Natural frequency method

In pulse version of MIA method the probes excite in tested object (TO) free attenuating pulses. Their carrier frequencies coincide with natural frequencies of transmitting probe vibrator loaded to the mechanical impedance Zg = / (Z -tZ,), where Z is elastic... 

A fan blade is continuously vibrating millions of cycles up and down ia operatioa over a short period of time. Each time a blade tip moves past an obstmction it is loaded and then unloaded. If forced by virtue of tip speed and number of blades to vibrate at its natural frequency, the ampHtude is greatly iacreased and internal stresses result. It is very important when selecting or rating a fan to avoid operation near the natural frequency. The most common method of checking for a resonance problem is by usiag the relatioa ... 

Ultrasonic Microhardness. A new microhardness test using ultrasonic vibrations has been developed and offers some advantages over conventional microhardness tests that rely on physical measurement of the remaining indentation size (6). The ultrasonic method uses the DPH diamond indenter under a constant load of 7.8 N (800 gf) or less. The hardness number is derived from a comparison of the natural frequency of the diamond indenter when free or loaded. Knowledge of the modulus of elasticity of the material under test and a smooth surface finish is required. The technique is fast and direct-reading, making it useful for production testing of similarly shaped parts. 

Alternative methods of verifying the rotor s dynamic characteristics, for example, variable frequency excitation with the pump at running speed to determine the rotor s natural frequencies, are available. The use of alternative methods and the interpretation of the results shall be agreed between the purchaser and manufacturer. 

In free vibration methods, the rubber test piece, with or without an added mass, is allowed to oscillate at the natural frequency determined by the dimensions and viscoelastic properties of the rubber and by the total inertia. Due to damping in the rubber, the amplitude of oscillations will decay with time and, from the rate of decay and the frequency of oscillation, the dynamic properties of the test piece can be deduced. 

If we neglect the terms in J,.2 and J J2, and consequently the nonharmonic character and the dependence of the y s on J, the energy is resolved into a rotational component and an oscillation component of the well-known form. As a nearer approximation we have a dependence of the oscillation frequency on the rotation quantum number and also the non-harmonic character of the oscillation. Naturally our method admits of more accurate calculations of the energy, involving higher powers of J and Je. 

Heat exchanger vibrations can be reduced either by increasing the tube bundle natural frequency or reducing excitation mechanisms. Methods to accomplish that and eventually prevent vibration and potential damage can be summarized as follows [130] ... 

Both the column thickness and the column natural frequency are important in determining the effect of wind on column sway and the stresses induced. To determine the natural frequency of the column, Rayleigh s method, based on harmonic displacement for all elements of the column, is used. The natural vibration frequency formula has been derived as follows ... 

In conclusion, the nature of the solvent can affect all the fluorescence parameters. Some examples, Table 3.3 shows the fluorescence lifetime measured with the frequency method of the nitrobenzoxadiazole dissolved in different solvents. One can notice that the fluorescence lifetime is solvent dependent. 

If the support is non-rigid, then its flexibility must be incorporated in the overall stiffness, 1,. In general, if the support is not infinitely stiff compared with the shaft, the resulting natural frequency will be lowered relative to the ideal rigid support case. For multiple impellers, intermediate and footstool bearings, the calculation methods would be more complex and the reader is referred to the use of Dunkerly s method for such configurations. ... 

A recent survey [70] classifies the vibration-based damage identification methods into four categories (1) natural frequency-based methods (2) mode shape-based methods (3) curvature/strain mode shape-based methods (4) other methods based... 

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