Resonance of Undamped Systems Structural Dynamics Response to Harmonic Excitation Example 3

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Structural Dynamics - Response to Harmonic Excitation Example 3 • The SDOF system shown below has the following properties: • Total Weight = 1000 lbs • Spring Stiffness = 2500 lbs/in • If the system is excited at resonance by a harmonic force with an amplitude of Fo = 500 lbs • Find the displacement amplitude of the force response after • A) 1 1/4 cycles • B) 10 1/4 cycles • C) 20 1/4 cycles • Bentley website: https://www.bentley.com/ • Bentley Youtube Channels: • / bentleysystems • / bentleystructural • / bentleystudentcenter • Check out our website: http://www.engineeringexamples.net/ • Please like our facebook page: / engineeringexamples • Our example covers forced harmonic response of an undamped single degree of freedom system. Damping is the mechanism through which energy is lost and, and forcing is the cause of excitation for the system. The forcing function in our problem is a periodic harmonic force. Periodic loads can either be harmonic or nonharmonic, but they are characterized as being repetitive and exhibit the same amplitude variation continuously over a number of cycles. In contrast, nonperiodic loads can be in the form of short-term impulsive events such as blast loading or long-duration events such as seismic or earthquake excitation. • Harmonic excitation can often be found in industrial and power applications where there is some type of force imbalance in rotating machinery such as fans, blowers, or compressors. This excitation will persist as long as the machinery is in operation, imparting sustained vibrations to the supporting structure. The resulting vibration has a transient component which is primarily affected by the initial conditions at startup and a steady-state component which continues long after the transient component has died out due to damping. If the excitation frequency approaches the natural frequency of the system, the steady-state response may exhibit extreme displacement amplitudes in a phenomenon known as resonance. Resonance is a highly undesirable condition and can lead to overstressing or failure of the system regardless of damping. • 1. Write complete displacement for resonant case. • 2. Find equivalent static deflection. • 3. Find mass and circular natural frequency • 4. Find displacement amplitude

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