Smart hybrid active/semi-active distributed structural acoustic control of thin- and thick-walled piezo-sandwich bimorph spherical shell cloaks

Abstract

A novel three dimensional underwater smart piezo-sandwich spherical shell cloak is designed and analyzed based on the hybrid active/semi-active distributed structural acoustic control strategy. The sandwich configuration consists of series- or parallel-connected piezoelectric (PZT) bimorph actuator skin layers collocated with a semi-active electro-rheological fluid (ERF) core layer. Two separate coupled elasto-acoustic formulations are systematically developed. The first model is based on the variational principle of structural mechanics and the approximate Kirchhoff-Love thin shell theory while the standard sliding mode control (SMC) scheme is utilized to activate the acoustic scattering extinction capability of the hybrid structure. The second model is built on the exact linear theory of 3D piezoelasticity and the classical state-space transfer matrix approach along with the active damping control (ADC) strategy. Extensive numerical simulations reveal that the best broadband backscattering cancellation performance can effectively be achieved with the smart hybrid active/semi-active bimorph piezo-sandwich spherical shell cloak operating in parallel connection. To quantify the overall cloaking performance of the proposed design, the percentage error (%Err) of the external cloaked field relative to the background incident pressure field is calculated at selected dominant structural resonance frequencies within eight designated frequency bands (regions I to VIII). The remarkable (near-perfect) cloaking performance of the parallel-connected thick-walled hybrid bimorph piezo-sandwich shell (25%shellcloak) is demonstrated in the intermediate to high frequency regions (i.e., below 1.5% error in regions I, and III to VIII). This excellent invisibility performance is somewhat degraded in a narrow low frequency band (i.e., up to 8% error in region II) which is primarily linked to the elasto-acoustic resonances due to the coherent coupling of various types of highly interacting fluid- and shell-borne peripheral waves. On the other hand, the superior cloaking performance of the parallel-connected thin-walled hybrid bimorph piezo-sandwich shell (7%shellcloak) is observed predominantly in the low frequency range (i.e., below 1.5% error in regions I and II), while this exceptional performance is gradually degraded as the incident wave frequency is increased (i.e., up to 6.5% error in regions III to VIII), where partial or directional cancellation of the scattered field mostly occurs. Also, some important practical issues and limitations regarding the experimental implementation of proposed hybrid active/semi-active acoustic cloaking device are briefly discussed.