Study on Bandgap Manipulation and Structural Vibration Control in Sandwich Metastructures

With the rapid development of infrastructure such as rail transit systems, metro over-track buildings, and high-rise buildings, engineering structures are increasingly exposed to problematic medium- and low-frequency vibrations induced by operational loads, environmental disturbances, and earthquakes. Although conventional vibration isolation and mitigation methods have been widely used, they still face limitations in broadband control of medium- and low-frequency vibrations, particularly in terms of effective bandwidth and robustness to parameter variations and changing operating conditions. In recent years, inspired by advances in acoustic and mechanical metamaterials, metastructures with wave manipulation capabilities have opened up new possibilities for structural vibration control. Compared with conventional vibration control approaches, metastructures can attenuate vibrations within specific frequency ranges through bandgap manipulation. Unlike metamaterials, which primarily emphasize effective material properties derived from artificially designed unit cells, metastructures place greater emphasis on the structural design of practical engineering components and are therefore better suited for vibration control in real structures. In particular, locally resonant metastructures show strong potential for low-frequency vibration mitigation by exploiting subwavelength wave manipulation. However, their effective control bandwidth is often narrow, and their practical application is still limited by the mass ratio of the resonant attachments and by structural layout constraints. Based on this background, this dissertation systematically investigates the design of metastructures and their broadband vibration control performance for mitigating medium- and low-frequency vibrations in engineering structures. To achieve vibration attenuation and suppress energy transmission under broadband excitation, a sandwich wave-filtering component integrating load-bearing and wave-filtering functions is proposed, and its core layer is designed through a dynamic-response-based topology optimization method. By introducing resonant units with spatially graded resonant frequencies, graded sandwich metabeams and metapanels are developed to achieve frequency-selective attenuation of vibration waves during propagation. To further satisfy broadband wave-filtering requirements, sandwich metastructures with attached nonlinear functional units are proposed. By exploiting the targeted energy transfer characteristics of nonlinear energy sinks, sandwich metastructures can more effectively capture vibration energy under broadband excitation while suppressing energy backflow from the attachments to the main structure. In addition, the concept of sandwich metastructures is extended to frame structures by transforming part of the structural self-mass into internal sandwich substructures capable of relative motion with respect to the outer frame, thereby forming a sandwich frame metastructure. On this basis, the lightweight design of seismic steel frames with sandwich metastructures is further carried out by considering multi-level seismic performance. The main contents and conclusions of this dissertation are summarized as follows: (1) To address the difficulty of simultaneously achieving load-bearing capacity and wave-filtering functionality in metastructures subjected to broadband medium- and low-frequency excitation, a sandwich wave-filtering device composed of steel face sheets and an elastic core layer is proposed. A dynamic-response-based topology optimization method is established, in which the core topology is optimized under periodic distribution constraints with the support energy transmission metric as the objective. The results show that the optimized configuration can effectively reduce energy transmission to the supports and improve vibration suppression under broadband excitation. However, within the frequency range dominated by lower-order modes, the vibration attenuation capability remains limited for both the optimized and unoptimized configurations. (2) To improve the insufficient vibration control performance of sandwich structures in dominant medium- and low-frequency bands, a graded sandwich metabeam with spatially distributed resonant frequencies is proposed. Topology-optimized core layers are fabricated by 3D printing and bonded with steel face sheets to form sandwich metabeam specimens, while cantilever-type resonant units are introduced as attached oscillators. Through quasi-static compression tests and broadband excitation tests, the mechanical properties of the core layer and the broadband wave-filtering performance of the sandwich metabeam are investigated. Combined with finite element analysis, the working mechanism is clarified from the perspectives of support energy transmission and internal energy redistribution. The results show that the graded sandwich metabeam can progressively capture and attenuate different frequency components along the wave propagation path, thereby effectively broadening the vibration control bandwidth. (3) To extend sandwich metastructures to two-dimensional structures and practical engineering scenarios, a graded sandwich metapanel is proposed. Based on the one-dimensional metabeam, the concept is extended along an additional spatial direction to form a two-dimensional sandwich metapanel, including unidirectional, bidirectional, and multi-graded shape distribution patterns. Considering bandgap characteristics under different periodic boundary conditions, as well as wave propagation and attenuation performance in different directions, systematic investigations are conducted on broadband wave-filtering performance, energy transmission characteristics, and robustness against variations in structural parameters and external excitations. The results show that the vibration transmission control capability of each configuration is closely related to the overlap of attenuation zones in the connection regions between adjacent resonant units. Among them, the multi-graded pattern achieves more robust vibration control through richer coupling and broader coverage of attenuation zones, and demonstrates promising engineering potential under rail transit excitation in metro over-track buildings. (4) To address energy backflow and insufficient sustained dissipation capacity in sandwich metabeams and metapanels with linear locally resonant units, sandwich metastructures with attached nonlinear attachment are proposed. Bistable nonlinear energy sinks and vibro-impact nonlinear energy sinks are introduced, respectively. Combined with targeted energy transfer mechanisms and amplitude-dependent dispersion characteristics, systematic investigations are carried out on the broadband vibration control performance, energy transfer mechanisms, and time-frequency energy evolution of nonlinear sandwich metastructures. The results show that, with increasing excitation amplitude, the control mechanism gradually shifts from bandgap-manipulation-dominated regulation to equivalent-damping-dominated dissipation. The introduction of nonlinear attachments leads to significant broadband energy spreading and enhanced high-frequency components, thereby enabling sustained energy transfer and efficient dissipation over a wider frequency range. (5) To overcome the limitation that the effective control bandwidth of locally resonant systems depends on the attached mass ratio, a sandwich frame metastructure that utilizes the structural self-mass as resonant units is proposed. Based on the band characteristics of finite periodic structures and the dynamic coupling relationship between internal substructures and the outer frame, the formation mechanisms of frequency splitting, modal reorganization, and the associated attenuation zones are revealed. On this basis, multi-objective optimization methods that balance vibration control performance and material usage efficiency are established for moment-resisting frames and eccentrically braced frames, respectively. Structural lightweight design is then carried out for typical high-rise steel frame examples under different design levels, and the corresponding embodied carbon emissions are further evaluated. The results show that the internal sandwich substructures can achieve vibration control and energy redistribution through relative motion with respect to the outer frame. Without requiring additional energy dissipation devices, the proposed sandwich steel frame metastructure can significantly reduce steel consumption and achieve corresponding embodied carbon reduction benefits.