This paper presents a theoretical study on the influence of a discrete element in the nonlinear dynamics of a continuous mechanical system subject to randomness in the model parameters. This system is composed by an elastic bar, attached to springs and a lumped mass, with a random elastic modulus and subjected to a Gaussian white-noise distributed external force. One can note that the dynamic behavior of the bar is significantly altered when the lumped mass is varied, becoming, on the right extreme and for large values of the concentrated mass, similar to a mass-spring system. It is also observed that the system response is more influenced by the randomness for small values of the lumped mass. The study conducted also show an irregular distribution of energy through the spectrum of frequencies, asymmetries and multimodal behavior in the probability distributions of the lumped mass velocity.

中文翻译：

---

具有离散离散元素的连续系统的非线性随机动力学

本文提出了一个理论研究，即离散参数对连续机械系统非线性动力学的影响，模型参数受到随机性的影响。该系统由一个弹性杆组成，该弹性杆连接到弹簧和集总块上，具有随机的弹性模量，并受到高斯白噪声分布的外力作用。可以注意到，当集总质量发生变化时，条的动态行为会发生显着变化，在右侧极限值上并且对于较大的集中质量值，类似于质量弹簧系统。还可以观察到，对于较小的集总质量，系统响应受随机性的影响更大。进行的研究还表明，能量在整个频谱范围内分布不规则，