In many dynamic systems large vibration amplitudes occur if the operation frequency is near the resonance frequency. Also during the resonance passage large amplitudes result. In order to reduce the amplitude of the oscillation a suitable excitation can be applied. The force driven single degree of freedom harmonic oscillator is used to analyse the reaction of the dynamic system to a variable excitation frequency. The analysis starts with a mathematical transformation of the excitation signal in order to identify the influence of the different excitation parameters. It is shown that for specific parameters the natural frequency of the system can be eliminated from the excitation signal. In both cases, the operation near the resonance frequency and the passage through resonance, suitable numerical values, correlations between the parameters and functions can be found to reduce the resulting vibration amplitude of the system.
Many rotor dynamic systems are faced with large oscillation amplitudes while passing through the resonance. The coupled differential equations for the position of the center of the shaft and the rotation angle describe the dynamic behaviour of the rotordynamic system. With an appropriate external excitation the amplitude of the oscillations can be reduced. An unbalance excited oscillator is used to study the effects of a modulated angular velocity, where the angular velocity is prescribed as linear increasing with a superimposed harmonic function. The resulting excitation force is expressed as a series of Bessel functions of the first kind. In order to achieve small amplitudes near the resonance frequency of the system, special conditions for the ratio of the modulation frequency and the angular acceleration and the argument of the Bessel function of the first kind with integer order zero are derived. These requirements are first developed for a linear oscillator with an excitation force. Due to the analogy of the solution of the equation of motion these solutions are then applied directly to an unbalance excited oscillator. The results show smaller displacement amplitudes compared to the case with only linear increasing angular velocity. For the resulting motion the required torque is computed.
Dynamic systems are faced with large vibration amplitudes if they operate near the resonance frequency of the system or while passing through the resonance. With a suitable external excitation a reduction of the amplitude of the oscillation can be achieved. The analysis of a variable excitation frequency was first carried out on the force driven single degree of freedom harmonic oscillator. The influence of various excitation parameters can be seen after a mathematical transformation of the excitation signal. The elimination of the natural frequency of the system from the excitation signal is possible with specially selected parameters. It is demonstrated that suitable numerical values, correlations between the parameters and functions allow to reduce the oscillation of the amplitude of the system if the operation takes place near the resonance frequency and also during the resonance passage. The theoretical assertions are validated with an experimental setup and a parameter identification has been made. In addition a worst case scenario is analysed on the test rig. The developed requirements are extended to force driven harmonic oscillators with multi degree of freedom.
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