Maximum Displacement of Vibration 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%
✖Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.ⓘ Applied Force [F_a]			+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%

✖Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.ⓘ Maximum Displacement of Vibration given Transmissibility Ratio [K]

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Maximum Displacement of Vibration given Transmissibility Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
K = (ε*F_a)/(sqrt(k^2+(c*ω)^2))
This formula uses 1 Functions, 6 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

Maximum Displacement - (Measured in Meter) - Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.
Transmissibility Ratio - Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.
Applied Force - (Measured in Newton) - Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.
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
Applied Force: 2500 Newton --> 2500 Newton 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

K = (ε*F_a)/(sqrt(k^2+(c*ω)^2)) --> (19.20864*2500)/(sqrt(60000^2+(9000.022*0.200022)^2))

Evaluating ... ...

K = 0.800000000035223

STEP 3: Convert Result to Output's Unit

0.800000000035223 Meter --> No Conversion Required

FINAL ANSWER

0.800000000035223 ≈ 0.8 Meter <-- Maximum Displacement

(Calculation completed in 00.020 seconds)

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

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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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

Maximum Displacement of Vibration given Transmissibility Ratio Formula

LaTeX Go

Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
K = (ε*F_a)/(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 Maximum Displacement of Vibration given Transmissibility Ratio?

Maximum Displacement of Vibration given Transmissibility Ratio calculator uses Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)) to calculate the Maximum Displacement, Maximum Displacement of Vibration given Transmissibility Ratio formula is defined as a measure of the maximum amplitude of vibration of a system in terms of the transmissibility ratio, which is a critical parameter in mechanical vibration analysis, used to evaluate the vibration isolation effectiveness of a system. Maximum Displacement is denoted by K symbol.

How to calculate Maximum Displacement of Vibration given Transmissibility Ratio using this online calculator? To use this online calculator for Maximum Displacement of Vibration given Transmissibility Ratio, enter Transmissibility Ratio (ε), Applied Force (F_a), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω) and hit the calculate button. Here is how the Maximum Displacement of Vibration given Transmissibility Ratio calculation can be explained with given input values -> 0.8 = (19.20864*2500)/(sqrt(60000^2+(9000.022*0.200022)^2)).

FAQ

What is Maximum Displacement of Vibration given Transmissibility Ratio?

Maximum Displacement of Vibration given Transmissibility Ratio formula is defined as a measure of the maximum amplitude of vibration of a system in terms of the transmissibility ratio, which is a critical parameter in mechanical vibration analysis, used to evaluate the vibration isolation effectiveness of a system and is represented as K = (ε*F_a)/(sqrt(k^2+(c*ω)^2)) or Maximum Displacement = (Transmissibility Ratio*Applied Force)/(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, Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations, 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 Maximum Displacement of Vibration given Transmissibility Ratio?

Maximum Displacement of Vibration given Transmissibility Ratio formula is defined as a measure of the maximum amplitude of vibration of a system in terms of the transmissibility ratio, which is a critical parameter in mechanical vibration analysis, used to evaluate the vibration isolation effectiveness of a system is calculated using Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)). To calculate Maximum Displacement of Vibration given Transmissibility Ratio, you need Transmissibility Ratio (ε), Applied Force (F_a), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω). With our tool, you need to enter the respective value for Transmissibility Ratio, Applied Force, 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 Maximum Displacement?

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

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

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