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A multi-objective mixed H 2 /H 1 robust output feedback control synthesis with regional pole placement constraints in a linear matrix inequalities framework is adopted for active low-frequency sound radiation control of an arbitrarily thick, rigidly baffled, simply supported, multi-layered piezo-composite circular panel. The adopted control system concurrently captures the benefits of both H 2 transient control performance and H 1 robust stability in the face of external disturbances and system uncertainties. Also, the implemented volumetric sensing/actuation configuration avoids the typical problems associated with conventional (spatially discrete) piezoelectric sensor/actuator patches, where the total volume velocity can be effectively cancelled with the main contribution being to the long wavelength acoustic power emission. The elasto-acoustic analysis is based on the spatial state-space method in the context of exact 3D elasticity theory along with the Rayleigh integral formula where Neumann's addition theorem is incorporated in the associated Hankel transform representation to arrive at a computationally efficient expression for the nonaxisymmetric pressure field within the acoustic half-space, valid in both near and far fields. Subspace system identification of the fully coupled structure-fluid interaction problem is performed, and the truncated modes are considered as multiplicative uncertainties in synthesis of the mixed-norm controller. Numerical simulations establish the ability of the implemented volumetric sensing/actuation methodology in cooperation with the multi-objective robust active control scheme for restraining low-frequency sound radiation from a Ba 2 NaNb 5 O 15 /steel/PZT4 circular piezo-laminated plate, without provoking instability of the closed-loop system. Also, superior bandwidth frequency and tracking performance in comparison to the H 2 and H 1 controllers are observed. This work is believed to be the first such attempt to exactly model (and actively control) the 3D nonaxisymmetric acousto-elastodynamic frequency response of an arbitrarily thick, smart piezo-laminated circular plate in heavy fluid loading condition (i.e. without using any kind of far-field, low-frequency, and/or light fluid coupling approximations), with straightforward extensibility for any arbitrary through-thickness variation of distributed material properties.

The active damping control strategy upgraded by a multi-objective particle swarm optimization algorithm is utilized for improved broadband suppression of sound transmission through a simply supported piezo-laminated rectangular panel of arbitrary thickness featuring an orthotropic functionally graded viscoelastic material interlayer. The controller parameters are tuned optimally through multi-objective particle swarm optimization which yields the Pareto optimal frontiers of certain applicable conflicting objective functions. Extensive numerical simulations include the calculated sound transmission loss of the passive, active, and hybrid (active–passive) piezo-composite panels under normally or obliquely incident plane waves. It is found that the overall sound transmission loss levels substantially rise with increasing thickness of (carbon fiber–reinforced) viscoelastic interlayer, which can further be improved by augmenting the fiber volume fraction. Also, the purely active multi-objective particle swarm optimization–based control system performs well in the low-frequency region, while the good performance of the hybrid smart panel is achieved by balancing an optimal trade-off between the active and passive control configurations in a relatively wide frequency range. Accuracy of formulation is confirmed by comparisons with the existing data as well as with those of a finite element model software package. Furthermore, a frequency-domain subspace identification scheme is applied to estimate the state matrices of proposed control systems, and the closed-loop stability is established based on eigenvalue analysis of identified systems.

In this paper, the nonlocal Euler-Bernoulli beam theory is presented to study the primary resonance and chaotic vibration of a curved single-walled carbon nanotube (CSWCNT). The CSWCNT is exposed to axial thermomagnetic and transverse harmonic forces resting on a viscoelastic foundation. A single-mode Galerkin approximation is implemented to transform the nonlinear governing partial differential equation into an ordinary one. The multiple scales method is employed to determine the primary resonance response of a clamped-clamped CSWCNT under harmonic external force. The effects of magnetic field strength, temperature change and amplitude of sinusoidal curvature, mode number and different boundary conditions including clamped-free and free-free are examined to study the jumping phenomenon and instability states in primary resonance frequency response. Moreover, by applying the Runge-Kutta numerical method, the bifurcation diagram and the largest Lyapunov exponent curve are generated to detect the chaotic values of external amplitude of excitation. The phase plane trajectories along with Poincare map are presented to show the chaotic and periodic vibration of a CSWCNT. The results show that the axial thermomagnetic forces have significant effects on the frequency response of a CSWCNT and the nonlinear chaotic vibration has a strong dependency on the amplitude of excitation.

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