## Working Principle
### Vibration Damping Dynamics Model Analysis  
In the practical application of the loss detection sensor, it is affixed to the rear of the wheat harvester, and the sensor is predominantly impacted by the mechanical operation vibrations operating at the same frequency. Excessive vibration interference could drown out the grain-knocking signal, resulting in the sensor detection accuracy being negatively affected. In an attempt to enhance the detection accuracy of the sensor, comprehensively analyze the factors influencing vibration interference, and determine the best method for vibration damping through the sensor damping structure, this paper establishes a vibration dynamics analysis model founded on the sensor structure. The vibration interference of the sensor can be modeled as a two-degree-of-freedom vibration system, as depicted in Figure 3. In this model, \(m_{2}\) corresponds to the mass of the stressed plate and piezoelectric ceramic, while \(m_{1}\) represents the mass of the counterweight metal. \(k_{2}\) and \(k_{1}\) denote the stiffness of the primary and secondary buffer mechanism materials, respectively, while \(c_{2}\) and \(c_{1}\) indicate the viscous damping coefficients of the primary and secondary buffer mechanism materials. The system experiences simple harmonic excitation, represented by \(F(t)\). Figure 3: Vibration damping structural dynamics analysis model. Figure 2: Sensor structure diagram. **1**. Impact plate; **2**. Piezoelectric ceramic vibrox; **3**. Primary buffer connection mechanism; **4**. Counterweight metal connection mechanism; **5**. Secondary buffer vibration reduction mechanism; **6**. Data processing module; **7**. Dustproof protective shell; **8**. Fixed bolts. Based on the kinetic analysis, it can be derived that the differential equation of motion of the two-degree-of-freedom vibration system model is expressed as Equation (1). \[ \begin{array}{l}[m]\Big{\{}\dot{x}(t)\Big{\}}+[c]\Big{[}\dot{x}\Big{\}}+[k] \big{\{}x(t)\big{\}}\\ =\{F\}e^{i\omega t}\end{array}  \tag{1}\]  
Formula  
\[\left\{ \begin{array}{l}\bigg{\{}x(t)=\bigg{\{}\begin{array}{l}x_{1}(t)\\ x_{1}(t)\end{array}\Big{\}},\{F\}=\bigg{\{}\begin{array}{l}F_{0}\\ 0\end{array}\Big{\}}\\ [m]=\bigg{[}\begin{array}{cc}m_{1}&0\\ 0&m_{2}\end{array}\Big{]},[c]=\bigg{[}\begin{array}{cc}c_{1}+c_{2}&-c_{2} \\ -c_{2}&c_{2}\end{array}\bigg{]}\\ [k]=\bigg{[}\begin{array}{cc}k_{1}+k_{2}&-k_{2}\\ -k_{2}&k_{2}\end{array}\bigg{]}\end{array} \right. \tag{2}\]  
where \(x_{0}\) is the amplitude of the base, and its amplitude is determined by the vibration of the machine itself; \(x_{2}\) and \(x_{1}\) are the amplitude response of the stressed plate and the counterweight metal, respectively, whereas the amplitude response is related to the parameters of the primary and secondary damping materials, that is, it is determined by \(k_{1}\), \(k_{2}\) and \(c_{1}\), \(c_{2}\). Incorporating Equation (2) into Equation (1), derived from the mechanical impedance equation, yields the system amplitude response Equation (3):  
\[\left\{ \begin{array}{l}\bigg{\{}\begin{array}{l}\big{|}X_{1}|\\ \big{|}X_{2}\big{|}\end{array}\Big{\}}=\frac{F_{0}\bigg{\{}\begin{array}{l} \sqrt{\left(k_{2}-\omega^{2}m_{2}\right)^{2}+\left(\omega c_{2}\right)}\\ \sqrt{k_{2}^{2}+\left(\omega c_{2}\right)^{2}}\end{array}\bigg{\}}}{\sqrt{A^{ 2}+B^{2}}}\\ A=\big{(}k_{1}-m_{1}\omega^{2}\big{)}\big{(}k_{2}-m_{2}\omega^{2}\big{)}-(k_{2} m_{2}+c_{1}c_{2})\omega^{2}\\ B=\big{(}k_{1}-m_{1}\omega^{2}\big{)}c_{2}\omega-m_{2}(c_{1}+c_{2})\omega^{3} +k_{2}c_{1}\omega\end{array} \right. \tag{3}\]  
Excluding the damping of the main system, \(c_{1}\) = 0, Equation (4) for the amplitude response variable can be obtained by simplification. \[\left\{ \begin{array}{l}\big{|}X_{1}|\\ \big{|}X_{2}\big{|}\end{array} \right\}=\frac{\delta_{\text{st}}\left\{ \begin{array}{l}\sqrt{\left(\alpha^{2}-\lambda_{1}^{2}\right)^{2}+\left(2 \delta_{2}\alpha\lambda_{1}\right)^{2}}\\ \sqrt{\lambda_{1}^{4}+\left(2\delta_{2}\alpha\lambda_{1}\right)^{2}}\end{array}