Lab 1 Instructions
.pdf
keyboard_arrow_up
School
University of Calgary *
*We aren’t endorsed by this school
Course
211
Subject
Mechanical Engineering
Date
Dec 6, 2023
Type
Pages
2
Uploaded by hassaanhyderzzz on coursehero.com
ENME 599, Winter 2023
Lab 1 Instructions
1 |
P a g e
Free Vibration (Transient Response) of Single Degree of Freedom Mechanical Systems
Objectives
1.
Working with a function generator and oscilloscope
2.
Experimental analysis of the dynamics of a single-degree-of-freedom (SDOF) mechanical system
3.
Quantitative characterization of the dynamics of an SDOF system
•
Data acquisition using accelerometer and NI (National Instruments) DAQ in LabVIEW
•
Identification of the natural frequency and the damping ratio using the logarithmic decrement method
4.
Comparison of the experimental and analytical results
Safety and Instrument Protection
The accelerometers used in this experiment are
very delicate
and
expensive
(up to $1000 per piece). They can
be easily damaged by shock (
e.g
., dropping or hitting a hard object). Please handle them with care. Also, take
care not to tangle the cords of the accelerometers, as they can be damaged. Check that all the signal cables
from/to the accelerometer, DAQ, BNC cables and oscilloscope are
disconnected
at the end of the lab.
Agenda
1.
A brief introduction to the free vibration of SDOF systems by the TA
2.
Demonstration of procedures by the technician (or TA) that needs to be followed by each group
•
Measurement of signals from a function generator and output of a potentiometer using an oscilloscope
•
Building a data acquisition block diagram in LabVIEW
•
Data acquisition of a slender beam without and with end-mass using accelerometer and DAQ in LabVIEW
Experiments
1.
Measurement using a function generator and oscilloscope:
The circuit shown in
Figure 1
is built and then
connected to a function generator. The input and output signals of the circuit are measured using the
oscilloscope. The connections must be as follows:
Figure 1:
Measurement setup consists of a function generator, potentiometer and oscilloscope
•
Connect the function generator to the input of the circuit.
•
Connect the function generator to
channel 1
and the output of the circuit to
channel 2
of the oscilloscope.
•
Measure the signals from the function generator and the potentiometer using cursors on the oscilloscope.
Function
generator
Oscilloscope
Ch1
Ch2
Ch3
Ch4
POT
(10 kΩ)
Ground
Input
Output
Input
Capacitor (10 μF)
Ground
BNC cables
ENME 599, Winter 2023
Lab 1 Instructions
2 |
P a g e
2.
Free vibration of SDOF system:
A LabVIEW program is used to acquire the signals with an appropriate
sampling rate. Figure 2 shows the experimental setup and the test procedure for the beam without and with
the end mass.
•
Measure the length, width and thickness of the beam and weight of the additional mass and fill out Table 1 on
the worksheet (already filled).
•
Attach the accelerometer by pressing and gently twisting it onto the beam.
•
Tape down the cables to avoid picking up additional noise during your measurements.
•
Connect the accelerometer to the DAQ 9234.
•
Turn on the accelerometer using NI-MAX according to the instruction. Use
m/s
2
as the unit for acceleration.
•
Apply a
10 mm
initial displacement at the end of the beam and then release it.
•
Acquire and save data in text format (1
st
column: time and 2
nd
column: acceleration) and use them to complete
the lab assignments.
Figure 2:
Single-degree-of-freedom experimental setup
Note 1:
When the experiment is performed with the end mass, the accelerometer must be attached to the top of the
mass.
Note 2:
Do not hit on the table or shake the cables when acquiring data.
Note 3:
The data files can be read using MATLAB, Excel or Notepad. The first column of the data files is the time (sec)
signal and the second column is the acceleration (m/s
2
) signal.
Lab Assignment:
1.
Use the data file of the beam without the end-mass (
Beam_Without_Mass.lvm
) and do the following calculations:
a.
Plot the acquired waveform and calculate the experimental period of oscillation
T
nE
, from the plotted data.
Consider at least ten oscillations and disregard the first three oscillations.
b.
Estimate the damping ratio
ξ
, using the logarithmic decrement method. Consider at least five oscillations.
c.
Calculate the analytical period of oscillations
T
nA
, by following the procedure presented in Table 2 of the
worksheet.
d.
