A Theoretical Model for Designing the Novel Embeddable Spherical Smart Aggregate

A type of novel embeddable spherical smart aggregate (SSA) has been developed successfully in the latest work. The SSA is formed by encapsulating a radially polarized spherical piezoceramic shell with epoxy resin and a spherical ultra-high performance concrete (UHPC) case, and its omnidirectional actuating and sensing capabilities in concrete structures have also been verified. Comparing to the early developed compressive and shear mode smart aggregates (SAs) that can only generate or receive the stress wave in a single direction, the SSA can generate or receive omnidirectional stress waves, which has a promising application in structural health monitoring of civil engineering structures. To understand better the performance of the SSA and guiding further its optimized design, a theoretical model is proposed to study the vibration characteristics of the SSA in this paper. Based on the linear theory of piezoelasticity, the dynamic analytical solution of an SSA subjected to a harmonic voltage excitation is derived, and the analytical expression of the electrical impedance is obtained. Furthermore, a parametric analysis is conducted to discuss the effects of the outer radius of the UHPC case, the thickness of the epoxy layer, the inner radius of the piezoceramic shell, the piezoelectric material types, and the piezoelectric material parameters on the vibration characteristics, such as the first and second resonance and anti-resonance frequencies. Furthermore, comparisons with some special cases in the previous work, the ANSYS simulation results and the experimental data of the SSA are also given to validate the reliability of the proposed model. The present investigations contribute to the comprehensive understanding of the vibration characteristics of the SSA, which is helpful to design the working frequencies range of the SSA.