Acta mechanica, ISSN 1619-6937, 11/2018, Volume 230, Issue 3, pp. 749 - 769

Aim of the paper is the formulation of a criterion of infinitesimal stability for a class of rods made of nonlocal elastic materials. To that end, the...

Engineering | Vibration, Dynamical Systems, Control | 74A60 | 74K10 | 74H55 | Classical and Continuum Physics | Solid Mechanics | Engineering Thermodynamics, Heat and Mass Transfer | Engineering Fluid Dynamics | Theoretical and Applied Mechanics | 74B20 | Mechanics | Technology | Science & Technology | Nonlinear equations | Constitutive relationships | Shear modulus | Twisting | Mathematical analysis | Stability criteria | Axial forces | Equilibrium equations | Product design | Rods | Elastic deformation | Constitutive equations

Engineering | Vibration, Dynamical Systems, Control | 74A60 | 74K10 | 74H55 | Classical and Continuum Physics | Solid Mechanics | Engineering Thermodynamics, Heat and Mass Transfer | Engineering Fluid Dynamics | Theoretical and Applied Mechanics | 74B20 | Mechanics | Technology | Science & Technology | Nonlinear equations | Constitutive relationships | Shear modulus | Twisting | Mathematical analysis | Stability criteria | Axial forces | Equilibrium equations | Product design | Rods | Elastic deformation | Constitutive equations

Journal Article

Journal of elasticity, ISSN 0374-3535, 8/2016, Volume 124, Issue 2, pp. 143 - 191

We formulate a nonlocal cohesive model for calculating the deformation inside a cracking body. In this model a set of physical properties including elastic and...

Î“ $\varGamma$ -Convergence | 74H55 | 34A34 | Mechanics | Dynamic brittle fracture | Automotive Engineering | Peridynamics | Process zone | 74R10 | Physics | Fracture toughness | Î“-Convergence | Engineering | Materials Science | Technology | Engineering, Multidisciplinary | Materials Science, Multidisciplinary | Science & Technology | Force and energy | Cohesion | Fracture mechanics | Dynamics | Evolution | Mathematical models | Displacement | Strain

Î“ $\varGamma$ -Convergence | 74H55 | 34A34 | Mechanics | Dynamic brittle fracture | Automotive Engineering | Peridynamics | Process zone | 74R10 | Physics | Fracture toughness | Î“-Convergence | Engineering | Materials Science | Technology | Engineering, Multidisciplinary | Materials Science, Multidisciplinary | Science & Technology | Force and energy | Cohesion | Fracture mechanics | Dynamics | Evolution | Mathematical models | Displacement | Strain

Journal Article

Journal of elasticity, ISSN 0374-3535, 10/2014, Volume 117, Issue 1, pp. 21 - 50

We consider the nonlocal formulation of continuum mechanics described by peridynamics. We provide a link between peridynamic evolution and brittle fracture...

Elastic moduli | Critical energy release rate | 74H55 | 34A34 | Mechanics | Automotive Engineering | Peridynamics | Dynamic fracture | 74R10 | Physics | Brittle materials | Engineering | Materials Science | Technology | Engineering, Multidisciplinary | Materials Science, Multidisciplinary | Science & Technology | Force and energy | Fracture mechanics | Dynamics | Mathematical analysis | Brittle fracture | Evolution | Elastic waves | Influence functions | Displacement

Elastic moduli | Critical energy release rate | 74H55 | 34A34 | Mechanics | Automotive Engineering | Peridynamics | Dynamic fracture | 74R10 | Physics | Brittle materials | Engineering | Materials Science | Technology | Engineering, Multidisciplinary | Materials Science, Multidisciplinary | Science & Technology | Force and energy | Fracture mechanics | Dynamics | Mathematical analysis | Brittle fracture | Evolution | Elastic waves | Influence functions | Displacement

Journal Article

Applied mathematics & optimization, ISSN 0095-4616, 4/2018, Volume 77, Issue 2, pp. 315 - 341

In this paper we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic Bresse system, where the heat conduction is given by...

Lack of exponential stability | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Cattaneoâ€™s law | Mathematics | Polynomial stability | Exponential stability | Mathematical Methods in Physics | 93D20 | 74H55 | Calculus of Variations and Optimal Control; Optimization | Thermoelasticicity second sound | 74H40 | Bresse systems | Numerical and Computational Physics, Simulation | 35B40 | Physical Sciences | Mathematics, Applied | Science & Technology | Conductive heat transfer | Well posed problems | Dimensional stability | Heat transfer | Conduction heating | ONE-DIMENSIONAL CALCULATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | THERMAL CONDUCTION | ASYMPTOTIC SOLUTIONS

Lack of exponential stability | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Cattaneoâ€™s law | Mathematics | Polynomial stability | Exponential stability | Mathematical Methods in Physics | 93D20 | 74H55 | Calculus of Variations and Optimal Control; Optimization | Thermoelasticicity second sound | 74H40 | Bresse systems | Numerical and Computational Physics, Simulation | 35B40 | Physical Sciences | Mathematics, Applied | Science & Technology | Conductive heat transfer | Well posed problems | Dimensional stability | Heat transfer | Conduction heating | ONE-DIMENSIONAL CALCULATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | THERMAL CONDUCTION | ASYMPTOTIC SOLUTIONS

