Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring and damper placed parallel to each other, model the isolator using the standard linear model. k ∞∞∞∞∞∞∞∞∞0 m base k₁ motion Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing frequency, damping ratio, and the ratio of the two spring constants: y = k₁/k Discuss the influence of the stiffness ratio on the performance of the isolator. For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent damping ratio reproduce the transmissibility curve accurately? Discuss. Provide one specific application where it is necessary to use the standard linear model.
Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring and damper placed parallel to each other, model the isolator using the standard linear model. k ∞∞∞∞∞∞∞∞∞0 m base k₁ motion Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing frequency, damping ratio, and the ratio of the two spring constants: y = k₁/k Discuss the influence of the stiffness ratio on the performance of the isolator. For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent damping ratio reproduce the transmissibility curve accurately? Discuss. Provide one specific application where it is necessary to use the standard linear model.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring
and damper placed parallel to each other, model the isolator using the standard linear model.
k
m
base
k₁ motion
Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing
frequency, damping ratio, and the ratio of the two spring constants:
y = k₁/k
Discuss the influence of the stiffness ratio on the performance of the isolator.
For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective
damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent
damping ratio reproduce the transmissibility curve accurately? Discuss.
Provide one specific application where it is necessary to use the standard linear model.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad0d55fe-d83b-4711-86a1-cee8ecea510f%2Fe1267e46-320c-4a6a-9042-89b2dc53297b%2Fv8yjjhe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the vibration isolation problem from base excitation. Instead of modeling the isolator as a spring
and damper placed parallel to each other, model the isolator using the standard linear model.
k
m
base
k₁ motion
Develop an expression for the displacement transmissibility of the isolator in terms of the normalized forcing
frequency, damping ratio, and the ratio of the two spring constants:
y = k₁/k
Discuss the influence of the stiffness ratio on the performance of the isolator.
For a damping ratio of 0.01 and stiffness ratio of 0.05, use the transmissibility curve to find the effective
damping ratio of the isolator (this is equivalent to having a spring and damper in parallel). Can the equivalent
damping ratio reproduce the transmissibility curve accurately? Discuss.
Provide one specific application where it is necessary to use the standard linear model.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 8 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Control Systems Engineering](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
![Mechanics of Materials (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
![Engineering Mechanics: Statics](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY