A semi-analytical framework for comprehensive vibration analysis of segment-coupled plates with embedded acoustic black holes

Abstract

This study introduces a semi-analytical framework for modeling and analyzing the vibration behavior of the acoustic black hole (ABH) structures, which have been drawing an increasing attention because of their outstanding vibration control and energy harvesting abilities. The proposed model combining with the segment-coupling strategy is developed to address the main issue in modeling ABH structures: the non-uniform wavelength distribution on the whole structure domain. The flexural displacement field, on basis of a set of modified Fourier series, is respectively assumed on uniform and ABH segments to avoid the non-uniform wavelength distribution. Such modified form of Fourier series expansion makes the solution applicable to any boundary conditions and available to the segment-coupling strategy. This framework allows one to study ABH vibration-concentrating capability with varying system parameters in a fast and efficient way. By means of the proposed segment-coupling strategy, the modeling of the periodic ABH structure can be easily achieved. Under the general Rayleigh–Ritz framework, the extremalization of the Hamiltonian over Lagrange’s equation yields the system governing equation, which can be solved for structural responses. The consistent with the FEM results and diverse numerical examples demonstrate that the proposed model is capable of providing an accurate prediction and flexible analysis of the plates with embedded acoustic black holes. Time–space transient response in forms of 2D visualization images is presented to show the vibration-concentrating effect. Free, forced, and transient vibration analysis are conducted to illustrate the typical ABH phenomena with varying ABH parameters, which may provide theoretical support for the acoustic design of damping structures based on acoustic black holes.