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The accurate prediction of the dynamic characteristics of a structure is key to successful vibration control strategies. A typical vibration and wave propagation control is performed through periodic and shunted piezoelectric patches, also known as a smart material. Therefore, the smart metamaterial considers periodic arrangement of shunted piezoelectric patches providing a beam with attenuation properties which depend on the resonant behaviour of the shunts. The vibration attenuation occurs due to an elastic-electrical system characterized by an internal resonance of the shunt circuit. The spectral element approach provides very accurate solutions for the structural dynamic response. In this paper, a beam-piezoelectric structure is introduced to focus on the control of flexural waves in beams with piezo-layers connected to single and multi resonant shunt approaches. The smart structure is modelled using the spectral element method. It is shown that the effective wavenumber present the locally resonant behaviour at the same frequencies of of the vibration attenuation for both single and multi shunt approached, indicating that each shunt circuit is independently associated to a attenuation frequency. The spectral element approach presented in this paper shows to be an accurate and simple approach for the design smart metamaterial beams.

Damage detection in structures and systems is essential for monitoring parameters that can affect their integrity. This paper evaluates the efficiency of four damage indices (DIs) commonly used with temporal wave signals. The root mean square deviation, mean absolute percentage deviation, covariance, and correlation coefficient deviation DIs are presented, and a normalization is then proposed. An Euler-Bernoulli beam is used as a guided wave modelled with the spectral element method and excited by a toneburst signal. It includes the theoretical background of the throw-off beam, undamaged and cracked beam spectral elements. The DIs for a single crack position and a map varying crack depth and positions are calculated with deterministic and random temporal signal responses derived from noise addition. Results showed that DIs could identify and quantify the damage conditioned to the pulse location point and the influence of noise in the estimation, which leads in an analysis comparable to practical applications.

Randomness in the media breaks its periodicity affecting the vibration and wave propagation performance. Such disorder caused by the variability may lead to interesting physical phenomena such as trapping and scattering waves, wave reflection, and energy localisation. While the randomness may be attributed to manufacturing irregularities and quantifying its effect is crucial for ensuring adequate performance of a range of smart systems, these effects can also be exploited for manipulating the wave properties. Here we investigate a smart metastructure in the form of a beam integrated with piezoelectric transducers coupled to a resonant shunt circuit. The piezoelectric shunt in a periodical arrangement can induce locally resonant bandgaps that can be employed in wave and vibration manipulation (and control). This paper quantifies the uncertainty associated with electrical circuit components that affect the circuit impedance. Such uncertainty essentially propagates to the beam smart metamaterial, influencing its wave and vibration control feature. Numerical results of the unimorph meta-beam with single and multi-frequency shunt configuration show that the bandgap behaviour is sensitive to the random disorder associated with circuit impedance parameters, which can, in turn, be exploited for enhanced functionalities based on optimal RL shunt circuits for controlling structural vibration response along with wave propagation and attenuation.

The study analyzes the dynamic behaviour and vibration attenuation of an Euler Bernoulli beam coupled with a piezoelectric layer. The vibration attenuation is given by the shunt circuit connected to the piezoelectric. This paper shows different shunt circuit impedances and how they affect the system's frequency response (FRF) functions. The spectral element method is used to model the intelligent material under analysis and has its function based on the exact solution of the wave equation, therefore, a single element is necessary to model the structure. The estimated responses for each shunt configuration express a relationship with the passive components used in the respective circuits. In each case, the circuit has a particular effect on FRFs.