374
Views
108
CrossRef citations to date
0
Altmetric
Original Articles

Waves in microstructured materials and dispersion

, , &
Pages 4127-4141 | Received 20 Apr 2004, Accepted 22 Nov 2004, Published online: 21 Feb 2007

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (3)

Ivan Sertakov & Jaan Janno. (2012) Periodic Waves in Microstructured Solids and Inverse Problems. Mathematical Modelling and Analysis 17:5, pages 599-617.
Read now
Jüri Engelbrecht, Arvi Ravasoo & Jaan Janno. (2010) Nonlinear Acoustic Nondestructive Evaluation (NDE): Qualitative and Quantitative Effects. Materials and Manufacturing Processes 25:4, pages 212-220.
Read now
J. Janno & J. Engelbrecht. (2009) Identification of microstructured materials by phase and group velocities. Mathematical Modelling and Analysis 14:1, pages 57-68.
Read now

Articles from other publishers (105)

Jianlin Yi, Zhiqiang Meng, Jianlin Chen & Chang Qing Chen. (2023) Dispersive higher harmonic generation and enhancement in mechanical metamaterials. International Journal of Mechanical Sciences 246, pages 108146.
Crossref
F. Gómez-Silva & H. Askes. (2023) Mass matrices for elastic continua with micro-inertia. Computers & Structures 275, pages 106938.
Crossref
Linjuan Wang, Qi Zhang & Jianxiang Wang. (2022) Microstructural effects on overall dynamics of composites: an analytical method via spatiotemporal nonlocal model. Archive of Applied Mechanics 93:1, pages 73-91.
Crossref
Alessandro Ciallella, Francesco D’Annibale, Francesco dell’Isola, Dionisio Del Vescovo & Ivan Giorgio. 2023. Sixty Shades of Generalized Continua. Sixty Shades of Generalized Continua 103 116 .
Arkadi Berezovski. 2023. Sixty Shades of Generalized Continua. Sixty Shades of Generalized Continua 53 62 .
Arkadi Berezovski. (2022) Causality in strain gradient elasticity: An internal variables approach. Mechanics Research Communications 125, pages 103997.
Crossref
Markus Lazar & Eleni Agiasofitou. (2022) Nonlocal elasticity of Klein–Gordon type: Fundamentals and wave propagation. Wave Motion 114, pages 103038.
Crossref
Kert Tamm, Tanel Peets & Jüri Engelbrecht. (2022) Mechanical waves in myelinated axons. Biomechanics and Modeling in Mechanobiology 21:4, pages 1285-1297.
Crossref
Jun Hong, Zhuangzhuang He, Gongye Zhang & Changwen Mi. (2021) Size and temperature effects on band gaps in periodic fluid-filled micropipes. Applied Mathematics and Mechanics 42:9, pages 1219-1232.
Crossref
Tomáš Roubíček. (2021) From quasi-incompressible to semi-compressible fluids. Discrete and Continuous Dynamical Systems - Series S 14:11, pages 4069.
Crossref
Jüri Engelbrecht, Kert Tamm & Tanel PeetsJüri Engelbrecht, Kert Tamm & Tanel Peets. 2021. Modelling of Complex Signals in Nerves. Modelling of Complex Signals in Nerves 21 43 .
Samuel Forest & Karam Sab. (2017) Finite-deformation second-order micromorphic theory and its relations to strain and stress gradient models. Mathematics and Mechanics of Solids 25:7, pages 1429-1449.
Crossref
Armando Majorana & Rita Tracinà. (2019) Numerical solutions to a microcontinuum model using WENO schemes. Continuum Mechanics and Thermodynamics 32:3, pages 945-957.
Crossref
Haiyong Qin, Mostafa M. A. Khater & Raghda A. M. Attia. (2020) Copious Closed Forms of Solutions for the Fractional Nonlinear Longitudinal Strain Wave Equation in Microstructured Solids. Mathematical Problems in Engineering 2020, pages 1-8.
Crossref
A. Nobili, E. Radi & C. Signorini. (2020) A new Rayleigh-like wave in guided propagation of antiplane waves in couple stress materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476:2235, pages 20190822.
Crossref
Arkadi Berezovski. 2020. Encyclopedia of Continuum Mechanics. Encyclopedia of Continuum Mechanics 830 837 .
Valeria Settimi, Patrizia Trovalusci & Giuseppe Rega. (2019) Dynamical properties of a composite microcracked bar based on a generalized continuum formulation. Continuum Mechanics and Thermodynamics 31:6, pages 1627-1644.
