俺妹不可能这么发育的

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Reference:

BASICS OF VIBRATION ISOLATION

俺妹不可能这么发育的
Vibration isolation is a technique to mitigate mechanical vibrations. There are two types of vibration isolation techniques; passive and active. In passive vibration isolation, vibrations are isolated with passive techniques such as rubber pads or springs. In active vibration isolation, vibrations are controlled with automated control systems.

Mechanical vibrations are generated due to unbalance of rotating and reciprocating components such as rotors of pumps, electric motors, combustion engines; or impact forces of hammers and presses; pressure loadings on surfaces due to the winds or acoustic noises; or moving on a bumpy and irregular road with a vehicle. Depending on conditions, mechanical vibrations can be dangerous for systems and can lead catastrophic failures if not analyzed and managed in a correct way. To reduce or eliminate the unwanted vibrations, vibration analyses are generally done by vibration engineers and vibration isolation techniques are incorporated into the design of systems. Control techniques for passive vibration isolation are summarized as follows:

**Minimization of the effect of excitation:** The source of the
mechanical vibration can be minimized. If it is a rotating component, the magnitude of
harmonic excitation force is proportional to square of the angular velocity and magnitude of unbalance. So for a rotating component, the rotation speed can be reduced and/or the rotating element can be balanced by using balancing machines to have less unbalance on the rotating part.

Dynamic Balancing of a Spindle

The change of excitation frequency of the input harmonic forcing to the system will
affect the amplitude of the response. As an example, if we think a single degree of freedom system
which creates a harmonic excitation, increasing excitation frequency beyond the system natural frequency will result a decrease in system response. The particular solution of the differential equation of the
sdof system is given below. Here w_{n} is system natural frequency of
the system and w is forcing frequency. If w = w_{n} are equal, the denominator of the formula will be small and X (excitation displacement) will be high.

So as a result, in real systems, if the excitation frequency can be adjusted to have a frequency larger than systems natural frequencies, then the system response will be significantly reduced.

The other method to minimize the effect of excitation is reduction of unbalance of the system. If it's a rotating system, the balance correction can be done by addition or removal of material according to results given by balancing machines. Different types of machines exist such as dynamic and static balancing machines. The proper balancing method shall be selected according to the application.

**Specify system parameters to reduce the effects:**
If we think the same single degree of freedom system with the governing formula given above,
system displacement X also depends on system parameters such as mass (m),
natural frequency (w_{俺妹不可能这么发育的n})
and damping ratio (ζ). The natural frequency of the system
(w_{n}) itself depends on system stiffness (k) and mass (m). ζ is damping ratio which depends on system’s damping coefficient c
(See following equations of w_{n} and ζ for the dependencies.) So system displacement X
is dependent on mass, stiffness and damping coefficient parameters of the
system. If the harmonic excitation frequency is known, designing system parameters to minimize steady-state amplitudes is possible. This may be achieved by addition of more viscous damping or design optimization of the structure to have optimal stiffness to reduce the vibration levels.
On the left side, very stiff fixture can be seen which is designed to reduce the
effects of mechanical vibrations.

Equation of system natural frequency (SDOF) | Equation of system damping ratio (SDOF) |

**Change of system configuration:**
Instead of altering design parameters of the system as defined above, changing
the configuration can reduce the vibration levels. If we
use the same system and add an additional mass-spring-damper on it, the new system will be two degree of freedom. If this
additional mass-spring-damper system is designed correctly, it will act like a vibration absorber. With addition of correctly tuned vibration absorber, system resonance frequencies can be moved away from the excitation frequency.

See following figure for the simple schematic of the two degree of freedom system after the addition of tuned vibration damper.

**Reduction of force transmission:**
If a machine is creating mechanical vibrations, the force transmission to its base can be reduced by implementing vibration isolators and isolation systems such as elastic rubbers,
vibration mounts, wire rope isolators, vibration pads, shock absorbers
and spring systems. A picture of spring isolator system is given in the
right side.

Information given here is for introductory purposes. For the isolation of systems from the mechanical vibrations, it shall be consulted to experts of vibration engineering for suitable design solutions.

- Kelly,S.G. (2000). Fundamentals of Mechanical Vibrations .2nd edition.McGraw-Hill

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