The natural frequency (f) of a piezoelectric cantilever beam is described by the following equation:, where E = Modulus of elasticity, I = Area moment of inertia, L = Length of the cantilever beam, and m = Mass of proof mass (or end mass). The area moment of inertia for an arbitrary shape R with respect to an arbitrary axis (for example, x-axis) is related by: (a) What is the dimension of an area moment of inertia? (b) If the thickness of a piezoelectric cantilever beam increases, does the natural frequency increase or decrease? (c) Both the thickness and width of a piezoelectric cantilever beam can change the natural frequency. Which parameter (thickness or width) will lead to the natural frequency change more significantly? Briefly explain your answer.
The natural frequency (f) of a piezoelectric cantilever beam is described by the following equation:, where E = Modulus of elasticity, I = Area moment of inertia, L = Length of the cantilever beam, and m = Mass of proof mass (or end mass). The area moment of inertia for an arbitrary shape R with respect to an arbitrary axis (for example, x-axis) is related by: (a) What is the dimension of an area moment of inertia? (b) If the thickness of a piezoelectric cantilever beam increases, does the natural frequency increase or decrease? (c) Both the thickness and width of a piezoelectric cantilever beam can change the natural frequency. Which parameter (thickness or width) will lead to the natural frequency change more significantly? Briefly explain your answer.
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
The natural frequency (f) of a piezoelectric cantilever beam is described by the following equation:, where E = Modulus of elasticity, I = Area moment of inertia, L = Length of the cantilever beam, and m = Mass of proof mass (or end mass). The area moment of inertia for an arbitrary shape R with respect to an arbitrary axis (for example, x-axis) is related by:
(a) What is the dimension of an area moment of inertia?
(b) If the thickness of a piezoelectric cantilever beam increases, does the natural frequency increase or decrease?
(c) Both the thickness and width of a piezoelectric cantilever beam can change the natural frequency. Which parameter (thickness or width) will lead to the natural frequency change more significantly? Briefly explain your answer.
Transcribed Image Text:1 3EI
f :
2n V mL
1
т
Transcribed Image Text:I̟ = [[ y² dx dy.
,2
R
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
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
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY