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

See similar textbooks

Related questions

Q: in figure. Find the elongat tensile force of 300 kN. Take Est- 14 140 300 Kn

Q: Aluminum D=20mm Steel 200kN 200KN Bronze D=25mm D=28mm 150kN

Q: Problem II. An exhaust gas piping fabricated as shown is subjected to a bending moment, an internal…

Q: If the maximum value for W is 15 kips and wires AB and AC are of the same diameteer, what is the…

Q: Find the magnitude P of the largest additional vertical force that can be applied to the bar decimal…

Q: Q2 The armature shaft of a 40 kW, 720 rpm electric motor, mounted on two bearings A and B, is shown…

Q: In the given figure, the wires AB and CD made of the same material are used to suspend a rigid block…

Q: Situation H. A 100m tape weighing 3kg that is standard at 10°C and a 30N pull is used to measure a…

A: Length of tape = 100m Weight of tape = 3kg Standard temperature = 10°C Measured length of Tape =…

Q: A solid uniform metal bar of diameter D mm and length l mm hangs vertically from its upper end. The…

Q: A circular steel tube of length L = 59 inches is loaded in torsion by torques T (see the figure).…

Q: For the figure shown, What is the maximum tensile stress in the beam? Hint: There will be two…

Q: A STEEL ROD HAVING A CROSS SECTIONAL AREA OF 560 mm² IS SUSPENDED VERTICALLY IN ONE END. IT SUPPORTS…

Q: Problem 7.1. An acrylic rod is 200mm long and 15mm in diameter. If a tensile axial load of 300N is…

Q: A metallic rod made of steel as shown below is used as support for a signage with length equal to…

A: given data L =150m P =20kN i have used simple concept to calculate total elongation by super…

Q: Mechanics of Deformable Bodies problem

A: Draw free body diagram Taking moments about A…

Q: A horizontal bar of negligible mass is hinged at A and assumed to be rigid. It is supported by an…

Q: A 2500 lb horizontal bar is supported by three 3/16-inch diameter wires as shown. The wires are…

A: Given:-P=2500 lb Diameter= 3/16 in L=20 feet=240 inches To find:- Stresses in wire Solution:-…

Q: 2. The beam shown in Figure is 150mm wide and 300mm deep. The allowable bending stress on extreme…

A: Given data: b=150 mm d=300mm fb=8 MPa

Q: 4. A steel wire 2 m long and 3 mm in diameter is extended by 0.75 mm when a weight W is suspended…

A: Given data: Length of steel wire, ls = 2 m = 2000 mm Diameter of steel wire, ds = 3 mm Elongation in…

Q: The rigid bar AB, attached to two vertical rods as shown in the figure, is horizontal before the…

Q: re change of the assembly that will cause a tensile stress of 50 MPa in the steel rod. Use lata: A…

Q: A steel rod is stretched between two walls. At 20°C, the tensile force in the rod is 3000 N. If the…

A: Solution: Given Data: T1=20°CT2=-20°CP=3000 NAllowable Stress=150 Mpaα=11.7×10-6/°C As per the first…

Q: SITUATION. The figure shows a pellet about to be fired from a sling. The total unstretched length of…

A: What is the force in each leg of the rubber,F=?

Q: A compound bar consisting of bronze, aluminum, and steel segments is loaded axially as shown in the…

A: Axial Deformation The deformation that occurs in a body due to axial loading is known as axial…

Q: The BC rod in the carrier system shown in the figure has a circular cross section. diameter 25 mm…

Q: The beam shown is made of a nylon for which the allowable stress is 24 MPa in tension and 30 MPa in…

A: Given : Allowable stress = 24 MPa in tension and 30 MPa in compression. This is a problem of Solid…

Q: A water tank made from a steel having a thickness of 12mm has the following dimensions. Internal…

Q: A steel rod of length 300 mm and diameter 30 mm, is subjected to a pull 'P' while the temperature Is…

Q: 2. A steel bar of 750 mm2 cross-sectional area is placed between two aluminum bars, each of 500 mm2…

A: Area of steel = 750mm2 Area of aluminum = 500mm2 Es = 210GPa Eal = 70GPa (σy)s = 240MPa…

Q: The acrylic plastic rod is 200 mm long and 15 mm in diameter. If an axial load of 400 N is applied…

Q: The standard pull of the tape is 5kg while the team pulled only at 4kg The field temperature is 300…

Q: A steel rod (E= 200 GPa) is subjected to the load shown, where P = 2500 kN . A gap a = 2.00 mm…

A: A1 = π4×592 = 2733.97 mm2A2 = π4×442 = 1520.53 mm2

Q: The figure below shows the cross section of unsymmetric I-beam. The I-beam experiences a maximum M=4…

Concept explainers

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)?

