The research objective of this award is to develop methods for vibration analysis and control of complex built-up frame structures. There has been an increasing interest in active vibration control due to the increasing demands for mechanical structures to be lighter and faster - lighter and faster structures are more prone to vibrations. The conventional modal vibration approach is greatly challenged when solving complex practical vibration problems due to the increased model uncertainty caused by the increased complexity of structures and the unavoidable spillover problems caused by modal truncation. In this study, a wave centered view of structures is proposed for vibration analysis and control of complex practical built-up structures. This research consists of theoretical analysis, computer simulation, and experimental verification. Deliverables include exact closed form solutions to vibration problems in planar and three-dimensional frame structures; ?active support? and ?active joint? design strategies for absorbing incoming vibration waves or shunting unwanted vibrations to less important structural members; and guidelines for designing complex periodical frame structures from vibration attenuation viewpoint.
If successful, the results of this research will provide practical solutions to vibrations in built-up frame structures and bridge a gap between academic research and real solutions to real world problems. The related experience will be brought back to the classroom for teaching and training the next generation of civil and mechanical engineers. A course on ?Wave Approach in Vibration Analysis and Control? will also be developed to reach engineers from local industry. Furthermore, this research allows the direct participation of undergraduate and graduate students. Hence, this research not only develops a cost-effective, convenient, and practical approach in vibration analysis and control of complex built-up structures, but also provides a vehicle for educating a broad spectrum of students and engineers, in the difficulties associated with suppressing vibrations in complex practical structures.
A wave centered view of structures is studied, in which the motion of a structure is described as waves propagating along a structural element, reflected and transmitted at various structural discontinuities. Assembling these propagation, reflection, and transmission matrices provides a concise and systematic approach for vibration analysis of built-up structures. A wave vibration based analytical approach has been developed for analyzing complex coupled vibrations in built-up planar and spatial frame structures. In the planar structure related study, coupled bending and longitudinal vibrations in various planar frames ranging from relatively simple L-shaped, H-shaped, and portal frames, to more complex multi-story single-bay, single-story multi-bay, and multi-story multi-bay frame structures are systematically studied from the wave vibration standpoint. Free and forced vibrations are obtained based on both classical and advanced vibration theories. In the spatial structure related study, coupled in and out-of-plane bending, torsion, and longitudinal vibrations in spatial Y-shaped and K-shaped frames, as well as multi-story space frames are analyzed from the wave standpoint based on classical vibration theories. The developed wave vibration based analytical approach has been validated through experimental studies and comparisons to the literature. This study not only provides an exact analytical approach to complex vibration problems in built up planar and spatial frame structures, but also provides a benchmark to existing numerical tools. Vibration control strategies have also been developed based on this unique wave vibration standpoint. Regardless of the complexity of a structure, from the wave vibration point of view, it consists of only two basic types of structural components: structural elements and structural joints. As a result, vibrations can be controlled by creating active discontinuities along a structural element or at a structural joint to dissipate vibration energy. Structural element and structural joint controllers have been designed based on both classical and advanced vibration theories. The controllers are applied to various built-up planar structures. Promising vibration suppression performance has been observed. Apart from the societal benefits of improved structural durability and safety of civil and mechanical structures, this research also addresses the need for training and educating the next generation of mechanical and civil engineers. Lecture notes have been developed based on this research. The materials have been incorporated in to the graduate vibration course that the PI teaches. The materials are well received by the students.
