The objective of this research is to study the dynamic response characteristics of a three-beam system with intermediate elastic connections under a moving load/mass-spring. In this study, the finite Sine-Fourier transform was performed for the dynamic partial differential equations of a simply supported three-beam system (SSTBS) under a moving load and a moving mass-spring, respectively. The dynamic partial differential equations were transformed into dynamic ordinary differential equations relative to the time coordinates, and the equations were solved and the displacement Fourier amplitude spectral expressions were obtained. Finally, based on finite Sine-Fourier inverse transform, the expressions for dynamic response of SSTBS under the moving load and moving mass-spring were obtained. The proposed method, along with ANSYS, was used to calculate the dynamic response of the SSTBS under a moving load/mass-spring at different speeds. The results obtained herein were consistent with the ANSYS numerical calculation results, verifying the accuracy of the proposed method. The influence of the load/mass-spring’s moving speed on the dynamic deflections of SSTBS were analyzed. SSTBS has several critical speeds under a moving load/mass-spring. The vertical acceleration incurred by a change in the vertical speed of SSTBS due to the movement of mass-spring and the centrifugal acceleration produced by the movement of massspring on the vertical curve generated by SSTBS vibration could not be neglected.

中文翻译：

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在运动的载荷/弹簧作用下具有中间弹性连接的三梁系统的动力响应

这项研究的目的是研究在移动载荷/质量弹簧的作用下具有中间弹性连接的三梁系统的动力响应特性。在这项研究中，分别对移动载荷和质量弹簧作用下的简单支撑三梁系统（SSTBS）的动力偏微分方程进行了有限Sine-Fourier变换。将动态偏微分方程转化为相对于时间坐标的动态常微分方程，进行求解，得到位移傅立叶振幅谱表达式。最后，基于有限的Sine-Fourier逆变换，获得了SSTBS在动载荷和动质量弹簧作用下的动力响应表达式。所提出的方法以及ANSYS 用来计算SSTBS在不同速度下的移动负载/质量弹簧下的动态响应。本文获得的结果与ANSYS数值计算结果一致，验证了所提方法的准确性。分析了载荷/质量弹簧的运动速度对SSTBS动力变形的影响。在负载/质量弹簧移动的情况下，SSTBS具有几个临界速度。不能忽略由于质量弹簧的运动而引起的SSTBS垂直速度的变化所引起的垂直加速度，以及由于SSTBS振动所产生的垂直曲线上的质量弹簧的运动所产生的离心加速度。验证所提出方法的准确性。分析了载荷/质量弹簧的运动速度对SSTBS动力变形的影响。在负载/质量弹簧移动的情况下，SSTBS具有几个临界速度。不能忽略由于质量弹簧的运动而引起的SSTBS垂直速度的变化所引起的垂直加速度，以及由于SSTBS振动所产生的垂直曲线上的质量弹簧的运动所产生的离心加速度。验证所提出方法的准确性。分析了载荷/质量弹簧的运动速度对SSTBS动力变形的影响。在负载/质量弹簧移动的情况下，SSTBS具有几个临界速度。不能忽略由于质量弹簧的运动而引起的SSTBS垂直速度的变化所引起的垂直加速度，以及由于SSTBS振动所产生的垂直曲线上的质量弹簧的运动所产生的离心加速度。