# Research on Non-Random Vibration Analysis of Concrete Pump Truck Boom Based on Dynamic Excitation
## 5 Experimental Design and Result Analysis
### Analysis of Boom Vibration Response  
Boom vibration not only results in material loss and increased costs during concrete pumping but may also cause early wear, fatigue damage, and reduced service life of boom components. The boom experiences complex loads during operation and is frequently exposed to unstable conditions, resulting in its vibration response significantly affecting the performance and structural integrity of the pump truck. Consequently, to guarantee the safety and reliability of the equipment and the precision of the concrete placement process, a thorough analysis and prediction of the boom's vibration characteristics is essential. This study optimizes the boom design, mitigates vibration-related issues, and offers maintenance and operational personnel timely alerts of failures, thereby preventing potential safety risks. This study addresses the issue of vibration in pump truck booms. The dynamic equations of this system are shown in Equation (24), determined by integrating the vibration characteristics of the pump truck boom, structural stiffness, mass distribution, and external  
Figure 5: Beginning with the boom’s initial portion, the forces at each joint turning point. loads. By modeling and analyzing this vibration system, the vibration response data of the boom under various operational situations may be acquired. These data not only enhance our comprehension of the potential vibration modes of the boom during operation but also establish a theoretical foundation for subsequent design optimization. The dynamic response of the boom during the pumping process significantly influences the concrete flow rate, pouring precision, and operational smoothness; therefore, comprehensive vibration analysis and optimization are essential in the initial design phase to guarantee the equipment's efficient and safe operation. \[[I]\Big{\{}\hat{\theta}(t)\Big{\}}+[C]\Big{\{}\hat{\theta}(t)\Big{\}}+[K]\{ \theta(t)\}=\{\tau(t)\} \tag{24}\]  
\(I\), \(C\), and \(K\) are 7 \(\times\) 7 matrices among them. Following analysis and simplification, each matrix element's specific forms are as follows:  
\[[I]= \begin{bmatrix}\frac{1}{2}md^{2}\\ &\frac{1}{3}mx^{2}\\ &&\frac{1}{3}mx^{2}\\ &&\frac{1}{3}mx^{2}\\ &&\frac{1}{3}mx^{2}\\ &&\frac{1}{3}mx^{2}\\ &&\frac{1}{3}mx^{2}\\ &&\frac{1}{3}mx^{2}\end{bmatrix}  \tag{25}\]  
\[[C]= \begin{bmatrix}c_{1}\\ c_{2}\\ &-c_{3}&c_{3}\\ &&-c_{4}&c_{4}\\ &&-c_{5}&c_{5}\\ &&&-c_{6}&c_{6}\\ &&&-c_{7}&c_{7}\end{bmatrix}  \tag{26}\]  
\[[K]= \begin{bmatrix}k_{1}\\ &k_{2}+k_{3}&-k_{3}\\ &-k_{3}&k_{3}+k_{4}&-k_{4}\\ &&-k_{4}&k_{4}+k_{5}&-k_{5}\\ &&-k_{5}&k_{5}+k_{6}&-k_{6}\\ &&&&&-k_{6}&k_{6}+k_{7}&-k_{7}\\ &&&&-k_{7}&k_{7}\end{bmatrix}  \tag{27}\]  
In the methods presented in this study for solving the arm dynamics equations, the influence of the first joint on the system dynamics equations is disregarded, as it merely serves as a directional change and is not susceptible to external pressures. The condition of the first joint is disregarded, and it is presumed to have no impact on the system's vibration characteristics. Consequently, as illustrated in Figure 5, the analysis commences at the second joint, namely the joint connecting the first boom, from which the dynamic response curves for the vibration angles of each joint are derived. In Figure 6, the gray lines depict the sample response curves produced by the Monte Carlo simulation approach, while the red and blue curves illustrate the maximum and lower limits of the dynamic response derived from the computational method presented in this paper, respectively. The analysis results indicate that when the uncertain excitation is represented by the interval process model, the interval curves derived from the numerical simulation fully encompass the Monte Carlo sample response, thereby confirming the validity and reliability of the computational method proposed in this paper for analyzinguncertain dynamic responses.