# Temperature Effects on the Natural Frequencies of Composite Girders
## 3 Experiments on Temperature Effects
### Modal Tests  
Modal tests were conducted to examine the natural frequencies of the specimen in response to temperature variations. Figure 5 schematically illustrates the modal testing process adopted in this study. The specimens were excited using an impact hammer (PCB 086C03). The excitation force was applied perpendicular to the concrete deck. Five excitation points (E1 to E5) were used to excite the specimen. Accelerations were measured using five accelerometers (A1 to A5) that were installed along the bottom flange of the steel beam, as shown in Figure 4. The acceleration signals were amplified using a signal conditioner (PCB 483C05) and acquired using a dynamic data logger (IOLITE 6 \(\times\) STG). The acquired data were analyzed using the Dewesoft X software to calculate the frequency response functions (FRFs) and natural frequencies. The five FRFs obtained by changing the impact point along the span were averaged to determine the modal frequencies under specific temperature conditions.  
To investigate the effects of temperature variation, modal tests were conducted by varying the top deck temperature from 20 to 50 \({}^{\circ}\)C. The room temperature was controlled at 20 \({}^{\circ}\)C. The FRFs were calculated using the fast Fourier transform algorithm. The frequency range was 0-200 Hz. As shown in Figure 6a, the second peak response of the FRFs, which corresponded to the bending mode, appeared between 35 and 40 Hz. The coherences in this frequency range were between 0.98 and 1, as shown in Figure 6b; hence, the FRFs were presumed to be reliable.  
Figure 7 presents the results obtained from the modal tests conducted at various temperatures. The frequency exhibited an inverse relationship with the temperature, which conforms to the results of previous studies [5; 6; 31; 32; 33; 34]. This phenomenon can be attributed to the reduction in the stiffness of the materials with increasing temperature. [PERSON] and [PERSON] [35] investigated a steel plate girder bridge model and observed that the frequency of the second bending mode decreased by approximately 0.44% when the temperature rose by one degree. [PERSON] et al. [6] investigated the natural frequencies of concrete slabs and the modal frequencies decreased by 0.226% per degree relative to the modal frequencies at a temperature of 0 \({}^{\circ}\)C. [PERSON] et al. [36] conducted a two-year dynamic test on a reinforced concrete slab in a laboratory and observed a reduction in the natural frequency of the bending mode of 0.13% to 0.23% per degree. In this study, linear regression analysis revealed that the frequency decreased at a rate of 0.36% per degree as the temperature increased, as indicated Equation (6).  
\[F=-0.0036T+37.82 \tag{6}\]  
Figure 5: Modal testing procedure.  
Here, \(F\) is the natural frequency and \(T\) is the temperature (\({}^{\circ}\)C).  
When comparing the test results to those of other studies, it became apparent that the frequency decreased with increasing temperature. The variation in rates among studies can be attributed to differences in materials and testing conditions. In general, the observed consistency in the decreasing trend underscores the impact of temperature on structural dynamics while recognizing diverse factors influencing these outcomes across different research contexts.  
Figure 6: Example modal test results obtained from the fifth accelerometer at 20 \({}^{\circ}\)C: (a) magnitude of FFRs; and (b) coherence.  
Figure 7: Natural frequency–temperature relationship.