Compute the error between the measured and calculated periods of oscillation.
e.
Explain possible causes of discrepancies between the measured and calculated periods of oscillation.
2.
Use the data file of the beam with the end-mass (
Beam_With_Mass.lvm
) and do the following calculations.
a.
Repeat sections
a to d
from question 1 for the beam with end mass.
b.
Formulate the equation of motion (EOM) and find the displacement of the beam
analytically
. Consider an initial
displacement of
X
0
= 0.01
m
and an initial velocity of
V
0
= 0 m/s as the initial condition of the problem. Except for
the damping ratio, which is identified experimentally, all other parameters (natural frequency,
etc
.) must be
calculated using analytical expressions (refer to the worksheet).
c.
Calculate the experimental displacement of the beam by dividing the experimental accelerations by
–
ω
n
2
(experimental).
d.
Plot the analytical displacement, from section b, and experimental displacement, from section c, in a single figure.
Only show twenty oscillations. Compare the results and discuss the deviations.
Note 4:
The worksheet should also be completed and provided with the lab report.
L
h
m
b
Accelerometer
Beam
NI 9234
AI0
AI1
AI2
AI4
y
0
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Questions
A vibrating system with mass 3 kg, stiffness 21 N-s/m and damper having damping coefficient 10 N-s/m When an exciting force of magnitude 27 sin2t is acting, what would be the time period of oscillations?
arrow_forward
It is observed from the magnitude plot of a compliance transfer function of a mass spring damper that the value at a very small frequency 0.0001 is 3.71 meters and at resonance 1.10 rad/s is 7.10 meters. What is the natural frequency, damping coefficient, stiffness, and mass of the system?
arrow_forward
machine dynamics
A car with a mass of 1503 kg, a spring constant of 307027 N/m of suspension springs, a damping degree of shock absorbers of 0.5, an amplitude of 5 cm, and a wavelength of 4 m, while driving on a bumpy sinusoidal road;a) The vibration amplitude of the car in the resonant wn=w state.b) At what speed will the car resonate?c) Find the regular regime vibration amplitude when the car is traveling at 80 km/h.
arrow_forward
Mechanical Vibrations
Question is image
A 300-kg machine is attached to an elastic foundation of stiffness 3.1 x E6 N/m and damping ratio 0.06. When excited by a frequency squared excitation at very large speeds, the machine's steady-state amplitude is 10 mm. What is the maximum steady-state amplitude the machine would experience at lower speeds?
arrow_forward
MECHANICAL VIBRATIONS
An unknown mass m is attached to the end of a linear spring with unknown stiffness coefficient k. The system has natural frequency of 30 rad/s. When a 0.5 kg mass is added to the unknown mass m, the natural frequency is lowered to 20 rad/s. Determine the mass m and the stiffness coefficient k.
arrow_forward
A spring mass system with a natural frequency fn = 20 Hz is attached to a vibration table. Thetable is set to vibrate at 16 Hz, with a maximum acceleration 0.25 g. Answer the followingquestions. Justify your answers
d. What is the maximum acceleration of the mass assuming the packaging can be modeled asa viscous damper with a damping ratio of 0.2?e. Is the motion of the mass in phase or out of phase with the motion of the table?
arrow_forward
Please show all work. will upvote, thanks
An input force f = F‧sin(ωt) is applied to the body in both systems along the direction x.
-Which of the two systems performs better in the frequency domain in terms of reducing the steady-state displacement amplitude X of the body ? Known are: m = 1kg, c = 5 Ns/m and k = 100 N/m?
arrow_forward
A weight of 10lb is suspended by a spring having a modulus of 15 lb-s/in. When displaced and permitted to oscillate freely, it is found that the amplitude diminished from 1.5 in to 1.316 in in exactly 10 cycles. a.) determine the system mathematical model, b.) time period of the system, c.) system percent overshoot
arrow_forward
A suspension system of Volvo articulated dump truck is to be modelled mathematically given the following data: keq = 10.5 MN/m, m = 30 tons, and c = 300 N-s/m. If the harmonic forcing function is 2000 cos 5t N with the initial displacement and velocity to be 0 and 30 m/s respectively, determine the steady state and total response of the system.
