Lab 1 Instructions

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University of Calgary *

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211

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Mechanical Engineering

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Dec 6, 2023

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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

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