Crossref
Anil Misra & Nima Nejadsadeghi. (2019) Longitudinal and transverse elastic waves in 1D granular materials modeled as micromorphic continua. Wave Motion 90, pages 175-195.
Crossref
I. Scala, G. Rosi, L. Placidi, V.-H. Nguyen & S. Naili. (2019) Effects of the microstructure and density profiles on wave propagation across an interface with material properties. Continuum Mechanics and Thermodynamics 31:4, pages 1165-1180.
Crossref
Mohamed Shaat. (2019) Size-dependence of Young's modulus and Poisson's ratio: Effects of material dispersion. Mechanics of Materials 133, pages 111-119.
Crossref
Ruize Hu & Caglar Oskay. (2019) Multiscale nonlocal effective medium model for in-plane elastic wave dispersion and attenuation in periodic composites. Journal of the Mechanics and Physics of Solids 124, pages 220-243.
Crossref
Nima Nejadsadeghi, Luca Placidi, Maurizio Romeo & Anil Misra. (2019) Frequency band gaps in dielectric granular metamaterials modulated by electric field. Mechanics Research Communications 95, pages 96-103.
Crossref
Linjuan Wang, Jifeng Xu, Jianxiang Wang & Bhushan L. Karihaloo. (2019) A mechanism-based spatiotemporal non-local constitutive formulation for elastodynamics of composites. Mechanics of Materials 128, pages 105-116.
Crossref
Francesco dell’Isola, Alessandro Della Corte, Antonio Battista & Emilio Barchiesi. 2019. Higher Gradient Materials and Related Generalized Continua. Higher Gradient Materials and Related Generalized Continua 19 41 .
Andrus Salupere, Martin Lints & Lauri Ilison. 2019. Applied Wave Mathematics II. Applied Wave Mathematics II 89 124 .
Victor A. Eremeyev. 2019. Applied Wave Mathematics II. Applied Wave Mathematics II 29 37 .
Harm Askes, Dario De Domenico, Mingxiu Xu, Inna M. Gitman, Terry Bennett & Elias C. Aifantis. 2019. Applied Wave Mathematics II. Applied Wave Mathematics II 239 255 .
Manfred Braun & Merle Randrüüt. 2019. Applied Wave Mathematics II. Applied Wave Mathematics II 3 27 .
Jüri Engelbrecht, Tanel Peets & Kert Tamm. (2018) Electromechanical coupling of waves in nerve fibres. Biomechanics and Modeling in Mechanobiology 17:6, pages 1771-1783.
Crossref
Jüri Engelbrecht, Tanel Peets & Kert Tamm. (2018) Solitons modelled by Boussinesq-type equations. Mechanics Research Communications 93, pages 62-65.
Crossref
Swee Hong TanLeong Hien Poh. (2018) Homogenized Gradient Elasticity Model for Plane Wave Propagation in Bilaminate Composites. Journal of Engineering Mechanics 144:9.
Crossref
Jüri Engelbrecht, Tanel Peets & Kert Tamm. (2018) Soliton trains in dispersive media. Low Temperature Physics 44:7, pages 696-700.
Crossref
G.Y. Zhang, X.-L. Gao, J.E. Bishop & H.E. Fang. (2018) Band gaps for elastic wave propagation in a periodic composite beam structure incorporating microstructure and surface energy effects. Composite Structures 189, pages 263-272.
Crossref
C. Broese, C. Tsakmakis & D. Beskos. (2017) Gradient Elasticity Based on Laplacians of Stress and Strain. Journal of Elasticity 131:1, pages 39-74.
Crossref
Arkadi Berezovski. 2017. Encyclopedia of Continuum Mechanics. Encyclopedia of Continuum Mechanics 1 7 .
Igor A. Gula & Alexander M. Samsonov. 2018. Generalized Models and Non-classical Approaches in Complex Materials 1. Generalized Models and Non-classical Approaches in Complex Materials 1 395 416 .
Jüri Engelbrecht, Andrus Salupere, Arkadi Berezovski, Tanel Peets & Kert Tamm. 2018. Generalized Models and Non-classical Approaches in Complex Materials 1. Generalized Models and Non-classical Approaches in Complex Materials 1 275 286 .
Matthew Russo & S. Roy Choudhury. (2017) Analytic solutions of a microstructure PDE and the KdV and Kadomtsev–Petviashvili equations by invariant Painlevé analysis and generalized Hirota techniques. Applied Mathematics and Computation 311, pages 228-239.