arrow_forward
2.A 31 kg skip attached to a steel rope on a crane is used to hoist bricks from the ground to the top of a construction site. The steel rope is wound onto a lifting drum with a diameter of 700 mm and rotational frequency of 52 revolutions per minute. The lifting drum is situated on the top floor which is 196 m high. How many seconds will it take to lift bricks, three quarters up the height of the building?
arrow_forward
Find the maximum velocity of a free vibration with a response of 4(d^2 x/dt^2) + 25x = 0. Initial displacement of 0 and velocity of 1 m/s.
arrow_forward
Determine the steady state time response x(t) of a viscously damped system subjected to harmonic base excitation for the following data : m = 15 kg, c = 25 N.s/m, k = 300 N/m, y(t) = 0.04 sin ( 5t ) m. %3D
arrow_forward
The block diagram given below;
A) Reduce it
B) G1(s)=2/s ; G2(s)=1/4s+2 ; G3(s)=4 ;H(s)=0.5 Given the values of the system; find the time constant, its natural frequency and damping rate and explain what kind of dynamic behavior it exhibits accordingly.
C)Find the poles and zeros of the system according to the values in (B).Is the system stable? Find the unit step response (Inverse Laplace).
arrow_forward
A block of mass m = 16 kg oscillates attached to a spring of spring constant K = 162 N/m. The motion of the block is also acted upon by a damping force proportional to the velocity of the form Fd = -bv, where b = 36√ 2 kg/s. The system is excited by a sinusoidal force of maximum value F0 = 7 N. If the excitation frequency varies, at what frequency ω (in rad/s) will resonance occur? Choose the closest value.
a) 63/4 rad/s
b) 9/28 rad/s
c) 567/4 rad/s
d) 9/4 rad/s
arrow_forward
A two degree of freedom damped system has natural frequencies 2 rad/s and 3 rad/s and corresponding mode shapes {21}{ 2 1 } and {1−1}{ 1 − 1 } . A damping ratio of 2% is assumed for both modes. The initial displacement is {10}{ 1 0 }mm and initial velocity is {21}{ 2 1 }mm/s. The displacement of the first degree of freedom in mm at time t=3 s is
arrow_forward
A certain mass is driven by base excitation through a spring (Figure P4.13). Its parameter values are m = 100 kg, c = 1000 N * s/m, and k = 10,000 N/m. Determine its peak frequency w_p, it’s peak M_p, and its bandwidth.
arrow_forward
In this Problem, the system of Fig. 5.4.14 (Attached) is taken as a model for an undamped car with the given parameters in fps units. (a) Find the two natural frequencies of oscillation (in hertz). (b) Assume that this car is driven along a sinusoidal washboard surface with a wavelength of 40 ft. Find thetwo critical speeds.
m = 100, I =1000, L1 =6, L2 = 4, k1 = k2 = 2000
arrow_forward
A particular naturally vibrating system is subject to damping. The system consists of a small mass m = 0.1 kg, the system stiffness k = 200 Nm-1 and the damping coefficient c = 0.25 kgs-1 . Determine the values of the natural and damped frequencies, the damping factor, damping ratio, periodic time and logarithmic decrement. Sketch and describe the nature of the motion
arrow_forward
If a mass of 6 kg oscillates on a spring having a mass 3
kg and stiffness 11200 N/m, then the natural frequency
of the system in rad/sec will be
arrow_forward
A 1.5-kg mass attached to an ideal massless spring with a spring constant of 20.0 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the mass is released from x = 0.0 cm with a velocity of 0.370 m/s to the left. Find the followingA. Time periodB. Total mechanical energy of the massC. AmplitudeD. Phase constant of motion. Discuss the two possible values of phase constant you get and explain how you arrived at the correct answer. Write the equation of motion.E. Maximum acceleration of the mass. (Acceleration is maximum when it ispositive). How long after the release does the maximum acceleration occur?F. Draw the position-time graph for one cycle of motion.
arrow_forward
Vibrations Question
The governing equation of motion of a single degree–of–freedom (SDOF) system is given by
5xdoubledot(t)+20xdot(t)+1800x(t)=10cos(15t)+30sin(5t)(assume the units are Newtons)
and the initial conditions of the system are given asx(0)=0.02m and v(0)=0.95m/sAnalytically obtain the total response of the system
arrow_forward
A 35 kg electric motor that operates at 40 + 10u Hz is mounted on an elastic
foundation of stiffness 3× 106 N/m. The phase difference between the excitation and
the steady state response is 21°. What is the damping ratio of the system?
