Wave Based Method (WBM) is an efficient method to analyze mid-frequency dynamic problems. This work extended the WBM to the transverse vibration analysis of a thermal beam with limited uncertain information. Novel wave functions and particular solution function for the thermal beam with deterministic parameters are derived to obtain the dynamic response. Then, by employing the interval perturbation method and sub-interval decomposition technique, the Sub-Interval Perturbation Wave Based Method (SIPWBM) is developed to analyze the uncertain propagation in thermal beams for the first time. Numerical simulations for thermal beams with deterministic parameters and interval parameters are conducted, respectively. The impacts of different thermal effects on deterministic dynamic response are investigated. Simulation results prove that the developed WBM could accurately predict the low- and mid-frequency transverse dynamic response of the thermal beam with deterministic parameters. The thermal stress effect plays a leading role in the low-frequency displacement frequency responses for beams under low-level temperature load. Whereas it is necessary to consider both the temperature-dependent material property effect and thermal stress effect in the mid-frequency transverse vibration analysis of thermal beams. By using the sub-interval decomposition technique and choosing a suitable sub-interval number, the SIPWBM could predict the bounds of the mid-frequency interval dynamic response accurately and efficiently.

基于波的方法（WBM）是分析中频动态问题的有效方法。这项工作将WBM扩展到具有有限不确定信息的热梁的横向振动分析。推导了具有确定性参数的热梁的新型波动函数和特定解函数，以获得动态响应。然后，通过采用区间扰动法和子区间分解技术，首次开发了基于子区间扰动波的方法（SIPWBM）来分析热束中的不确定传播。分别对具有确定性参数和间隔参数的热束进行了数值模拟。研究了不同热效应对确定性动态响应的影响。仿真结果表明，所开发的WBM能够在确定参数的情况下准确预测热梁的中低频横向动态响应。在低水平温度载荷下，梁的低频位移频率响应中，热应力效应起着主导作用。然而，在热梁的中频横向振动分析中，必须同时考虑温度相关的材料特性效应和热应力效应。通过使用子区间分解技术并选择合适的子区间数，SIPWBM可以准确，有效地预测中频区间动态响应的范围。在低水平温度载荷下，梁的低频位移频率响应中，热应力效应起着主导作用。然而，在热梁的中频横向振动分析中，必须同时考虑温度相关的材料特性效应和热应力效应。通过使用子区间分解技术并选择合适的子区间数，SIPWBM可以准确，有效地预测中频区间动态响应的范围。在低水平温度载荷下，梁的低频位移频率响应中，热应力效应起着主导作用。然而，在热梁的中频横向振动分析中，必须同时考虑温度相关的材料特性效应和热应力效应。通过使用子区间分解技术并选择合适的子区间数，SIPWBM可以准确，有效地预测中频区间动态响应的范围。