Parametric Resonance and Stochastic Dynamic Stability of Structures: Theory, Experiments, and Applications

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One of the most important tasks in civil engineering is assessing structural safety and reliability under dynamic loads (e.g., buildings during earthquake, bridges excited by turbulent winds, and underground mine pillars subjected to rock blasting). These loadings are often random forces and would appear as one of the coefficients in the governing equations of motion. Such systems are said to be parametrically excited and the associated instability is called parametric resonance. With the construction of more and more high-rise buildings, long bridges and underground structures, investigations of dynamic stability of structures under stochastic excitation are increasingly important. Parametric resonance is more dangerous than ordinary resonance because it is characterized by exponential growth of the response amplitude-even in the presence of damping-whereas ordinary resonance is characterized by linear growth of the response amplitude. Parametric resonance occurs over a region of parameter space and the excitation frequencies may be higher or lower than the natural frequency. Moreover, parametric resonance may interact with ordinary resonance in unexpected ways. Over the last 18 years, the applicant and collaborators have made significant progress in the study of stochastic dynamics. In particular, approximate algorithms were developed and applied to linear single degree-of-freedom systems, and preliminary lab experiments were conducted at Lakehead University. The knowledge, expertise, and experimental skills acquired by my research team will benefit the proposed NSERC program for stochastic stability of structures. In order to apply the developed methods to real structural systems, it is imperative to extend the study to higher-dimensional systems. The objective of the proposed research program is to theoretically and experimentally study parametric resonance and dynamic stability of fractional viscoelastic non-linear structures subjected to stochastic loads, with applications to civil and mining engineering. We will develop efficient analytical and numerical methods to determine the dynamic stability of various systems with both strong and weak non-linearity, such as coupled systems with commensurable and non-commensurable frequencies, gyroscopic systems, time-delay systems, and multiple degree-of-freedom systems excited by both multiplicative and additive loads. The proposed research will contribute significantly to the advancement of knowledge and technologies associated with dynamic stability of structures. Enhanced understanding of stochastic parametric resonance will inform protocols and measures, by adjusting structural parameters or blasting variables, to avoid or alleviate dynamic disasters due to seismic, wind, or stress wave loadings. This research program will provide unique and leading-edge opportunities to train HQP in these related subjects. Thus, this program will benefit the construction and excavation industries in Canada.