?url_ver=Z39.88-2004&rft_id=arXiv%3A1706.08754&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3741%2F&rft.title=Multi-parametric+sensitivity+analysis+of+the+band+structure+for+tetrachiral+inertial+metamaterials&rft.creator=Lepidi%2C+Marco&rft.creator=Bacigalupo%2C+Andrea&rft.subject=T+Technology+(General)&rft.subject=TA+Engineering+(General).+Civil+engineering+(General)&rft.description=Tetrachiral+materials+are+characterized+by+a+cellular+microstructure+made+by+a+periodic+pattern+of+stiff+rings+and+flexible+ligaments.+Their+mechanical+behaviour+can+be+described+by+a+planar+lattice+of+rigid+massive+bodies+and+elastic+massless+beams.+The+periodic+cell+dynamics+is+governed+by+a+monoatomic+structural+model%2C+conveniently+reduced+to+the+only+active+degrees-of-freedom.+The+paper+presents+an+explicit+parametric+description+of+the+band+structure+governing+the+free+propagation+of+elastic+waves.+By+virtue+of+multiparametric+perturbation+techniques%2C+sensitivity+analyses+are+performed+to+achieve+analytical+asymptotic+approximation+of+the+dispersion+functions.+The+parametric+conditions+for+the+existence+of+full+band+gaps+in+the+low-frequency+range+are+established.+Furthermore%2C+the+band+gap+amplitude+is+analytically+assessed+in+the+admissible+parameter+range.+In+inertial+tetrachiral+metamaterials%2C+stop+bands+can+be+opened+by+the+introduction+of+intra-ring+resonators.+Perturbation+methods+can+efficiently+deal+with+the+consequent+enlargement+of+the+mechanical+parameter+space.+Indeed+high-accuracy+parametric+approximations+are+achieved+for+the+band+structure%2C+enriched+by+the+new+optical+branches+related+to+the+resonator+frequencies.+In+particular%2C+target+stop+bands+in+the+metamaterial+spectrum+are+analytically+designed+through+the+asymptotic+solution+of+inverse+spectral+problems.%0D%0ASubjects%3A%09Materials+Science+(cond-mat.mtrl-sci)%0D%0ACite+as%3A%09arXiv%3A1706.08754+%5Bcond-mat.mtrl-sci%5D%0D%0A+%09(or+arXiv%3A1706.08754v1+%5Bcond-mat.mtrl-sci%5D+for+this+version)&rft.publisher=arXiv&rft.date=2017&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.rights=cc_by_nc_nd&rft.identifier=http%3A%2F%2Feprints.imtlucca.it%2F3741%2F1%2F1706.08754.pdf&rft.identifier=++Lepidi%2C+Marco+and+Bacigalupo%2C+Andrea++Multi-parametric+sensitivity+analysis+of+the+band+structure+for+tetrachiral+inertial+metamaterials.++Working+Paper+++arXiv+++++++(Submitted)+++&rft.relation=https%3A%2F%2Farxiv.org%2Fabs%2F1706.08754&rft.relation=arXiv%3A1706.08754