?url_ver=Z39.88-2004&rft_id=arXiv%3A1512.07803&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3667%2F&rft.title=High-frequency+parametric+approximation+of+the+Floquet-Bloch+spectrum+for+anti-tetrachiral+materials&rft.creator=Bacigalupo%2C+Andrea&rft.creator=Lepidi%2C+Marco&rft.subject=T+Technology+(General)&rft.description=The+engineered+class+of+anti-tetrachiral+cellular+materials+is+phenomenologically+characterized+by+a+strong+auxeticity+of+the+elastic+macroscopic+response.+The+auxetic+behavior%2C+accompanied+by+a+marked+anisotropy%2C+is+activated+by+rolling-up+deformation+mechanisms+developed+by+the+periodic+pattern+of+stiff+rings+and+flexible+ligaments+realizing+the+material+micro-structure.+In+the+absence+of+a+soft+matrix%2C+a+linear+beam+lattice+model+is+formulated+to+describe+the+free+dynamic+response+of+the+periodic+cell.+After+a+static+condensation+of+the+passive+degrees-of-freedom%2C+a+general+procedure+is+applied+to+impose+the+quasi-periodicity+conditions+of+free+wave+propagation+in+the+low-dimension+space+of+the+active+degrees-of-freedom.+The+effects+of+different+mechanical+parameters+on+the+band+structure+are+analyzed+by+comparing+the+exact+dispersion+curves+with+explicit%2C+although+approximate%2C+dispersion+functions%2C+obtained+from+asymptotic+perturbation+solutions+of+the+eigenproblem+rising+up+from+the+Floquet-Bloch+theory.+A+general+scheme+for+the+formulation+and+solution+of+the+perturbation+equations+is+outlined%2C+for+the+desired+approximation+order+and+depending+on+the+dimension+of+the+perturbation+vector.+A+satisfying+approximation+accuracy+is+achieved+for+low-order+asymptotic+solutions+in+wide+regions+of+the+parameter+space.+The+explicit+dependence+of+the+dispersion+functions+on+the+main+parameters%2C+including+the+cell+aspect+ratio%2C+the+ligament+slenderness+and+the+ring+density%2C+allows+the+in-depth+discussion+and+-+in+a+design+perspective+-+the+fine+assessment+of+the+spectrum+properties%2C+including+specific+features+like+wave+velocities+and+band+gap+amplitudes.&rft.publisher=arXiv&rft.date=2015&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F3667%2F1%2F1512.07803.pdf&rft.identifier=++Bacigalupo%2C+Andrea+and+Lepidi%2C+Marco++High-frequency+parametric+approximation+of+the+Floquet-Bloch+spectrum+for+anti-tetrachiral+materials.++Working+Paper+++arXiv+++++++(Submitted)+++&rft.relation=https%3A%2F%2Farxiv.org%2Fabs%2F1512.07803&rft.relation=arXiv%3A1512.07803