Crossref
Kert Tamm, Tanel Peets, Jüri Engelbrecht & Dmitri Kartofelev. (2017) Negative group velocity in solids. Wave Motion 71, pages 127-138.
Crossref
Tanel Peets, Kert Tamm & Jüri Engelbrecht. (2017) On the role of nonlinearities in the Boussinesq-type wave equations. Wave Motion 71, pages 113-119.
Crossref
J. Marchais, L. Chamoin & C. Rey. (2016) Wave filtering through a selective perfectly matched layer in multiscale couplings with dynamically incompatible models. International Journal for Numerical Methods in Engineering 110:8, pages 745-775.
Crossref
Arkadi Berezovski & Peter VánArkadi Berezovski & Peter Ván. 2017. Internal Variables in Thermoelasticity. Internal Variables in Thermoelasticity 113 120 .
Arkadi Berezovski & Peter VánArkadi Berezovski & Peter Ván. 2017. Internal Variables in Thermoelasticity. Internal Variables in Thermoelasticity 85 98 .
Arkadi Berezovski & Peter VánArkadi Berezovski & Peter Ván. 2017. Internal Variables in Thermoelasticity. Internal Variables in Thermoelasticity 1 18 .
Andrus Salupere. (2016) On hidden solitons in KdV related systems. Mathematics and Computers in Simulation 127, pages 252-262.
Crossref
Tanel Peets. (2016) Internal scales and dispersive properties of microstructured materials. Mathematics and Computers in Simulation 127, pages 220-228.
Crossref
Arkadi Berezovski, Ivan Giorgio & Alessandro Della Corte. (2015) Interfaces in micromorphic materials: Wave transmission and reflection with numerical simulations. Mathematics and Mechanics of Solids 21:1, pages 37-51.
Crossref
Li Li, Yujin Hu & Ling Ling. (2015) Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Composite Structures 133, pages 1079-1092.
Crossref
Tong Hui & Caglar Oskay. (2015) Laplace-domain, high-order homogenization for transient dynamic response of viscoelastic composites. International Journal for Numerical Methods in Engineering 103:13, pages 937-957.
Crossref
Ye Zhao & Miao-chao Chen. (2015) Stability/instability of solitary waves with nonzero asymptotic value for a PDE in microstructural solid materials. Acta Mathematicae Applicatae Sinica, English Series 31:3, pages 693-700.
Crossref
Jüri Engelbrecht & Arkadi Berezovski. (2015) Reflections on mathematical models of deformation waves in elastic microstructured solids. Mathematics and Mechanics of Complex Systems 3:1, pages 43-82.
Crossref
Jüri Engelbrechtjüri Engelbrecht. 2015. Questions About Elastic Waves. Questions About Elastic Waves 91 149 .
Jüri EngelbrechtJüri Engelbrecht. 2015. Questions About Elastic Waves. Questions About Elastic Waves 19 42 .
A. Piccolroaz & A.B. Movchan. (2014) Dispersion and localisation in structured Rayleigh beams. International Journal of Solids and Structures 51:25-26, pages 4452-4461.
Crossref
H. G. Georgiadis, P. A. Gourgiotis & D. S. Anagnostou. (2014) The Boussinesq problem in dipolar gradient elasticity. Archive of Applied Mechanics 84:9-11, pages 1373-1391.
Crossref
J. Engelbrecht & A. Salupere. (2013) Scaling and hierarchies of wave motion in solids. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 94:9, pages 775-783.
Crossref
P. A. Gourgiotis & A. Piccolroaz. (2014) Steady-state propagation of a mode II crack in couple stress elasticity. International Journal of Fracture 188:2, pages 119-145.
Crossref
Rémi Dingreville, Joshua Robbins & Thomas E. Voth. (2014) Wave propagation and dispersion in elasto-plastic microstructured materials. International Journal of Solids and Structures 51:11-12, pages 2226-2237.
Crossref
Tong Hui & Caglar Oskay. (2014) A high order homogenization model for transient dynamics of heterogeneous media including micro-inertia effects. Computer Methods in Applied Mechanics and Engineering 273, pages 181-203.
Crossref
Ivan Sertakov, Jüri Engelbrecht & Jaan Janno. (2014) Modelling 2D wave motion in microstructured solids. Mechanics Research Communications 56, pages 42-49.
