A Spectral-Element Approach for the Eikonal Equation

2015 ◽  
Author(s):  
Scott M. Murman ◽  
Laslo T. Diosady
Keyword(s):  
Eikonal Equation ◽  
Spectral Element ◽  
Element Approach

Spectral Element Approach for Flexural Waves Control in Smart Material Beam With Single and Multiple Resonant Impedance Shunt Circuit

2020 ◽  
Vol 15 (12) ◽  
Author(s):  
Marcela R. Machado ◽  
Adriano T. Fabro ◽  
Braion B. de Moura
Keyword(s):  
Control Strategies ◽  
Spectral Element ◽  
Smart Material ◽  
Smart Structure ◽  
Flexural Waves ◽  
Structural Dynamic ◽  
Vibration Attenuation ◽  
Resonant Behavior ◽  
Element Approach ◽  
Shunt Circuit

Abstract 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 behavior 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 piezolayers connected to single and multiresonant shunt approaches. The smart structure is modeled using the spectral element method. It is shown that the effective wavenumber presents the locally resonant behavior at the same frequencies of the vibration attenuation for both single and multishunt approached, indicating that each shunt circuit is independently associated with 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.

A spectral boundary element approach to three-dimensional Stokes flow

1995 ◽  
Vol 298 ◽  
pp. 167-192 ◽  
Author(s):  
G. P. Muldowney ◽  
J. J. L. Higdon
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Spectral Element ◽  
Companion Paper ◽  
Porous Membrane ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Reynolds Number Flow ◽  
Periodic Models ◽  
Element Approach

A novel method is introduced for solving the three-dimensional Stokes equations via a spectral element approach to the boundary integral method. The accuracy and convergence of the method are illustrated through applications involving rigid particles, deformable droplets and interacting particles. New physical results are obtained for two applications in low Reynolds number flow: the permeability of periodic models of a porous membrane and the instability of a toroidal droplet subject to non-axisymmetric perturbations. Further applications are described in the companion paper (Higdon & Muldowney 1995).

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