Natural frequency of vibration

Effect of Vibration. Tfll objects have a natural frequency of vibration when stmck sharply and fan rings, blades, stmcture, etc are no exception. Vibration is usually siausoidal and its frequency measured ia Hertz. The travel or displacemeat of the vibratioa is measured ia mils (1 /1000 of an iach) ia the United States but ia micrometers elsewhere. Another measuremeat is velocity (mm/ s) of movement. 

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

A better way of measuring is to measure the natural frequency of vibration of a round rod of the material, simply supported at its ends (Fig. 3.4) and heavily loaded by... 

But soundboards are much more than just radiating surfaces. They have their own natural frequencies of vibration and will respond much better to notes that fall within the resonance peaks than notes which fall outside. The soundboard acts rather like a selective amplifier, taking in the signal from the string and radiating a highly modified output and, as such, it has a profound effect on the tone quality of the instrument. 

Making a small change in the size of a valve spindle and thus changing its natural frequency of vibration (see Section 9.1.2 a). 

When equipment receives impulses at its own natural frequency of vibration, excessive vibration (resonance) occurs, and this can lead to rapid failure. A control valve was fitted with a new spindle with slightly different dimensions. This changed its natural frequency of vibration to that of the impulses of the liquid passing through it (the frequency of rotation of the pump times the number of passages in the impeller). The spindle failed after three months. Even a small change in the size of spindle is a modification [24]. 

It can be seen from equation 13.136 that the critical speed of a centrifuge will depend on the mass of the bowl and the magnitude of the restoring force it will also depend on the dimensions of the machine and the length of the spindle. The critical speed of a simple system can be calculated, but for a complex system, such as loaded centrifuges, the critical speed must be determined by experiment. It can be shown that the critical speed of a rotating system corresponds with the natural frequency of vibration of the system. 

Thus, application of delta function is equivalent to exciting all the circular frequencies with equal emphasis. This is the basis of finding the natural frequency of any oscillator via impulse response. When the oscillator is subjected to an impulse, all frequencies are equally excited and the system dynamics picks out the natural frequency of vibration, leaving others to decay in due course of time. It is noted that this result also applies to Laplace transform and we are going to use it often by replacing time by space and circular frequency by wave numbers. 

We have mentioned that absorption of light in the infrared region of the spectrum involves the excitation of molecular vibrations and also shown that resonance occurs when the frequency of the incident light corresponds to one of the natural frequencies of vibration of a material. But, we djd not explain how the light interacted with the sample to force this vibration. It turns out that even if the frequency of the infrared... 

The natural frequency of vibrations in DWP minima is related to the vibration frequency in an individual well, coq, by... 

Calculate the natural frequency of vibration for a ball of mass 10 g attached to a spring with a force constant of 1 N m. ... 

Vibration is the term used where an object is oscillated back and forth in a direction at a certain speed (frequency) and by a distance (amplitude). The frequency of vibration (cycles of movement per second) will not in itself cause damage and is not really a concern except in the special case of resonance, which is the natural frequency of vibration at which a object will vibrate most freely. At the resonant frequency the amplitude increases quite dramatically and can lead to the pack/product being severely damaged. 

The simplest classical theory for electronic polarization treats the atom or ion, of atomic number Z, as an electrical shell of charge Z,e and mass Z,m, attached to an undeformable ion nucleus (Fig. 14.6c). If the natural frequency of vibration of the system is cjq, it follows that the corresponding restoring force is... 

The ions are assumed to be attached to one another by a spring having a natural frequency of vibration cjjon which is directly related to the coulombic attraction holding the ions together. 

Electronic polarization involves the displacement of the electrons relative to their nucleus and exhibits a resonance when the frequency of the applied field is comparable to the natural frequency of vibration of the electronic cloud. The latter is determined by several factors, the most important being the volume of the ion involved. Electronic polarization is quite insensitive to temperature and is exhibited by all matter. 

Since every type of bond has a different natural frequency of vibration, and since two of the same type of bond in two different compounds are in two shghtly different environments, no two molecules of different structure have exactly the same infrared absorption pattern, or infrared spectrum. Although some of the frequencies absorbed in the two cases might be the same, in no case of two different molecules will their infrared spectra (the patterns of absorption) be identical. Thus, the infrared spectrum can be used for molecules much as a fingerprint can be used for hrrmans. By comparing the infrared spectra of two substances thought to be identical, you can establish whether they are, in fact, identical. If their infrared spectra coincide peak for peak (absorption for absorption), in most cases the two substances wdl be identical. 

The natural frequency of vibration of the molecule must equal the frequency of the incident radiation. 

It is on this basis that the mass per unit length of a fiber or filament is determined using the Vibroscope. Although the instrument is capable of being used by relatively unskilled operators, some care is needed to avoid confusing the natural frequency of vibration with the third harmonic frequency (see ASTM D 1577). 

When specimen is deflected from its equilibrium state by pulsed deformation, it returns to its state of equilibrium in free damped vibrations. The natural frequency of vibration, as well as the decrease of vibration amplitude with time, depends on the viscoelastic properties of the material. The principle of free damped vibrations has its practical application in torsion pendulum testing according to ISO 6721-2. The storage modulus G, the loss modulus G" and the loss factor tan S can be determined at frequency ranges from 10 Hz to 10 Hz. 

The finite element (FE) technique is an approximate numerical method for solving differential equations. Within the field of adhesive technology, it is most commonly used to determine the state of stress and strain within a bonded joint. It can also be used to determine moisture diffusion, natural frequencies of vibration and other field problems. Although this article will concentrate on the stress analysis, the same concepts can be applied to these other applications of finite element analysis. The basis of any finite element method is the discretization of the (irregular) region of interest into a number of... 

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