Torsion and transverse sensing of conical shells

Conical shells are widely used as payload/rocket adapters in rocket fairing systems. Generally, the conical shells are clamped at the major end and free at the minor end, where the payload is mounted. This study focuses on the dynamic sensing of conical shells with fix-free boundary conditions (BCs) by using distributed piezoelectric helical sensors. Two types of motion are studied, i.e., the transverse modes and the torsion modes. The shear-type sensors for shells sensing are presented first. Formulations of sensing signals of a general shell of revolution are presented, and then simplified to conical shells. For sensing of transverse vibrations, thin piezoelectric sensors are laminated on the top surface. Two types of sensor distribution are considered: a fully distributed and a helical or diagonal laminated. The total signal consists of four components resulting from the four strain components, and each of them is evaluated in detail. For sensing of torsion vibrations, a meridional polarized shear-type sensor with side electrodes is layered on the top surface of the shell structure. Sensing signals of natural shell modes are also evaluated. Analyses show that, in low order modes, the sensing signals induced by the circumferential membrane strains are the primary components of the total signal generations. The numerical results indicate the optimal location of the sensors. The proposed method is capable of determining the modal participation factors, while the testing signal is available; it is also capable of determining the mode shapes by using several distributed sensor segments.