Distributed sensing signals of truncated conical shells with clamped-free boundary conditions

In aerospace structures, vehicles, civil structures, conical shells are used to support a part or connect different parts, such as spacecraft adaptors, fixtures of machine tools. This type of structures has the possibility of vibration isolation. The final purpose of the on-going research is to isolate the supported part from the vibration transferred from the other end. As a phase of the research, the present paper emphasizes on the distributed sensing signals and modal voltages of the truncated conical shell. To simulate free vibrations of supported part, one end of the truncated conical shell is clamped and the other end is free. The piezoelectric patches are attached on top skin of the shell along diagonal helical line. This paper presents an analytical procedure of sensing of truncated conical shell supporting a mass. The displacement functions satisfying the special boundary conditions are given. Based on the thin-shell theory and Donnel-Mushtari-Valsov theory, sensing equations of the piezoelectric stripes are derived. The sensing signals consist of four components, i.e. sensing signals due to meridional and circular membrane strains, meridional and circular bending strains. These components are studied separately to show their distributions to the sensing signals. Finally, a case study is carried out using a sample truncated conical shell model with laminated piezoelectric stripes.