A cantilever beam has length, L 150 um; width, w 10 um; thickness, t 15 µm;density, p= 2330 kg/m'; damping coefficient, b 3 x 10 Ns/m; and modulus of elasticity, EM =1.5 x 10" N/m?. In this micro-electro-mechanical (MEMS) device, the spring constant, k, of arectangular cantilever beam is given by: k = (EMwt)/(4L³)a. What is the beam's damped resonance frequency, fres (Hz)? (Do not forget: ment=0.24*m for acantilever beam in the question for damped resonance frequency).b. What is the quality factor?c. Can we detect a mass of 200 pg (picogram) added to the cantilever beam?(Note: 1 pg 1015 kg)?

Question is based on cantilever beam. Dimension's of beam, Damping coefficient , modulus of…

A cantilever beam has length, L 150 um; width, w 10 um; thickness, t 15 um; density, p= 2330 kg/m'; damping coefficient, b 3 x 10 Ns/m; and modulus of elasticity, EM= 1.5 x 10" N/m. In this micro-electro-mechanical (MEMS) device, the spring constant, k, of a rectangular cantilever beam is given by: k = (E,wt³)/(4L') a. What is the beam's damped resonance frequency, fres (Hz)? (Do not forget: men= 0.24*m for a cantilever beam in the question for damped resonance frequency). b. What is the quality factor? c. Can we detect a mass of 200 pg (picogram) added to the cantilever beam? (Note: I pg - 1015 kg)?

A cantilever beam has length, L 150 um; width, w 10 um; thickness, t 15 um; density, p= 2330 kg/m'; damping coefficient, b 3 x 10 Ns/m; and modulus of elasticity, EM= 1.5 x 10" N/m. In this micro-electro-mechanical (MEMS) device, the spring constant, k, of a rectangular cantilever beam is given by: k = (E,wt³)/(4L') a. What is the beam's damped resonance frequency, fres (Hz)? (Do not forget: men= 0.24*m for a cantilever beam in the question for damped resonance frequency). b. What is the quality factor? c. Can we detect a mass of 200 pg (picogram) added to the cantilever beam? (Note: I pg - 1015 kg)?

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Material Properties

Construction in civil engineering demands high strength, durability, and longevity. These targets can be achieved by better design and analysis, along with the correct choice of materials. Different materials have different properties and hence, they respond and performs differently under the various condition of external loadings. It is therefore a critical task of an engineer to select the right material based on the property that the material is supposed to function in real-time. When speaking about the property, there are different categories of material properties like chemical property, physical property, mechanical property, electrical property, magnetic property, thermal property, etc. These material properties form the basis of material selection in various applications.

Question

A cantilever beam has length, L 150 um; width, w 10 um; thickness, t 15 µm;
density, p= 2330 kg/m'; damping coefficient, b 3 x 10 Ns/m; and modulus of elasticity, EM =
1.5 x 10" N/m?. In this micro-electro-mechanical (MEMS) device, the spring constant, k, of a
rectangular cantilever beam is given by: k = (EMwt)/(4L³)
a. What is the beam's damped resonance frequency, fres (Hz)? (Do not forget: ment=0.24*m for a
cantilever beam in the question for damped resonance frequency).
b. What is the quality factor?
c. Can we detect a mass of 200 pg (picogram) added to the cantilever beam?
(Note: 1 pg 1015 kg)?

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