###### Abstract  
The effect of temperature on structural response is a concern in engineering applications. The literature has highlighted that applied temperature loads change the system vibration behaviour. However, there is limited information available about temperature impacting the dynamic response. This paper investigated the heating rates effects on modal parameters for both with crack and without crack conditions in a cantilever beam. A beam subjected to three heating rates was considered: 2, 5, and 8 \({}^{\circ}\)C/min. The first one was assumed as a slow heating rate while the others were assumed as moderate and high, respectively. This controlled rate of heating was achieved by using a proportional-integral-derivative (PID) temperature controller. The results showed that heating at different rates has little impact on modal parameters. While this effect is minimal at lower temperatures and more evident at higher temperatures. The results of temperature ramped at 2, 5, and 8 \({}^{\circ}\)C/min were compared with the numerical and analytical results only for all the isothermal conditions. It was observed that the beam natural frequency and its modal amplitude decrease with the increase in temperatures and crack depths. Therefore, it is concluded that the rate of heating can make a slight impact on the dynamics response of any mechanical system. thermal distribution; vibration analysis; vibration testing; modal response; fracture mechanics 202114375. [[https://doi.org/10.3390/app11104375](https://doi.org/10.3390/app11104375)]([https://doi.org/10.3390/app11104375](https://doi.org/10.3390/app11104375))  
Kamei, Kamei, M.A.K. increase in temperature mainly derived from thermal loads and changes in material properties. In the same way, the thermal effect on the vibration behaviour of functionally graded material influenced the natural frequencies at high temperatures [14,15]. [PERSON] and [PERSON] [17] observed that temperature-dependent material properties have little influence on the natural frequency at low temperature. However, there was a large influence when the temperature increased. [PERSON] [20] studied the temperature-dependent material properties under thermal loads on functionally graded material. They noticed that there was an attenuation rate of dimensionless frequency at high temperatures. [PERSON] et al. [18] investigated modal analysis in a non-uniform temperature distribution heated rectangular plate with the help of digital image correlation. They found that resonant frequencies of the plate were higher for transverse heating than longitudinal heating. [PERSON] et al. [21] observed that a decrease in Young's modulus at varying temperatures decreases the vibrating amplitude. In the literature, the vibration or dynamic response of cracked structures has been investigated by different approaches [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35]. However, the existing research on crack growth did not consider the effect of the rate of heating with different temperature exposure times. When the mechanical structure is exposed to high temperatures for a long duration, it may modify the mechanical properties of the material and hence influence the structural dynamic response. Furthermore, the dynamic behaviour of the structure depends on many factors associated with the applications and design. In this paper, the modal response of the structure is evaluated in the presence of thermal and mechanical loads. It investigated the heating rate's effect on modal parameters for both with crack and without crack conditions in a cantilever beam. A beam subjected to three heating rates was considered: 2, 5, and 8 \({}^{\circ}\)C/min. The first one was assumed as a slow heating rate while the others were assumed as moderate and high, respectively. This controlled rate of heating was achieved by using a proportional-integral-derivative (PID) temperature controller. The results showed that heating at different rates has little impact on modal parameters.