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This paper discusses the underlying mechanisms for the deformation of coherent structures which occurs in the initial stage of the axis switching of noncircular jets. The generalized shooting method is applied to jets with elliptic-core and equilateral-triangular-core regions of constant flow. The analysis reveals that in order to have the deformation, three requirements must be present in the behavior of the eigenmodes of noncircular jets: 1) the eigenfunctions are localized without excessive overlapping; 2) the amplification rates of the corresponding eigenmodes are comparable; and 3) sufficient phase speed difference exists between the eigenmodes. The qualitative behavior of the noncircular jets found through the numerical analysis is compared with experimental results and are in good correlation with them.

The generalized shooting method, previously developed for the analysis of spatial instability modes of arbitrary shape jets, is applied to incompressible jets with triangular core regions of constant flow. The instability modes of these jets are classified, and calculations are carried out for spatial growth rates, phase velocities, and velocity fluctuation eigenfunctions of three fundamental and two overtone modes. All of the calculated eigenfunctions show negligible velocity fluctuations at the triangle vertices, in good correlation with experimental findings.

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The complete set of equations for describing the mechanical and electrical behavior of a piezoelectric medium is given. From these equations, the electromechanical equations describing the dynamical behavior of discrete PZTs and their mounting plate are derived. The electromechanical equations are used to explain active damping with the PZTs as actuators and an accelerometer as the sensor. The active damping model is applied to a more realistic case. The transverse displacement and the plate vibration damping are calculated using the electromechanical equations and compared with the experimental results. A comparison of the open loop transverse displacement of the plate as a function of the applied PZT voltage with the corresponding experimental case shows good agreement. The damping of the plate vibration is found to be approximately 20 dB for both the calculation and the corresponding experiment when the plate is driven at the lowest modal plate frequency. A sensor equation describing the output of a PZT used as a sensor is derived with the PZT terminated with an arbitrary impedance. Using the sensor equation, a concise and unified approach is developed for constructing both active and passive damping methods. Two limiting active damping cases (the terminal impedance zero or infinity) and one passive damping case are considered using the sensor equation. A useful design guide for the corresponding active and passive damping methods is determined.