The next component is a 1 Hz sine wave with an amplitude of 0.64. This is shown by the line at 1 Hz. In other words, to efficiently pump energy into both mass and spring requires that the energy source feed the energy in at a rate equal to the natural frequency. The values of the spring and mass give a natural frequency of 7 Hz for this specific system. The figure illustrates the resulting vibration. a square wave). Types of Free Vibrations. The corresponding mode shape is called the rigid-body mode. Sine (one-frequency-at-a-time) tests are performed to survey the structural response of the device under test (DUT). The most widely studied and most common type of segmental vibration exposure is hand-arm vibration exposure which affects the hands and arms. The proportionality constant, k, is the stiffness of the spring and has units of force/distance (e.g. The Some vibration test methods limit the amount of crosstalk (movement of a response point in a mutually perpendicular direction to the axis under test) permitted to be exhibited by the vibration test fixture. In a previous section only a simple harmonic force was applied to the model, but this can be extended considerably using two powerful mathematical tools. For higher frequencies (typically 5 Hz to 2000 Hz), electrodynamic shakers are used. The eigenvalues for this problem given by an eigenvalue routine is: As in the case of the swing, the force applied need not be high to get large motions, but must just add energy to the system. Please refer to the references at the end of the article for detailed derivations. For example, if a known force over a range of frequencies is applied, and if the associated vibrations are measured, the frequency response function can be calculated, thereby characterizing the system. Vibration can be desirable: for example, the motion of a In many cases, however, vibration is undesirable, wasting The studies of sound and vibration are closely related. An unrestrained multi-degree of freedom system experiences both rigid-body translation and/or rotation and vibration. The solution to the The major points to note from the solution are the exponential term and the cosine function. the sum of the kinetic and the potential energies remains constantIn this method, the maximum kinetic energy at the mean position is made equal to the maximum potential energy( or strain energy) of the extreme position.The displacement of the mass âmâ from the mean position at any instant is given byConsider, âmâ = man of the spring wire per unit lengthKE of the spring = 1/3 * KE of a mass equal to that of the spring moving with the same velocity as the free end.When an elastic body is set in vibratory motion, the vibrations die out after some time due to the internal molecular friction of the mass of the body and the friction of the medium in which it vibrates. Transverse vibration Using this coordinate transformation in the original free vibration differential equation results in the following equation. A force of this type could, for example, be generated by a rotating imbalance. Alternately, a DUT (device under test) is attached to the "table" of a shaker. For example, calculating the FRF for a mass–spring–damper system with a mass of 1 kg, spring stiffness of 1.93 N/mm and a damping ratio of 0.1. Also, the magnitude can be reduced if the natural frequency can be shifted away from the forcing frequency by changing the stiffness or mass of the system. The negative sign indicates that the force is always opposing the motion of the mass attached to it: Examples of this type of vibration are pulling a child back on a swing and letting it go, or hitting a tuning fork and letting it ring. The following are some other points in regards to the forced vibration shown in the frequency response plots. Sound, or pressure Vibration testing is accomplished by introducing a forcing function into a structure, usually with some type of shaker. Exposed occupational groups include operators of chain saws, chipping tools, jackhammers, jack leg drills, grinders and many other workers who operate hand-held vibrating tools. Resonance is simple to understand if the spring and mass are viewed as energy storage elements – with the mass storing kinetic energy and the spring storing potential energy. The damper, instead of storing energy, dissipates energy. The phase of the FRF was also presented earlier as: In practice, this is rarely done because the frequency spectrum provides all the necessary information.