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A high-order layerwise multiresolution method that utilizes Daubechies wavelet and scaling functions for the approximation of state variables is presented for the enhanced simulation of guided waves in composite strips. The multiresolution approximation yields a hierarchical set of equations of motion involving the coarse component of generalized displacements, and finer components can be added on the coarse one, forming improved predictions until the desired precision is accomplished. The multiresolution approach is combined with a high-order layerwise laminate theory, enabling the accurate prediction of both symmetric and antisymmetric wave modes, the modeling of surface traction, and localized intra-ply and delamination damage types. Numerical results for the simulation of guided waves in laminated composite strips are presented, exhibiting significant reduction in computing times and remarkable convergence rates compared to single-resolution approaches and traditional finite element methods. Moreover, it is shown that each resolution can model specific bandwidths of wavenumbers, thus providing unique inherent capabilities to localize and isolate coexisting wave modes and detect converted and reflected waves, induced by degraded material regions and delaminations.

A multiresolution finite wavelet domain method, that utilizes Daubechies wavelet and scaling functions for the hierarchical approximation of state variables, is presented. The multiresolution approximation yields a hierarchical set of equations of motion involving the coarse component of generalized displacements, while additional equations of finer components are subsequently added. A coarse solution is first calculated, and finer solutions can be sequentially superimposed on the coarse solution until convergence to the final solution is achieved. Moreover, it is shown that each resolution can model specific bandwidths of wavenumbers, thus providing a unique capability to separate coexisting wave modes and detect converted and reflected waves in the presence of damage. Two wavelet-based beam elements are explored, the first encompasses the Timoshenko shear beam theory and the second a high-order layerwise laminate theory for the accurate prediction of both symmetric and antisymmetric guided waves. Numerical results illustrate the inherent property of the method to a priori localize and isolate coexisting guided wave modes and their conversions, induced by different material regions and weak or debonded layer interfaces, thus demonstrating the method's intrinsic capabilities towards the design of wave-based SHM systems.

A Multi-resolution wavelet-based numerical method is developed for the fast prediction of transient response in elastic homogeneous and heterogeneous rods and beams. The method takes advantage of the remarkable mathematical properties of Daubechies wavelet and scaling functions as basis functions for the spatial approximation of state variables. The Multiresolution capability of the Daubechies wavelet family, provides the hierarchical computational framework that incorporates both scaling and wavelet functions. An uncoupled solution system between each resolution is formulated, using an explicit time integration scheme. The first level of analysis provides the coarse solution, while finer approximations are sequentially calculated and superimposed on the coarse solution, until the desired level of accuracy is achieved, without discarding the previous results obtained at coarser resolutions. Additionally, due to the orthogonality and compact support of Daubechies wavelet family, the decoupled mass matrices of each resolution are diagonal, or block diagonal and the stiffness matrices are banded. The proposed method uses a uniform grid which remains practically unchanged when increasing the order of interpolation (p-method), owing to its meshless character. Numerical results for the simulation of high-frequency wave propagation in isotropic and orthotropic rods and beams are presented and compared against confirmed models, demonstrating substantial reduction in computational effort. Furthermore, additional benefits of the proposed method are shown, such as the localization capabilities of the fine solutions, which exhibit high sensitivity in detecting discontinuities resulted from material inhomogeneity.

Aircraft vibrations induced by low-frequency unsteady aerodynamic loads affect the comfort of passengers and reduce the airframe fatigue life. In order to attain high and broadband vibration attenuation levels, a Semi-Active Tuned Mass Damper (SATMD) is developed, that exhibits robust vibration control capabilities and requires minimal structural interference. The SATMD consists of a piezoelectric device, connected to an external Resistive-Inductive electrical circuit, and a small auxiliary mass. Simulations and testing of this damper have shown high sensitivity of its performance to: (1) the location of its structural integration and (2) its electromechanical characteristics. The current paper investigates the tailoring of these design parameters on a lab-scale airframe model, aiming at simultaneous control of 3 modes. The numerical results reveal a favorable strategy to tailor the electromechanical properties. The proposed SATMD leads to more than 10dB simultaneous reduction to all targeted modes, highlighting the robustness of the proposed damping device and the importance of the tailoring process.