Journal Article

International Journal of Nonlinear Sciences and Numerical Simulation, ISSN 1565-1339, 08/2014, Volume 15, Issue 5, pp. 241 - 249

This paper deals with analysis of the mechanical behavior of an electro-statically-actuated micro-beam resonator from the bifurcation view of point. The...

bifurcation | 74G60 | 74H55 | micro-resonator | non-local theory of elasticity | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Physics, Mathematical | Mechanics | Mathematics | Mathematics, Applied | Physics | Science & Technology | Elasticity | Theory | Models

bifurcation | 74G60 | 74H55 | micro-resonator | non-local theory of elasticity | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Physics, Mathematical | Mechanics | Mathematics | Mathematics, Applied | Physics | Science & Technology | Elasticity | Theory | Models

Journal Article

Journal of elasticity, ISSN 0374-3535, 3/2014, Volume 115, Issue 1, pp. 47 - 59

The stability of dynamic anti-plane sliding at an interface between an elastic layer and an elastic half-space with dissimilar elastic properties is studied....

Stability | 74H55 | 74B05 | Mechanics | Elasticity | Bifurcation | Automotive Engineering | Rate- and state-friction | 74J05 | Physics | Engineering | Materials Science | Technology | Engineering, Multidisciplinary | Materials Science, Multidisciplinary | Science & Technology | Elastic constants | Half spaces | Friction | Sliding | Instability | Bonding | Contact

Stability | 74H55 | 74B05 | Mechanics | Elasticity | Bifurcation | Automotive Engineering | Rate- and state-friction | 74J05 | Physics | Engineering | Materials Science | Technology | Engineering, Multidisciplinary | Materials Science, Multidisciplinary | Science & Technology | Elastic constants | Half spaces | Friction | Sliding | Instability | Bonding | Contact

Journal Article

Zeitschrift fÃ¼r angewandte Mathematik und Physik, ISSN 0044-2275, 6/2015, Volume 66, Issue 3, pp. 1095 - 1108

We consider the coupled linear system
$$\left\{\begin{array}{ll} \partial_{tt} u + \partial_{xxxx}u + \gamma \partial_t u + k(u - v) + h\partial_{t} (u-v) =...

String-beam system | Theoretical and Applied Mechanics | 74K05 | Suspension bridge | Contraction semigroup | Coupled wave equations | Engineering | Mathematical Methods in Physics | 74K10 | Stability and exponential stability | 74H55 | Primary 35B40 | 74H40 | Secondary 47D03 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Bridges, Suspension | Analysis | Models

String-beam system | Theoretical and Applied Mechanics | 74K05 | Suspension bridge | Contraction semigroup | Coupled wave equations | Engineering | Mathematical Methods in Physics | 74K10 | Stability and exponential stability | 74H55 | Primary 35B40 | 74H40 | Secondary 47D03 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Bridges, Suspension | Analysis | Models

Journal Article

Calculus of variations and partial differential equations, ISSN 0944-2669, 1/2014, Volume 49, Issue 1, pp. 729 - 752

In this paper we study two-dimensional models for the motion of a viscoelastic material with a non-monotone stress-strain relationship. We prove existence of...

49J10 | 74G35 | 74H55 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 74N05 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Mathematical problems | Mathematical models | Asymptotic properties

49J10 | 74G35 | 74H55 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 74N05 | Mathematics | Physical Sciences | Mathematics, Applied | Science & Technology | Mathematical problems | Mathematical models | Asymptotic properties

Journal Article

Applied mathematics and mechanics, ISSN 0253-4827, 2016, Volume 37, Issue 2, pp. 265 - 274

In this study, a model for dynamic instability of embedded single-walled car- bon nanotubes ï¼ˆSWCNTsï¼‰ is presented. SWCNTs are modeled by the sinusoidal shear...

single-walled carbon nanotubes (SWCNTs) | sinusoidal shear deformation beam theory (SSDBT) | modified couple stress theory (MCST) | 74H55 | O341 | Classical Mechanics | Bolotin method | Mathematics | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | dynamic instability | Mechanics | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Stress relieving (Materials) | Strains and stresses | Analysis | Nanotubes | Mechanical properties | Models | Stress relaxation (Materials) | Hamiltonian systems | Usage | Mathematical models | Nanoelectromechanical systems | Parameters | Beam theory (structures) | Differential equations | Dynamic stability | Shear deformation | Size effects | Single wall carbon nanotubes

single-walled carbon nanotubes (SWCNTs) | sinusoidal shear deformation beam theory (SSDBT) | modified couple stress theory (MCST) | 74H55 | O341 | Classical Mechanics | Bolotin method | Mathematics | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | dynamic instability | Mechanics | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Stress relieving (Materials) | Strains and stresses | Analysis | Nanotubes | Mechanical properties | Models | Stress relaxation (Materials) | Hamiltonian systems | Usage | Mathematical models | Nanoelectromechanical systems | Parameters | Beam theory (structures) | Differential equations | Dynamic stability | Shear deformation | Size effects | Single wall carbon nanotubes

Journal Article

Journal of elasticity, ISSN 0374-3535, 7/2012, Volume 108, Issue 2, pp. 209 - 223

This paper is concerned with some general theorems for the linear dynamic theory of magnetoelectroelasticity. First, the spatial behavior of solutions is...

