VIBRATION DAMPING VIBRATIONAL

Vibration analysis Vibration control Vibration damping Vibration isolation Vibrations... 

Resihency provides another opportunity for the mbber functioning as a cushion between stainless steel loop clamps and fuel—hydraulic fluid lines in aircraft. Pratt and Whitney E-lOO military jet engine use (12) provides vibration damping without the clamp abraiding the tube surfaces in normal service as well as at temperatures down to —55°C. 

The transmissibihty of an isolator varies with frequency and is a function of the natural frequency (J/) of the isolator and its internal damping. Figure 7 shows the transmissibihty for a family of simple isolators whose fundamental frequency can be represented as follows, where k is the stiffness of the isolator, N/m and m is the supported mass, kg. Figure 7 shows that an isolator acts as an amplifier at its natural frequency, with the output force being greater than the input force. Vibration isolation only occurs above a frequency of aboutv times the natural frequency of the isolator. 

Bellows can vibrate, both from internal fluid flow and externally imposed mechanical vibrations. Internal flow liner sleeves prevent flow-induced resonance, which produces bellows fatigue failure in minutes at high flow velocities. Mechanically induced resonant vibration is avoided by a bellows with a natural frequency far away from the forcing frequency, if known. Multiple-ply bellows are less susceptible to vibration failure because of the damping effect of interply friction. 

Free- Vibration Methods. Free-vibration instmments subject a specimen to a displacement and allow it to vibrate freely. The oscillations are monitored for frequency and damping characteristics as they disappear. The displacement is repeated again and again as the specimen is heated or cooled. The results are used to calculate storage and loss modulus data. The torsional pendulum and torsional braid analy2er (TBA) are examples of free-vibration instmments. 

Master curves can be used to predict creep resistance, embrittlement, and other property changes over time at a given temperature, or the time it takes for the modulus or some other parameter to reach a critical value. For example, a mbber hose may burst or crack if its modulus exceeds a certain level, or an elastomeric mount may fail if creep is excessive. The time it takes to reach the critical value at a given temperature can be deduced from the master curve. Frequency-based master curves can be used to predict impact behavior or the damping abiUty of materials being considered for sound or vibration deadening. The theory, constmction, and use of master curves have been discussed (145,242,271,277,278,299,300). 

Similar information can be obtained from analysis by dynamic mechanical thermal analysis (dmta). Dmta measures the deformation of a material in response to vibrational forces. The dynamic modulus, the loss modulus, and a mechanical damping are deterrnined from such measurements. Detailed information on the theory of dmta is given (128). 

Example The differential equation My" + Ay + ky = 0 represents the vibration of a linear system of mass M, spring constant k, and damping constant A. If A < 2 VkM. the roots of the characteristic equation... 

Gray iron has outstanding damping properties—that is, ability to absorb vibration—as well as wear resistance. However, gray iron is brittle, with poor resistance to impact and shock. Machinability is excellent. 

Vibration during Check plow and linkage for loose compo-plowing out—can nents/wear lead to premature. sharpen plow or use serrated blade for hardened equipment failure heels and a potential ignition source— Manually remove heel more frequently see above. Plow at lower bowl speed Advance plow more slowly Make sure plow system is well damped Avoid air actuated plows Avoid use of full depth plows with hard cakes Use nitrogen knife to scrape centrifuge ... 

These spectra represent the nature of peak displacement/ velocity/forces and their magnitudes that may generate in a vibrating system of different damping levels and periods on the occurrence of an earthquake. They form... 

Figure 14.20 A typical free vibration record (sine wave) illustrating natural frequency of vibration and level of damping of an object F f>...

This is an important equation that defines the behaviour of a vibrating body under different conditions of applied force or motion F y From this it can be inferred that the response or movement of object x will depend upon t) and 7 is termed the fraction of critical damping and w , the angular natural frequency of the system. With the help of these equations, the response characteristics of an object to a force can be determined. 

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