Abstract
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.
An Euler-Bernoulli beam in the thermal environment
The computational cost for SIPWBM with different sub-interval numbers
原文链接：https://doi.org/10.1016/j.ast.2020.106438