arrow_forward
Don't give incorrect solution..A structure is modeled as a damped oscillator having a spring constant k = 30 kip/in and undamped natural frequency = 25 rad/sec. Experimentally it was found that a force of 1 kip produced a relative velocity of 1.0 in/sec in the damping element. Determine:
a) The damping ratio §.
b) The damped period TD.
arrow_forward
SEE MORE QUESTIONS
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
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
Related Questions
- A vibrating system with mass 3 kg, stiffness 21 N-s/m and damper having damping coefficient 10 N-s/m When an exciting force of magnitude 27 sin2t is acting, what would be the time period of oscillations?arrow_forwardIt is observed from the magnitude plot of a compliance transfer function of a mass spring damper that the value at a very small frequency 0.0001 is 3.71 meters and at resonance 1.10 rad/s is 7.10 meters. What is the natural frequency, damping coefficient, stiffness, and mass of the system?arrow_forwardmachine dynamics A car with a mass of 1503 kg, a spring constant of 307027 N/m of suspension springs, a damping degree of shock absorbers of 0.5, an amplitude of 5 cm, and a wavelength of 4 m, while driving on a bumpy sinusoidal road;a) The vibration amplitude of the car in the resonant wn=w state.b) At what speed will the car resonate?c) Find the regular regime vibration amplitude when the car is traveling at 80 km/h.arrow_forward
- Mechanical Vibrations Question is image A 300-kg machine is attached to an elastic foundation of stiffness 3.1 x E6 N/m and damping ratio 0.06. When excited by a frequency squared excitation at very large speeds, the machine's steady-state amplitude is 10 mm. What is the maximum steady-state amplitude the machine would experience at lower speeds?arrow_forwardMECHANICAL VIBRATIONS An unknown mass m is attached to the end of a linear spring with unknown stiffness coefficient k. The system has natural frequency of 30 rad/s. When a 0.5 kg mass is added to the unknown mass m, the natural frequency is lowered to 20 rad/s. Determine the mass m and the stiffness coefficient k.arrow_forwardA spring mass system with a natural frequency fn = 20 Hz is attached to a vibration table. Thetable is set to vibrate at 16 Hz, with a maximum acceleration 0.25 g. Answer the followingquestions. Justify your answers d. What is the maximum acceleration of the mass assuming the packaging can be modeled asa viscous damper with a damping ratio of 0.2?e. Is the motion of the mass in phase or out of phase with the motion of the table?arrow_forward
- Please show all work. will upvote, thanks An input force f = F‧sin(ωt) is applied to the body in both systems along the direction x. -Which of the two systems performs better in the frequency domain in terms of reducing the steady-state displacement amplitude X of the body ? Known are: m = 1kg, c = 5 Ns/m and k = 100 N/m?arrow_forwardA weight of 10lb is suspended by a spring having a modulus of 15 lb-s/in. When displaced and permitted to oscillate freely, it is found that the amplitude diminished from 1.5 in to 1.316 in in exactly 10 cycles. a.) determine the system mathematical model, b.) time period of the system, c.) system percent overshootarrow_forwardA suspension system of Volvo articulated dump truck is to be modelled mathematically given the following data: keq = 10.5 MN/m, m = 30 tons, and c = 300 N-s/m. If the harmonic forcing function is 2000 cos 5t N with the initial displacement and velocity to be 0 and 30 m/s respectively, determine the steady state and total response of the system.arrow_forward
- 2.A 31 kg skip attached to a steel rope on a crane is used to hoist bricks from the ground to the top of a construction site. The steel rope is wound onto a lifting drum with a diameter of 700 mm and rotational frequency of 52 revolutions per minute. The lifting drum is situated on the top floor which is 196 m high. How many seconds will it take to lift bricks, three quarters up the height of the building?arrow_forwardFind the maximum velocity of a free vibration with a response of 4(d^2 x/dt^2) + 25x = 0. Initial displacement of 0 and velocity of 1 m/s.arrow_forwardDetermine the steady state time response x(t) of a viscously damped system subjected to harmonic base excitation for the following data : m = 15 kg, c = 25 N.s/m, k = 300 N/m, y(t) = 0.04 sin ( 5t ) m. %3Darrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
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