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Unformatted text preview: Department of Aerospace Engineering, IIT-Bombay 1 Title: Measurement of natural frequencies and modal damping constant for a cantilever beam using sine sweep Objectives: This experiment is designed to acquaint students with the following: 1. Identifying the natural frequencies of a system and identifying the associated mode shapes (bending or torsion) 2. Identifying the locations of nodal points in case of bending modes 3. Calculation of damping associated with each mode 4. Understanding the functioning of various instruments like accelerometer, charge amplifier, magnetic transducer, frequency generator, oscilloscope etc. Equipments used: 1. Steel rule 2. Accelerometer 3. Charge amplifier 4. Magnetic transducer 5. Digital signal oscilloscope 6. Frequency generator 7. Excitation amplifier Theory: This experiment deals with the forced vibration of a beam like structure. Here we intend to obtain the natural frequencies and mode shapes of the given structure by providing sinusoidal excitation of varying frequencies. For any structure, resonance is said to occur when the excitation frequency is equal to a natural frequency of the system. Theoretically, in the absence of any damping, the response of the structure at resonance is infinite. However, all structures possess damping in one form or the other, leading to a finite response even at the resonance condition. In this context, it may be noted that, unlike the case of zero damping, the peak response of a structure with viscous damping does not occur at the system natural frequencies. At AE 317 and AE 727 - Aircraft Structures Lab Lab Manual Series – Autumn 2009 EXPERIMENT 10: VIBRATION –2 Department of Aerospace Engineering, IIT-Bombay 2 low and moderate damping levels, the difference between the system natural frequency and resonant frequency is small enough to be ignored. At the resonance condition the phase difference between the excitation and the response is always 90 degrees irrespective of any damping in the structure. This property is used to identify the frequency at which resonance occurs. The excitation signal and the response signal are plotted against each other on the DSO. A phase difference of 90 degrees between the excitation signal and the response signal leads to the plot of an ellipse on the DSO, indicating that the excitation frequency is equal to one of the system natural frequencies. that the excitation frequency is equal to one of the system natural frequencies....
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This note was uploaded on 10/22/2009 for the course AE 317 taught by Professor Mira during the Spring '09 term at IIT Bombay.
- Spring '09