Elena Bozhevolnaya

Nonlinear closed-form high-order analysis of curved sandwich panels

Closed-form high-order theory of sandwich panels, including transverse flexibility and shear rigidity of a core, as well as geometrical nonlinearity of unsymmetric faces is generalized for sandwich panels of constant curvature. Variational calculus is used to derive the set of governing equations describing a stress-deformation response of the panel to arbitrary loads. Boundary conditions are presented both in the local and global formulations. The procedure for the numerical solution of the governing nonlinear differential equations is based on the finite-difference method with deferred corrections. The solution technique is illustrated through numerical examples. Influence of the geometrical nonlinearity on the overall behaviour of the sandwich panel and localized effects are demonstrated.

Local effects across core junctions in sandwich panels

Sandwich beams and panels with symmetric faces and cores of varying stiffness are investigated. The paper presents a theoretical and experimental study of the local effects that occur in the vicinity of intersections between cores of different stiffness in such sandwich panels. These local effects manifest themselves by a significant rise of the bending stresses in the faces in the vicinity of the core junctions. Closed-form estimates of the stress/strain fields induced by local effects are presented for sandwich beams and panels loaded in cylindrical bending. The accuracy of the derived closed-form estimates is verified experimentally for the case of a sandwich beam in three-point bending.

Free Vibrations of Curved Sandwich Beams with a Transversely Flexible Core

A high-order model for free vibrations of singly curved sandwich beams is presented. The model takes into account the transverse flexibility of the sandwich core while the faces of the sandwich are treated as thin beams. Linear equations of motion as well as the natural boundary conditions are derived. Verification of the model is performed for straight beams via a number of asymptotic cases. For the straight and curved sandwich beams, it is shown that there exist four eigenmodes. Their nature is clarified, and simple theoretical estimations for the eigenfrequencies are obtained. A numerical analysis of free vibration of the simply supported beams is carried out. Effects of design parameters of the sandwich constituents on the eigenmodes and their appropriate frequencies are investigated. The developed model may find its use in the context of various applications of curved sandwich members in the high-performance vehicles.

Energy partition for ballistic penetration of sandwich panels

Ballistic impact and penetration in sandwich panels at projectile velocities above the ballistic limit are considered. An analytic model is developed that deals with partition of the energy of absorption, allowing for quantitative estimation of the energy fraction consumed via panel elastic response and the one consumed via irreversible damage. The analysis is based on simultaneous solution of two differential equations describing bending and shear deformation of a sandwich panel and taking into account the energy conservation. The solution technique includes the direct and inverse Hankel transformations and results in practical expressions for elastic response and damage energy fractions. Numerical results are corroborated with experimental data obtained from intermediate-velocity impact tests performed for sandwich panels with FRP composite laminate faces and foam cores.

Self-consistent model for photon scanning tunneling microscopy: implications for image formation and light scattering near a phase-conjugating mirror

A macroscopic self-consistent model for photon scanning tunneling microscopy with an uncoated fiber tip is developed by use of integral plane-wave representations of the total electric field in two-dimensional geometry. The model framework allows one to treat the incident field with an arbitrary angular spectrum and the presence of a thin-layer medium with a subwavelength structure on the sample surface. Imaging with the photon scanning tunneling microscope and light scattering near a phase-conjugating mirror are considered with our model by use of numerical simulations. We show that the near-field optical images provided by the microscope can be quite different from the light intensity distributions that exist near the sample surface in the absence of the fiber tip. We demonstrate that the self-consistent field at the site of a scatterer placed in front of a phase-conjugating mirror can be significantly enhanced as a result of multiple phase conjugation of the scattered light.

Free Vibration Analysis of Curved Sandwich Beams

A study of free vibrations of singly curved sandwich beams is presented. The model takes into consideration both radial and circumferential displacements of the beam core with the assumption of linear distribution across the thickness. The faces of the sandwich are treated as thin beams. Linear equations of motion as well as the boundary conditions are derived with the help of calculus of variations. Verification of the model is performed via a number of asymptotic cases. It is shown that there exist four types of eigen modes. Numerical analyses of free vibrations of the simply supported and clamped beams are carried out. Effect of the curvature on the eigen modes and their frequencies is investigated. A coupling coefficient is introduced to study the dynamic coupling of different types of motions in an eigen mode.

Extension of the macroscopic model for reflection near-field microscopy: regularization and image formation

A macroscopic self-consistent model for external-refraction near-field microscopy is extended to include the consideration of arbitrary fiber tips and the image formation of surface structures. An appropriate regularization procedure is developed to produce a stable solution of the self-consistent equation. This equation is generalized to treat the presence of a thin-layer medium with a subwavelength structure on the sample surface. Numerical results for two trapezium-shaped fiber tips are presented. This modeling confirms that the sharper tip ensures better imaging properties of the microscope but that the lateral resolution is limited by a fraction of the wavelength because of the microscopic sizes of the fiber tips.

Macroscopic self-consistent model for external-reflection near-field microscopy

The self-consistent macroscopic approach based on the Maxwell equations in two-dimensional geometry is developed to describe tip–surface interaction in external-reflection near-field microscopy. The problem is reduced to a single one-dimensional integral equation in terms of the Fourier components of the field at the plane of the sample surface. This equation is extended to take into account a pointlike scatterer placed on the sample surface. The power of light propagating toward the detector as the fiber mode is expressed by using the self-consistent field at the tip surface. Numerical results for trapezium-shaped tips are presented. We show that the sharper tip and the more confined fiber mode result in better resolution of the near-field microscope. Moreover, it is found that the tip–surface distance should not be too small so that better resolution is ensured.

Theoretical model for phase conjugation of optical near fields

A macroscopic self-consistent model for external-reflection near-field microscopy together with a similar model for photon scanning tunneling microscopy is used to describe phase conjugation of light that is emitted by a fiber tip placed near a phase-conjugating mirror. The appropriate relations are obtained for a two-dimensional configuration, and numerical results for various trapezium-shaped fiber tips are presented. This modeling accounts for the main features of recent experiments on phase conjugation of optical near fields and emphasizes the significance of taking into consideration field components that are evanescent in air but propagating in the phase-conjugating mirror. The influence of fiber tip parameters on the spatial confinement of phaseconjugated light is discussed.

Parametric study of structurally graded core junctions

In practical sandwich constructions it is often necessary to reinforce the core with high strength inserts to facilitate concentrated loads. The junction between the main core and the core insert is a potential weak spot of the sandwich structure. This section of the sandwich structure is investigated using finite element analysis and the results are compared with experimental data. Furthermore, parameters concerning the shape of the core junction are investigated using finite element analysis.