Transient waves in inhomogeneous isotropic elastic plates

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

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Self-dual singularity through lasing and antilasing in thin elastic plates

Physical Review B ◽

10.1103/physrevb.103.134101 ◽

2021 ◽

Vol 103 (13) ◽

Author(s):

M. Farhat ◽

P.-Y. Chen ◽

S. Guenneau ◽

Y. Wu

Keyword(s):

Elastic Plates ◽

Thin Elastic Plates

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Spacetime modulation in floating thin elastic plates

Physical Review B ◽

10.1103/physrevb.104.014308 ◽

2021 ◽

Vol 104 (1) ◽

Author(s):

Mohamed Farhat ◽

Sebastien Guenneau ◽

Pai-Yen Chen ◽

Ying Wu

Keyword(s):

Elastic Plates ◽

Thin Elastic Plates

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Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

Nanomaterials ◽

10.3390/nano11010087 ◽

2021 ◽

Vol 11 (1) ◽

pp. 87

Author(s):

Giovanni Tocci Monaco ◽

Nicholas Fantuzzi ◽

Francesco Fabbrocino ◽

Raimondo Luciano

Keyword(s):

Strain Gradient ◽

Thermal Environment ◽

Scale Effects ◽

Nonlocal Theory ◽

Elastic Plates ◽

Critical Temperatures ◽

Buckling Behavior ◽

Linear Vibrations ◽

Nonlocal Strain Gradient ◽

Plate Kinematics

An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

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