Rotationally periodic structures, like turbine, bladed disks, stators and rotors of electric machinery or satellite
antennae, play a very important role in many fields of the technology. It is well known that when even small
structural imperfections are present, destroying the perfect periodicity of the structure, each couple of degenerate
modal frequencies splits into two different values (mistuning) and the corresponding modal shapes exhibit peaks
of vibration amplitude (localization phenomenon). In this paper, a continuous model describing the in-plane
vibrations of an imperfect bladed rotor is derived via the homogenization theory and is applied to the analysis
of the localization phenomenon. Imperfections are modeled as perturbations of the geometrical dimensions and
material characteristics of some blades, and a perturbation approach is adopted in order to find out the split
eigenfrequencies and eigenmodes of the imperfect structure. Numerical simulations show that the proposed
model is suitable and effective for the identification and analysis of the localization phenomenon, requiring much
lower computational effort than classical finite element models.
Vibrations of structures equipped with a piezoelectric actuator
can be damped by connecting the electrodes of the actuator to a
suitable electric circuit. The insertion of a negative capacitance
in the electric circuit, able to compensate the reactive impedance
of the piezoelectric actuator, rise up the damping performance of
the device. In this paper different circuits containing a negative
capacitance are proposed and optimized for both single-mode and
multi-mode damping. A theoretical analysis is performed in the
former case, yielding closed-form expressions for the achieved
exponential time-decay rate of vibrations, whereas a numerical
optimization is employed in the latter case. The proposed circuits
show good performances in simulation for both single-mode and
multi-mode damping.
Vibration damping of a cantilever plate is achieved by using a piezoelectric element simultaneously as passive single-mode device and active broad-band actuator. Control strategies are designed on the basis of a modal model of the coupled electro- mechanical structure. This model is obtained by using a suitable finite-element formulation together with a modal analysis. A purely passive single-mode control composed of an optimally tuned external RL shunt circuit and a purely active control based on classical LQG techniques are compared to a semi-active control obtained by tuning the external shunt circuit on the second vibration mode of the structure and using a LQG controller designed on the only first-mode model.
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