Spatial behavior | 74F15 | Piezoelectromagnetism | 74H99 | 74H55 | Uniqueness | Mechanics | Automotive Engineering | Continuous dependence | Domain of influence | Physics | Engineering | Materials Science | Technology | Engineering, Multidisciplinary | Materials Science, Multidisciplinary | Science & Technology

Spatial behavior | 74F15 | Piezoelectromagnetism | 74H99 | 74H55 | Uniqueness | Mechanics | Automotive Engineering | Continuous dependence | Domain of influence | Physics | Engineering | Materials Science | Technology | Engineering, Multidisciplinary | Materials Science, Multidisciplinary | Science & Technology

Journal Article

Applied mathematics and mechanics, ISSN 1573-2754, 02/2018, Volume 39, Issue 4, pp. 561 - 580

By means of a comprehensive theory of elasticity, namely, a nonlocal strain gradient continuum theory, size-dependent nonlinear axial instability...

O344.1 | 74H55 | nanomechanics | Classical Mechanics | Mathematics | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | perturbation technique | nonlinear instability | nonlocal strain gradient theory | functionally graded material (FGM) | Mechanics | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Mechanical properties | Elasticity | Analysis | Materials | Stability | Parameters | Deformation mechanisms | Small scale | Scale effect | Shell theory | Postbuckling | Strain | Shear deformation | Size effects | Functionally gradient materials | Buckling | Boundary layer

O344.1 | 74H55 | nanomechanics | Classical Mechanics | Mathematics | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | perturbation technique | nonlinear instability | nonlocal strain gradient theory | functionally graded material (FGM) | Mechanics | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Mechanical properties | Elasticity | Analysis | Materials | Stability | Parameters | Deformation mechanisms | Small scale | Scale effect | Shell theory | Postbuckling | Strain | Shear deformation | Size effects | Functionally gradient materials | Buckling | Boundary layer

Journal Article

Journal of thermal stresses, ISSN 1521-074X, 03/2018, Volume 41, Issue 6, pp. 758 - 775

In this article, we study the initial boundary value problem in one space variable for an elastic-thermoelastic bar with the elastic part being surrounded by...

transmission problem | past history | second sound | thermoelasticity | general decay | 74F05 | 35B37 | 74H55 | 35B35 | Mechanics | Thermodynamics | Physical Sciences | Technology | Science & Technology | Conductive heat transfer | Boundary value problems | Functionals | Decay | Conduction heating | Thermoelasticity | Heat transfer | Fourier law

transmission problem | past history | second sound | thermoelasticity | general decay | 74F05 | 35B37 | 74H55 | 35B35 | Mechanics | Thermodynamics | Physical Sciences | Technology | Science & Technology | Conductive heat transfer | Boundary value problems | Functionals | Decay | Conduction heating | Thermoelasticity | Heat transfer | Fourier law

Journal Article

International journal of nonlinear sciences and numerical simulation, ISSN 1565-1339, 05/2020, Volume 21, Issue 3, pp. 303 - 318

A nonlocal elasticity theory is a popular growing technique for mechanical analysis of the micro- and nanoscale structures which captures the small-size...

nano-beam | 74H55 | saddle node bifurcation | nonlocal elasticity theory | 74H60 | capacitive | 74G60 | centrifugal force | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Physics, Mathematical | Mechanics | Mathematics | Mathematics, Applied | Physics | Science & Technology | Nonlinear equations | Parameters | Beam theory (structures) | Saddle points | Van der Waals forces | Bifurcations | Reduced order models | Equations of motion | Clamping | Motion stability | Mechanical analysis | Initial conditions | Size effects | Centrifugal force | Angular velocity | Mathematical models | Galerkin method | Linear equations | Euler-Bernoulli beams | Nonlocal elasticity | Linearization

nano-beam | 74H55 | saddle node bifurcation | nonlocal elasticity theory | 74H60 | capacitive | 74G60 | centrifugal force | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Physics, Mathematical | Mechanics | Mathematics | Mathematics, Applied | Physics | Science & Technology | Nonlinear equations | Parameters | Beam theory (structures) | Saddle points | Van der Waals forces | Bifurcations | Reduced order models | Equations of motion | Clamping | Motion stability | Mechanical analysis | Initial conditions | Size effects | Centrifugal force | Angular velocity | Mathematical models | Galerkin method | Linear equations | Euler-Bernoulli beams | Nonlocal elasticity | Linearization

Journal Article