Engineering principles of acoustics: Noise and vibration by Douglas D. Reynolds

By Douglas D. Reynolds

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119) tan'-^ (2 c r). 121) + (2cr)2}''= shows the transmissibility plotted as a function of the frequency ratio r. Rotating and Reciprocating Unbalance Many vibration problems are due to rotating unbalance in rotating machines such as blowers, turbines, The unbalance present in these machines is expressed in terms of an equivalent mass electric motors, etc. m with an eccentricity of e and is generally given as the product The schematic of a rotating machine with a me. 23 vertical direction. If the unbalanced mass m rotates with an angular velocity .

51) . n A and B are evaluated by applying the initial A = y 'o and conditions y(0) B = v on /oi = y and y(0) = v . When this is done, . 52) . n Generally it is desirable to write the above equation in terms of one trigometric function. To do this, first let V — (i) = - Y sin ((. and y ''0 = Y cos 4. 53) SEC. 7 = y{t) Y(cos * cos t - sin u) <(i sin u) 23 t) which can be reduced to Y is Ycos = y(t) (a)^t + *). 54). 7 Y=/(^)2+y„2. or ° "n or * = tan"' (- —^). 4, when they are set into motion by an initial displacement or velocity, they will continue to vibrate about their static equilibruim positions, theoretically, until time equals infinity.

The minus sign indicates power is being Newton's method can be used on vibrating systems with more than one degree of freedom, but the energy method described above can only be used on one-degree-of-freedom systems. The use of these two methods will be illustrated with several examples. 1(a) using Newton's method. When ///////// ///////// ///////// a mass M is attached to the unstretched distance downwards. 5, the spring deflects This causes the static restoring force on a the mass which equals the weight of the mass.

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