§ 79. General Analysis of Vibrations
Periodic reciprocating motions of the elements of an elastic system can be termed vibrations or oscillations. The problem of helicopter vibrations remained unresolved for a long time ; therefore, large-scale helicopter flying was not possible. Experimental flights performed prior to the middle 1940’s frequently terminated in accidents as a result of severe vibrations.
Several hundred different vibrations of individual parts and of the entire helicopter as a unit can he counted on a helicopter.
Parameters of oscillatory motions. We consider an elastic plate with one end clamped and a small weight on the other end (Figure 109a). If the end with the weight is deflected and then released, oscillations of the plate develop. This will be the simplest example of vibrations (Figure 109b). The oscillatory motions are characterized by three basic parameters: period,
frequency, and amplitude. The period is the time for a complete oscillation (T).
Frequency is the number of periods per unit time
Amplitude is the largest deviation of an oscillating point from the neutral position
Oscillatory motion modes. With regard to nature of onset, oscillatory motions can be excited.
Forced vibrations are those which are caused by periodic external forces. Such forces are exciting. Forced vibrations take place with a frequency equal to that of the exciting forces. Damping forces or forces which attenuate the vibrations arise during all vibrations. The damping forces may be either internal or external. The internal damping forces arise as a result of elasticity of the material itself from which the structure is fabricated. External damping forces arise as a result of resistance of the medium in which the vibrations take place. The larger the damping forces, the faster the vibrations decay.
Natural vibrations are those which continue after termination of the action of the disturbing forces. The basic characteristic of natural vibrations is that each structure has a very definite vibration frequency, which is independent of the exciting force and is determined by the mass and stiffness of the structure.
The larger the mass of the structure, the lower the natural vibration frequency. The greater the structure stiffness, the higher the natural vibration frequency.
With regard to nature of the amplitude variation, vibrations can be divided into damped and increasing. If the amplitude decreases, in the course of time, the vibrations will be damped. Natural vibrations are always
damped. If the amplitude increases with time, the vibrations will be increasing. Increasing vibrations develop at resonance.
Resonance is coincidence of the frequency of the exciting forces with /179
the frequency of the natural vibrations of the structure. Vibrations of helicopter parts are most often forced vibrations.