Abstract This paper reports dynamical effects in onedimensional locally resonant piezoelectric metastructures that can be leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The nonlinear electromechanical unit cell is built upon a linear host oscillator coupled to a nonlinear electrical circuit via piezoelectricity. Its dynamical response to prescribed longitudinal harmonic displacements is approached in the frequency and time domains. Semi-analytical harmonic balance (HB)-based dispersion relations are derived to predict the location and edges of the nonlinear attenuation band. Numerical responses show that weakly and moderately nonlinear piezoelectric metastructures (NPMSs) promote a class of nonlinear attenuation band where a bandgap and a wave supratransmission band coexist, while also imparting nonlinear attenuation at the resonances around the underlying linear bandgap. Besides, strongly nonlinear regimes are shown to elicit broadband chaotic attenuation. Negative capacitance (NC)-based essentially cubic piezoelectric attachments are found to potentiate the aforementioned effects over a broader bandwidth. Excellent agreement is found between the predictions of the HB based dispersion relations and the nonlinear transmissibility functions of undamped and weakly damped NPMSs at weakly and moderately nonlinear regimes, even in the presence of NC circuits. This research is expected to pave the way towards fully tunable smart periodic metastructures for vibration control via nonlinear piezoelectric attachments.PACS 05.45.-a . 62.30.+d . 62.65.+kMathematics Subject Classification (2010) 37N15 . 74H45 . 74H65 . 74J30
Most of the active noise and vibration control applications are intended to globally reduce physical quantities such as sound pressure or structural vibration. However, there are other situations where not only through controlling the magnitude but also (or merely) by the relative phase of the components of the periodic disturbance, a system could lead to desired results. Synchronization of chaotic systems, vibration of hysteretic systems and the recently investigated sound quality control based on auditory Roughness are examples of such situations. This paper presents an active control scheme which features the independent controlling of the amplitude and/or relative phase of a number of harmonic components of disturbances such as the internal combustion engine noise. A delayless, frequency-domain approach based on time-domain algorithms such as the PSC-FxLMS and the NEX-LMS is the core of the control scheme. Also, an algorithm for estimating and resolving slight frequency variations is included into the controller, which guarantees relative phase control of the desired components of the disturbance. The proposed scheme can tackle pure harmonic-level problems (e. g. Loudness) as well as more complex multi-harmonic problems (e. g. Auditory Roughness) thus presenting a complete sound quality control system that is capable of exploring a wide range of possibilities in vehicle sound design. Computer simulations are conducted to demonstrate the capabilities of the adaptive control algorithm.
Loudness Scattering due to Vibro-Acoustic Model VariabilityThe use of numerical simulation in the design and evaluation of products performance is ever increasing.To a greater extent, such estimates are needed in an early design stage, when physical prototypes are not available.When dealing with vibro-acoustic models, known to be computationally expensive, a question remains, which is related to the accuracy of such models in view of the well-known variability inherent to the mass manufacturing production techniques.In addition, both the academia and industry have recently realized the importance of actually listening to a products sound, either by measurements or by virtual sound synthesis, in order to assess its performance.In this work, the scatter of significant parameter variations on a simplified vehicle vibro-acoustic model is calculated on loudness metrics using Monte Carlo analysis.The mapping from the system parameters to sound quality metric is performed by a fully-coupled vibro-acoustic finite element model.Different loudness metrics are used, including overall sound pressure level expressed in dB and Specific Loudness in Sones.Sound quality equivalent sources are used to excite this model and the sound pressure level at the driver's head position is acquired to be evaluated according to sound quality metrics.No significant variation has been perceived when evaluating the system using regular sound pressure level expressed in dB and dB(A).This happens because of the third-octave filters that average the results under some frequency bands.On the other hand, Zwicker Loudness presents important variations, arguably, due to the masking effects.