Crossref
Andrus Salupere & Kert Tamm. (2013) On the influence of material properties on the wave propagation in Mindlin-type microstructured solids. Wave Motion 50:7, pages 1127-1139.
Crossref
T. Peets, D. Kartofelev, K. Tamm & J. Engelbrecht. (2013) Waves in microstructured solids and negative group velocity. EPL (Europhysics Letters) 103:1, pages 16001.
Crossref
A. Berezovski, J. Engelbrecht, A. Salupere, K. Tamm, T. Peets & M. Berezovski. (2013) Dispersive waves in microstructured solids. International Journal of Solids and Structures 50:11-12, pages 1981-1990.
Crossref
P.A. Gourgiotis, H.G. Georgiadis & I. Neocleous. (2013) On the reflection of waves in half-spaces of microstructured materials governed by dipolar gradient elasticity. Wave Motion 50:3, pages 437-455.
Crossref
Igor V. Andrianov, Vladyslav V. Danishevs’kyy, Oleksandr I. Ryzhkov & Dieter Weichert. (2013) Dynamic homogenization and wave propagation in a nonlinear 1D composite material. Wave Motion 50:2, pages 271-281.
Crossref
Kert Tamm & Tanel Peets. (2013) On the influence of internal degrees of freedom on dispersion in microstructured solids. Mechanics Research Communications 47, pages 106-111.
Crossref
Tong Hui & Caglar Oskay. (2013) A nonlocal homogenization model for wave dispersion in dissipative composite materials. International Journal of Solids and Structures 50:1, pages 38-48.
Crossref
A.V. Porubov, I.V. Andrianov & V.V. Danishevs’kyy. (2012) Nonlinear strain wave localization in periodic composites. International Journal of Solids and Structures 49:23-24, pages 3381-3387.
Crossref
Tong Hui & Caglar Oskay. (2012) Computational modeling of polyurea-coated composites subjected to blast loads. Journal of Composite Materials 46:18, pages 2167-2178.
Crossref
G. Carta & M. Brun. (2012) A Dispersive Homogenization Model Based on Lattice Approximation for the Prediction of Wave Motion in Laminates. Journal of Applied Mechanics 79:2.
Crossref
Kert Tamm & Andrus Salupere. (2012) On the propagation of 1D solitary waves in Mindlin-type microstructured solids. Mathematics and Computers in Simulation 82:7, pages 1308-1320.
Crossref
Mihhail Berezovski & Arkadi Berezovski. (2012) On the stability of a microstructure model. Computational Materials Science 52:1, pages 193-196.
Crossref
Jüri Engelbrecht, Andrus Salupere & Kert Tamm. (2011) Waves in microstructured solids and the Boussinesq paradigm. Wave Motion 48:8, pages 717-726.
Crossref
Arkadi Berezovski, Jüri Engelbrecht & Mihhail Berezovski. (2011) Waves in microstructured solids: a unified viewpoint of modeling. Acta Mechanica 220:1-4, pages 349-363.
Crossref
Harm Askes & Elias C. Aifantis. (2011) Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results. International Journal of Solids and Structures 48:13, pages 1962-1990.
Crossref
Harm Askes, Duc C. D. Nguyen & Andy Tyas. (2011) Increasing the critical time step: micro-inertia, inertia penalties and mass scaling. Computational Mechanics 47:6, pages 657-667.
Crossref
Arkadi Berezovski, Jüri Engelbrecht & Gérard A. Maugin. (2010) Generalized thermomechanics with dual internal variables. Archive of Applied Mechanics 81:2, pages 229-240.
Crossref
Arkadi Berezovski, Jüri Engelbrecht & Mihhail Berezovski. 2011. Vibration Problems ICOVP 2011. Vibration Problems ICOVP 2011 699 705 .
Jaan Janno & Jüri EngelbrechtJaan Janno & Jüri Engelbrecht. 2011. Microstructured Materials: Inverse Problems. Microstructured Materials: Inverse Problems 147 154 .
Jaan Janno & Jüri EngelbrechtJaan Janno & Jüri Engelbrecht. 2011. Microstructured Materials: Inverse Problems. Microstructured Materials: Inverse Problems 1 3 .
Arkadi Berezovski, Jüri Engelbrecht & Tanel Peets. (2010) Multiscale modeling of microstructured solids. Mechanics Research Communications 37:6, pages 531-534.
