## 3 Dynamic Response for an Accessory Structure Equipped on the Primary Structure
### Parameter Sensitivity Analysis of the Theoretical Model Considering Excitation \(P_{2}\)  
Figure 13 illustrates the influence of the excitation amplitude ratio \(F_{21}\) on the subsidiary structure's dynamic response. It is noted that the second peak value significantly increases with increasing parameter \(F_{21}\) and the first peak becomes increasingly inconspicuous as the excitation amplitude \(F_{2}\) increases. The reason for this is that the external force \(P_{2}\), which directly impacts the subsidiary structure, has more influence on the accessory structure's dynamic response than the excitation \(P_{1}\). As the amplitude ratio \(F_{21}\) increases, the external force \(P_{2}\) will make a major contribution to the dynamic behavior of the accessory structure and the contribution from excitation \(P_{1}\) can be ignored. Generally speaking, the value of parameter \(F_{21}\) cannot be very large in the case of a small mass ratio \(m_{21}\), thus the parameter \(F_{21}\) is considered equal to 0.0001 in the following analysis. As shown in Figure 14, there are two peaks in the amplitude coefficient curves in the case of \(\omega_{12}\leq 1\) and the peak corresponding to the higher excitation frequency disappears when \(\omega_{12}>1\). Generally speaking, the vibration frequency of the accessory structure is usually higher than that of the large-scale primary structure and the value of \(\omega_{12}\) is considered to be 0.1 in the following analysis. Therefore, it is considered that the dynamic response of the subsidiary structure in the case of \(\omega_{0}=\omega_{1}\)  
Figure 12: Frequency response for the subsidiary structure with varying parameter \(\xi_{1}\): (a) the entire graph; (b) partial enlarged graph. Figure 13: Frequency response for the subsidiary structure with varying parameter \(F_{21}\). is greater than that in the case of \(\omega_{0}=\omega_{2}\). The possible reason for this is that the dynamic behavior of the subsidiary structure is significantly amplified by the resonance of the primary structure when \(\omega_{0}=\omega_{1}\) and the excitation \(P_{2}\) is not large enough to make a major contribution for the accessory structure's dynamic response. The influence of the damping ratio \(\xi_{2}\) on the dynamic response of the accessory structure is investigated under the condition of \(\omega_{12}=0.1\), \(m_{12}=50,000\), \(\xi_{1}=0.05\) and \(F_{12}=0.0001\). It is noted that the peak value decreases with increase of the damping ratio \(\xi_{2}\) in the case of \(\omega_{0}=\omega_{2}\) (i.e., \(\omega_{01}=10\)) and the varying parameter \(\xi_{2}\) has no influence on the first peak of the curves, which indicates that the maximum possible value for the amplification factor is not reduced. Moreover, the influence of the damping ratio \(\xi_{1}\) on the accessory structure dynamic response is investigated under the condition of \(\omega_{12}=0.1\), \(m_{12}=50,000\), \(\xi_{2}=0.04\) and \(F_{12}=0.0001\). The first peak value significantly decreases with increase of the damping ratio \(\xi_{1}\) in the case of \(\omega_{0}=\omega_{1}\) (i.e., \(\omega_{01}=1\)), and the second peak value slightly decreases with increasing \(\xi_{1}\) when \(\omega_{0}=\omega_{2}\) (i.e., \(\omega_{01}=10\)). Therefore, the maximum possible dynamic response of the accessory structure will be effectively reduced when the primary structure damping ratio increases and the values of the parameters \(\omega_{12}\), \(\xi_{2}\), \(m_{12}\) and \(F_{12}\) remain unchanged. To avoid redundancy, the figures for the frequency response of the subsidiary structure with varying parameters \(\xi_{1}\) and \(\xi_{2}\) are not given. According to Figure 15, the mass ratio \(m_{12}\) has complex effects on the second peak of the frequency response curves under the condition of \(\omega_{12}=0.1\), \(\xi_{1}=0.05\), \(\xi_{2}=0.04\) and \(F_{12}=0.0001\).