The influence of prestressing force on natural frequencies of beams - Gan, Bing-Zheng (2019)
This thesis investigates the effect of prestressing force on the natural frequencies of beams. Two representative theories were proposed long time ago. One of them suggested that the natural frequencies would decrease with prestress due to the “compression (P-Δ) effect” induced by the prestressing force. The other indicated that the natural frequencies would not be affected by the prestressing force since the prestressing force did not change the overall stiffness property of the system. Although there are discrepancies in the conclusion, it is widely accepted now that both of their conclusions are correct but they should be used in different situations. However, there are some misunderstandings on their scopes of applications. The scenarios explained by these two theories are just two extreme examples and there are many prestressed beams with external tendons between them whose natural frequencies cannot be predicted by either of them. These prestressed beams are not considered in the discussions mentioned above. Hence a comprehensive conclusion about this problem including all the scenarios is needed. In addition, the effect of a particular form of the external prestressing tendon (trapezoidal profile tendon) on the fundamental natural frequency is investigated by the energy method in this thesis. As a widely used tendon profile and a typical example of the scenarios (Manisekar et al. 2018, Kianmofrad et al. 2017, El-Zohairy and Salim, 2017, Cui et al., 2017) which cannot be fitted into the two theories as mentioned, no quantitative estimation of the effect of prestressing force can be found by the existing theories. The mathematical solution is provided and this new method can be extended to calculate the natural frequencies of other prestressed beams with external tendons. After synthesizing the theories from a purely theoretical point of view involving no ambiguity, some inconsistent experiments results got from tests conducted on prestressed concrete beams need to be considered. These tests showed an increasing trend of the natural frequencies with the prestressing force which cannot be explained by either of the theories. Some researchers believed that the theoretical solution could not be applied to real beams given the diverging experiment evidence. One of the research targets in this thesis is to provide a systematic explanation of the reasons causing the contradictions. Firstly, the existing experiments on prestressed concrete beams are reviewed, and experimental data are discussed in light of the effect of shrinkage cracks. Then, numerical simulations using finite element models are carried out to simulate the influence of the prestressing force on natural frequencies with the existence of these shrinkage cracks. The results demonstrate that such shrinkage-type cracks inside the concrete indeed tend to close when the prestress is applied, and this, in turn, increases the bending stiffness and consequently results in an increase of the natural frequencies of the beams. Finally, a coherent conclusion on the effect of prestressing force on natural frequencies of beams is proposed.