Crossref
J. Song, J. Shen & X.F. Li. (2010) Effects of initial axial stress on waves propagating in carbon nanotubes using a generalized nonlocal model. Computational Materials Science 49:3, pages 518-523.
Crossref
Tanel Peets & Kert Tamm. 2010. IUTAM Symposium on Recent Advances of Acoustic Waves in Solids. IUTAM Symposium on Recent Advances of Acoustic Waves in Solids 349 354 .
Jüri Engelbrecht, Arkadi Berezovski & Mihhail Berezovski. 2010. IUTAM Symposium on Recent Advances of Acoustic Waves in Solids. IUTAM Symposium on Recent Advances of Acoustic Waves in Solids 19 29 .
Andrus Salupere & Lauri Ilison. 2010. Mechanics of Microstructured Solids 2. Mechanics of Microstructured Solids 2 21 28 .
Lauri Ilison & Andrus Salupere. (2009) Propagation of sech2-type solitary waves in hierarchical KdV-type systems. Mathematics and Computers in Simulation 79:11, pages 3314-3327.
Crossref
J.A. Leto & S.R. Choudhury. (2009) Solitary wave families of a generalized microstructure PDE. Communications in Nonlinear Science and Numerical Simulation 14:5, pages 1999-2005.
Crossref
A. V. Porubov, E. L. Aero & G. A. Maugin. (2009) Two approaches to study essentially nonlinear and dispersive properties of the internal structure of materials. Physical Review E 79:4.
Crossref
Eduard Rohan, Bernadette Miara & František Seifrt. (2009) Numerical simulation of acoustic band gaps in homogenized elastic composites. International Journal of Engineering Science 47:4, pages 573-594.
Crossref
Arkadi Berezovski, Jüri Engelbrecht & Gérard A. Maugin. 2009. Mechanics of Microstructured Solids. Mechanics of Microstructured Solids 21 28 .
Alexey V. Porubov. 2009. Mechanics of Microstructured Solids. Mechanics of Microstructured Solids 119 126 .
Arkadi Berezovski, Mihhail Berezovski & Jüri Engelbrecht. 2009. Applied Wave Mathematics. Applied Wave Mathematics 55 81 .
Jüri Engelbrecht. 2009. Applied Wave Mathematics. Applied Wave Mathematics 13 30 .
Andrus Salupere. 2009. Applied Wave Mathematics. Applied Wave Mathematics 301 333 .
Arkadi Berezovski, Jüri Engelbrecht & Gérard A. Maugin. 2009. IUTAM Symposium on Scaling in Solid Mechanics. IUTAM Symposium on Scaling in Solid Mechanics 69 80 .
J Janno & J Engelbrecht. (2008) Inverse problems related to a coupled system of microstructure. Inverse Problems 24:4, pages 045017.
Crossref
Harm Askes, Beibei Wang & Terry Bennett. (2008) Element size and time step selection procedures for the numerical analysis of elasticity with higher-order inertia. Journal of Sound and Vibration 314:3-5, pages 650-656.
Crossref
A. Salupere, K. Tamm & J. Engelbrecht. (2008) Numerical simulation of interaction of solitary deformation waves in microstructured solids. International Journal of Non-Linear Mechanics 43:3, pages 201-208.
Crossref
T. Peets, M. Randrüüt & J. Engelbrecht. (2008) On modelling dispersion in microstructured solids. Wave Motion 45:4, pages 471-480.
Crossref
Terry Bennett, Inna M. Gitman & Harm Askes. (2008) Elasticity Theories with Higher-order Gradients of Inertia and Stiffness for the Modelling of Wave Dispersion in Laminates. International Journal of Fracture 148:2, pages 185-193.
Crossref
Marko Vendelin, Valdur Saks & Jüri Engelbrecht. 2007. Molecular System Bioenergetics. Molecular System Bioenergetics 407 433 .
J. Engelbrecht, A. Berezovski & A. Salupere. (2007) Nonlinear deformation waves in solids and dispersion. Wave Motion 44:6, pages 493-500.
Crossref
Jüri Engelbrecht, Franco Pastrone, Manfred Braun & Arkadi Berezovski. 2006. Universality of Nonclassical Nonlinearity. Universality of Nonclassical Nonlinearity 29 47 .
Franco Pastrone. 2006. Universality of Nonclassical Nonlinearity. Universality of Nonclassical Nonlinearity 15 27 .
J. Janno & J. Engelbrecht. (2005) Waves in microstructured solids: Inverse problems. Wave Motion 43:1, pages 1-11.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.