Expert Solution

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!

SEE SOLUTION Check out a sample Q&A here

Step 1 Introduction

VIEW

Step 2 Data Given

VIEW

Step 3 Calculation of beam's damped resonance frequency

VIEW

Step 4 Calculation of Quality factor

VIEW

Step 5 Conclusion

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

Mechanics of Deformable Bodies Problem: The figure shows the upper half of a built up girder( the cross section is symmetric about the neutral axis). All rivets used in fabrication have a diameter of 22 mm. The moment of inertia of the entire cross sectional area of the girder about the neutral axis is l=4770x10⁶mm⁴. The working stresses are 100 MPa for rivets in shear and 280 MPa for bearing of the web plate. If the maximum shear force carried by the girder is 450 kN, determine the largest allowable spacing of rivets that join the angles to the web plate.
An aluminum rectangular bar has a cross-section of 25 mm x 50 mm and a length of 500 mm. The Modulus of Elasticity of E = 70 GPa and a Poisson’s ratio of ν = 0.25. Determine the percentage change in the volume of the bar when an axial force of 300 kN is applied to the bar.
The assembly shown in the figure consists of an aluminum tube AB and a steel rod BC. The rod is attached to the tube through the rigid collar at B and passes through the tube. The cross-sectional area of the rod is 75 mm2 and the cross-sectional area of the tube is 400 + UV in mm2, where UV is 99. A tensile load of 80 kN is applied to the rod. Take Est = 200 GPa for the steel rod, Eal = 70 GPa for the aluminum tube. Determine: (a) the displacement of end C with respect to end B (i.e., the elongation of the steel rod), (b) the displacement of end B with respect to the fixed end A (i.e., the shrink of the aluminum tube), (c) the displacement of the end C of the rod (i.e., (a) + (b)).
Help me please
A plastic bar ACE having two different solid circular cross-sections is held between rigid supports, as shown in the figure. The diameters in the left-and right-hand parts are 50 mm and 75 mm. respectively. The corresponding lengths are 225 mm and 300 mm. Also, the modulus of elasticity Eis 6.0 GPa. and the coefficient of thermal expansion a is 100 x10-6 l°C. The bar is subjected to a uniform temperature increase of 30°C. a.Calculate the following quantities: (I) the compressive force Nin the bar. (2) the maximum compressive stress at and (3) the displacement Se, Df point C. b.Repeat part (a) if the rigid support at A is replaced by elastic support having spring constant k = 50 MN/m (see figure part b; assume that only the bar ACE is subject to the temperature increase).
As a construction engineer, you are asked to evaluate the maximum allowable vertical shear Vmax that may act on the hollow stainless-steel beam having a rectangular cross section as shown in Figure Q4. Discuss the effect of geometry on the shear stress developed in the beam | 20 mm y 350 mm V 10 mm- -10 mm 1 30 mm E 200 mm
1 - An aluminum plate is subjected to uniform stress along its boundaries, as shown in the figure. Determine the change of length of diagonal BD. 120mm 120 MPa 160mm C B V 100MPa -200 MPa E-80GPa ✓=0.3 G=30MPa
need help.
A 50 mm diameter cylindrical aluminum block is connected to 2 hollowed cylindrical steel blocks as shown in Figure Q1. Both hollowed steel cylinders are of 60 mm and 40 mm outer and inner diameters respectively. The assembly is then connected to a rigid steel plate. Four bolts of diameter 10 mm are then used to rigidly fix the assembly to a wall. A force P is then applied to the assembly. The Modulus of elasticity(E) of steel is 200 GPa while aluminum has Modulus of elasticity(E) of 70 GPa. Both steel and aluminum have a yield strength(oy) of 250 MPa. The bolts have a yield stress (oy) of 800 MPa. All connections and joints are considered rigid. Q3 Determine the allowable value of P that can be applied to the assembly taking into consideration the yielding of all parts of the assembly and bolts. Use a factor of safety of 1.5. b. a. Based on the value of P obtained part (a), determine the total elongation of the cylindrical steel block. Based on the value of P obtained in part (a),…
1. An axial force of 250 kN is applied to the assembly shown, made of cylindrical brass core surrounded by an aluminum shell. The axial force is applied through rigid end plates. a) Determine the normal stress in each of the metal components, given that Ebrass = 105 GPa and Ealum = 70 GPA. 100mm b) What is the axial deformation of the assembly? 200mm 200mm
Given a cantilever beam with given loadings and cross-section as shown in the figures, what is the absolute value of the maximum flexural shear stress? (in MPa) 40 AN/m b00 mm GOomm Sm 600 mm GOomm
Subject: STRENGTH OF MATERIALS (Civil Engineering) Round off to three decimal places