In this paper, the problem of non-linear vibrations of an articulated column subjected to two loads was considered. The first load is axial compression associated with the action of the mass element. The second is the heat load in the form of a local heat source. In such a system, the problem analysis was divided into two parts. The first illustrates the influence of temperature on the physical and mechanical properties of the structure. The second - concerning non-linear vibrations of the system. The problem of heat flow in the column was formulated on the basis of the classical Fourier heat conduction equation and solved with the use of the Finite Element Method. Distribution of material properties (Young’s modulus) was obtained in subsequent moments of exposure of the column to the heat source. The obtained results were used in the problem of system vibrations, which was formulated on the basis of Hamilton’s principle. Due to the non-linearity, the perturbative small parameter method was used to finally derive the differential equations describing the behaviour of the system during vibrations. Numerical calculations were carried out on the basis of which the characteristic curves of the system (on the load - natural frequency plane) for various stages of heating the column were determined. Moreover, the influence of the heating time of the system on its non-linear natural frequency was presented. The significant influence of the longitudinal inertia of the mass element causing the load on the vibrations of the structure was shown. The mathematical model and the correctness of the performed numerical simulations were verified by experimental research.

在本文中，考虑了承受两个载荷的铰接柱的非线性振动问题。第一载荷是与质量元件的作用有关的轴向压缩。第二个是局部热源形式的热负荷。在这样的系统中，问题分析分为两个部分。第一个示例说明了温度对结构的物理和机械性能的影响。第二-关于系统的非线性振动。柱中的热流问题是根据经典的傅立叶热传导方程式提出的，并使用有限元方法解决了。在柱子暴露于热源的随后时刻获得材料特性（杨氏模量）的分布。所得结果用于基于汉密尔顿原理的系统振动问题。由于非线性，微扰小参数方法最终用于导出描述系统在振动过程中行为的微分方程。在此基础上进行了数值计算，从而确定了在加热塔的各个阶段系统的特性曲线（在载荷-固有频率平面上）。此外，提出了系统加热时间对其非线性固有频率的影响。示出了引起载荷的质量元件的纵向惯性对结构的振动的显着影响。