Resonant forced vibration

Dynamic techniques are used to determine storage and loss moduli, G and G respectively, and the loss tangent, tan 5. Some instmments are sensitive enough for the study of Hquids and can be used to measure the dynamic viscosity T 7 Measurements are made as a function of temperature, time, or frequency, and results can be used to determine transitions and chemical reactions as well as the properties noted above. Dynamic mechanical techniques for sohds can be grouped into three main areas free vibration, resonance-forced vibrations, and nonresonance-forced vibrations. Dynamic techniques have been described in detail (242,251,255,266,269—279). A number of instmments are Hsted in Table 8. Related ASTM standards are Hsted in Table 9. 

Resonance-Forced Vibration. Resonance-forced vibration devices drive the vibration of the specimen. This can be over a range of frequencies that includes the resonant frequency, which is detected as a maximum in the ampHtude, or the instmment can be designed to detect the resonant frequency and drive the specimen at that frequency. An example of the resonance-forced vibration technique is the vibrating reed. A specimen in... 

Resonance forced vibration is separated into flexural, longitudinal, and torsional vibration methods [4]. Because the flexural vibration method is... 

Forced (resonant) vibration. In forced vibration the usual driving frequency in rotating machinery is the shaft speed or multiples of this speed. 

Figure 5-20. Characteristic of forced vibration or resonance in rotating machinery. (Ehrich, F.F., Identification and Avoidance of Instabiiities and Seif-Excited Vibrations in Rotating Machinery, Adopted from ASME Paper 72-DE-21, Generai Eiectric Co., Aircraft Engine Group, Group Engineering Division, May 11, 1972.)...

Resonant vibration. Any of the forced vibration loads, such as cyclic or misalignment loads, may have a frequency that coincides with a natural frequency of the rotating-shaft system, or any component of the complete power plant and its foundation, and may, thus, excite vibration resonance. 

For damped forced vibrations, three different frequencies have to be distinguished the undamped natural frequency, = y KgJM the damped natural frequency, q = /KgJM — cgJ2M) and the frequency of maximum forced amplitude, sometimes referred to as the resonant frequency. 

Dynamic measurements can be made using either free or forced vibrations, and at resonance or outside of resonance conditions. Since the material depends on time and temperature, characterization over wide frequency ranges may be simplified by applying the WLF (118) equation for time-temperature equivalence. This relationship is generally useful in many propellant studies when used with caution under conditions which have established validity. 

Before considering particular test methods, it is useful to survey the principles and terms used in dynamic testing. There are basically two classes of dynamic motion, free vibration in which the test piece is set into oscillation and the amplitude allowed to decay due to damping in the system, and forced vibration in which the oscillation is maintained by external means. These are illustrated in Figure 9.1 together with a subdivision of forced vibration in which the test piece is subjected to a series of half-cycles. The two classes could be sub-divided in a number of ways, for example forced vibration machines may operate at resonance or away from resonance. Wave propagation (e.g. ultrasonics) is a form of forced vibration method and rebound resilience is a simple unforced method consisting of one half-cycle. The most common type of free vibration apparatus is the torsion pendulum. 

The results of dynamic tests are dependent on the test conditions test piece shape, mode of deformation, strain amplitude, strain history, frequency and temperature. ISO 4664 gives a good summary of basic factors affecting the choice of test method. Forced vibration, non-resonant tests in simple shear using a sinusoidal waveform are generally preferred for design data as... 

There are several possible approaches to the measurement of dynamic properties using forced oscillation of the test piece and the methods can be classified in various ways. The first distinction is between forced vibration at or near resonance and forced vibration away from resonance, with measurements at frequencies away from resonance being by far the most common. 

The forced vibration methods away from resonance can again be subdivided into those which apply deformation cycles and those which apply force cycles, the more usual being deformation cycles. An alternative form of test uses transient loading instead to continuous cycling. 

In the process of scattering and absorption, the electric component of the incident wave excites the vibrations of the oscillator. Under the effect of this component the electron performs forced vibrations. If the eigenfrequency ojq of the oscillator coincides with that of the light wave u>i, resonance absorption is observed. If these frequencies do not coincide, we have non-resonant scattering of light. 

A truly radical improvement was the development of quartz crystals, used in high-Q resonators. The vibrations of a quartz timing force cantilever can be transformed into a voltage across the faces of the crystal, by the piezoelectric effect The space group of a-quartz is P3221, and a voltage... 

The ground-state vibrational normal modes of thymine have been extensively studied, both experimentally and computationally. Vibrational spectra of thymine in the polycrystalline state [96-104], in Ar and N2 matrices [105-109], and in the gas phase [110] have been measured. In the least interactive environments, only the 1 -d, 3-d, and 1,3-d2 derivatives have been measured, while a number of 2H and 15N isotopomers in the polycrystalline state have been measured for thymine [104], Semi-empirical [111,112] and ab initio [98,113-115] calculations have been used to assign the vibrational bands for natural abundance thymine. However, the most robust reconciliation of experiment and computation is a recent attempt to computationally reproduce the experimentally observed isotopic shifts in 10 different isotopomers [116] of thymine. The success of that attempt is an indication of the reliability of the resulting force field and normal modes. The resonance Raman vibrations of thymine, and their vibrational assignments, are given in Table 9-1. 

Potato of the first kind involves acoustic coupling to the resonator of vibrations in the field modulation coils that arise from forces determined by the cross product of current and magnetic field. It is controlled by mechanical damping and acoustic isolation. 

For s = 0 and for s - as, the interferogram given by Eq. (A 1.2) exhibits the properties quoted in Section 3.2. The functions I (v) and I (s) are a Fourier transform pair well known from the theory of forced vibrations and resonance of damped oscillators. One reason why they are very useful to demonstrate problems of Fourier transform spectroscopy is that the different contributions to I v) and to I (s) can be studied separately (cf. Fig. 12). 

The objective of this investigation was to determine the effects of vibration on heat 1 transfer and scaling mechanisms related to saline water conversion processes. During the initial phases of this study the effect of both vibration of the heat transfer surface and resonant acoustic vibrations in water on forced convection heat transfer was explored. Forced convection heat transfer was considerably more influenced by a vibrating heat transfer surface than by a standing acoustic wave in the flow medium. The major portion of this study was therefore concentrated on forced convection heat transfer from a vibrating heat transfer surface. 

Effect of Resonant Acoustic Vibrations in Water on Forced Convection Heat Transfer... 

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