Mechanical resonances can adversely affect the performance—even the life—of your electronic equipment. It is the condition under which the magnitude of vibratory response, described in terms of displacement, velocity, acceleration, or force, maximally exceeds the magnitude (displacement, velocity, acceleration, or force) of vibratory input.
Figure 1 is a plot of transmissibility.
Transmissibility is maximum when the frequency ratio is unity; that is, when
forcing frequency (ff) exactly equals natural frequency (fn). What is the maximum transmissibility, often called mechanical Q? It depends on how much friction or damping C is present. Figure 1 is plotted for several different damping ratios
C
Cc
Cc is the amount of damping called critical damping. This latter term is analogous to the electrical engineer’s critical electrical damping. A critically damped mechanical or electrical system, after being disturbed, quickly returns to its rest position without overshoot or oscillation.
Most systems are underdamped; that is, they oscillate after a disturbance. Generally, they respond with a fairly high Q. Were there no damping or friction in the system (obviously impossible), Q would theoretically reach infinity.
Why Is Resonance Generally Bad?
At the very least, resonant behavior can be uncomfortable. Most of us have observed and felt automobiles and aircraft shaking, bending, and emitting noises at certain speeds.
Resonance speeds up the fatigue process toward failure. Consider Figure 2. Generally, the higher the stress, the fewer cycles to failure. Resonance can lead to higher stresses within your products so that fewer cycles and less time elapse before cracking and outright failure occur.
Is Resonance Ever Useful?
Sometimes. Resonance helps us perform environmental stress screening, a final step in electronics production. We are looking for defects such as poorly soldered connections, bits of wire, and tiny blobs of solder. We deliberately overstress just-built or just-repaired products while applying power and monitoring behavior so that defects reveal themselves.
One useful stress is rapidly changing temperature. This stress makes parts quickly expand and contract. The other useful stress is broad-spectrum random vibration that simultaneously excites all possible resonances. Multiaxis shaking is more effective than sequential-axis shaking.
How Do You Recognize Resonance in Existing Hardware?
Sometimes you can hear the effects of resonance as larger velocities more strongly excite nearby air molecules. Indeed, sometimes you can see large displacements. A stroboscopic light or laser vibrometer can help, or you can feel increased displacements with your fingertips.
For example, you are concerned that a PCB located deep inside your equipment might be resonating. Perhaps a circuit on the PCB has been malfunctioning at certain vibration frequencies, and you suspect resonance. Hearing, seeing, or feeling won’t work. Look for increased strain levels using strain gages or increased acceleration using tiny accelerometers. Measure what happens mechanically to the PCB at those forcing frequencies at which electrical malfunctioning occurs.
How Can I Lessen Existing Resonance Problems?
Perhaps you can change materials, substituting ones with greater hysteretic damping or friction. For thin sections with high surface strains, perhaps you can apply viscoelastic materials (as with undercoating automobile instrument panels or door panels) or sticky viscoelastic tape. A thin metal layer on top of the tape is especially effective.
A bit more difficult, but sometimes very effective, method: shift one or more natural frequencies to avoid stacking resonances. Remember that Q values don’t just add—they multiply.
About the Author
Wayne Tustin founded Equipment Reliability Institute, an affiliation of reliability educators and consultants. During his career, more than 50 of his articles have appeared in EE-Evaluation Engineering. Equipment Reliability Institute, 1520 Santa Rosa Ave., Santa Barbara, CA 93109, (805) 564-1260, e-mail: [email protected].
Copyright 1998 Nelson Publishing Inc.
April 1998