.2086 = \frac{0.8m \cdot \sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}{2500N}

19.2086 = \frac{0.8 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{2500}

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Transmissibility Ratio Solution

Follow our step by step solution on how to calculate Transmissibility Ratio?

FIRST Step Consider the formula

ε = \frac{K \cdot \sqrt{k^{2} + {(c \cdot ω)}^{2}}}{F a}

Next Step Substitute values of Variables

∴

ε = \frac{0.8m \cdot \sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}{2500N}

Next Step Prepare to Evaluate

∴

ε = \frac{0.8 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{2500}

Next Step Evaluate

∴

ε = 19.2086399991543

LAST Step Rounding Answer

∴

ε = 19.2086

Transmissibility Ratio Formula Elements

Variables

Functions

Transmissibility Ratio

Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Transmissibility Ratio

Maximum Displacement

Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.

Symbol: K

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Maximum Displacement

Stiffness of Spring

Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.

Symbol: k

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Spring

Damping Coefficient

Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.

Symbol: c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value should be greater than 0.

Formulas to find Damping Coefficient

Angular Velocity

Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity

Applied Force

Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.

Symbol: F_a

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Applied Force

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.

Syntax: sqrt(Number)

Other Formulas to find Transmissibility Ratio

Go Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient

ε = \frac{\sqrt{1 + (\frac{2 \cdot c \cdot ω}{{(c c \cdot ω n)}^{2}})}}{\sqrt{{(\frac{2 \cdot c \cdot ω}{c c \cdot ω n})}^{2} + {(1 - {(\frac{ω}{ω n})}^{2})}^{2}}}

Go Transmissibility Ratio given Natural Circular Frequency and Magnification Factor

ε = D \cdot \sqrt{1 + {(\frac{2 \cdot c \cdot ω}{c c \cdot ω n})}^{2}}

Go Transmissibility Ratio if there is No Damping

ε = \frac{1}{{(\frac{ω}{ω n})}^{2} - 1}

Go Transmissibility Ratio given Magnification Factor

ε = \frac{D \cdot \sqrt{k^{2} + {(c \cdot ω)}^{2}}}{k}

Other formulas in Vibration Isolation and Transmissibility category

Go Angular Velocity of Vibration using Force Transmitted

ω = \frac{\sqrt{{(\frac{F T}{K})}^{2} - k^{2}}}{c}

Go Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

F a = \frac{K \cdot \sqrt{k^{2} + {(c \cdot ω)}^{2}}}{ε}

Go Applied Force given Transmissibility Ratio

F a = \frac{F T}{ε}

Go Damping Coefficient using Force Transmitted

c = \frac{\sqrt{{(\frac{F T}{K})}^{2} - k^{2}}}{ω}

How to Evaluate Transmissibility Ratio?

Transmissibility Ratio evaluator uses Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force to evaluate the Transmissibility Ratio, Transmissibility Ratio formula is defined as a measure of the ratio of the amplitude of the force transmitted to the foundation to the amplitude of the force applied to the system, providing insight into the vibration isolation efficiency in mechanical systems. Transmissibility Ratio is denoted by ε symbol.

How to evaluate Transmissibility Ratio using this online evaluator? To use this online evaluator for Transmissibility Ratio, enter Maximum Displacement (K), Stiffness of Spring (k), Damping Coefficient (c), Angular Velocity (ω) & Applied Force (F_a) and hit the calculate button.

FAQs on Transmissibility Ratio

What is the formula to find Transmissibility Ratio?

The formula of Transmissibility Ratio is expressed as Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force. Here is an example- 19.20864 = (0.8*sqrt(60000^2+(9000.022*0.200022)^2))/2500.

How to calculate Transmissibility Ratio?

With Maximum Displacement (K), Stiffness of Spring (k), Damping Coefficient (c), Angular Velocity (ω) & Applied Force (F_a) we can find Transmissibility Ratio using the formula - Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Transmissibility Ratio?

Here are the different ways to Calculate Transmissibility Ratio-

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

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Transmissibility Ratio Formula

​GoTransmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Formula

​GoTransmissibility Ratio given Natural Circular Frequency and Magnification Factor Formula

Transmissibility Ratio Example

Transmissibility Ratio Solution

Transmissibility Ratio Formula Elements

Other Formulas to find Transmissibility Ratio

Other formulas in Vibration Isolation and Transmissibility category

How to Evaluate Transmissibility Ratio?

FAQs on Transmissibility Ratio

Variable Name

GoTransmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Formula

GoTransmissibility Ratio given Natural Circular Frequency and Magnification Factor Formula