scholarly journals Bloch oscillation of elastic waves in the graded lattice of 3D-printed hollow elliptical cylinders

2019 ◽  
Vol 114 (10) ◽  
pp. 101905
Author(s):  
Hyunryung Kim ◽  
Xiaotian Shi ◽  
Eunho Kim ◽  
Jinkyu Yang
Keyword(s):  
Elastic Waves ◽  
Bloch Oscillation ◽  
3D Printed ◽  
Graded Lattice ◽  
Elliptical Cylinders

Elastic waves in arrays of elliptic inclusions

2005 ◽  
Vol 220 (9-10) ◽  
Author(s):  
Sebastien Guenneau ◽  
Alexander B. Movchan
Keyword(s):  
Cross Sections ◽  
Elastic Waves ◽  
Fused Silica ◽  
Periodic Array ◽  
Filling Fraction ◽  
Elliptical Cross ◽  
Macro Cell ◽  
Doubly Periodic Array ◽  
Elliptical Cylinders

AbstractWe consider in-plane elastic waves propagating through a doubly periodic array of cylinders of Tantalum (with both circular and elliptical cross-sections) which are embedded in a matrix of fused silica. We find some sonic gap for fairly small filling fractions of the cylinders which eventually vanish in the limit of high-filling fraction. In the case of a doubly periodic array of elliptical cylinders, removal of a cylinder within a macro-cell leads to two localised eigenstates.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

3D Printed Models for Surgical Planning and Reconstructive Implant Design in Sphenoorbital Tumor Surgery

2016 ◽  
Vol 77 (S 02) ◽  
Author(s):  
Hassan Othman ◽  
Sam Evans ◽  
Daniel Morris ◽  
Saty Bhatia ◽  
Caroline Hayhurst
Keyword(s):  
Surgical Planning ◽  
Implant Design ◽  
Tumor Surgery ◽  
3D Printed

That which Is Unseen: A 3D-Printed Case-Based Didactic Approach to Teaching Pediatric Cerebrovascular Neurosurgery

2019 ◽  
Author(s):  
Avital Perry ◽  
Soliman Oushy ◽  
Lucas Carlstrom ◽  
Christopher Graffeo ◽  
David Daniels ◽  
...  
Keyword(s):  
3D Printed ◽  
Approach To Teaching ◽  
Case Based
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