Edoardo Scarpetta

On the fundamental solutions in micropolar elasticity with voids

SummaryBy means of an uncoupling representation, we derive the fundamental solution for the differential system of micropolar elasticity with voids in the steady vibration case. Reciprocity properties are also explored.

On wave propagation in elastic solids with a doubly periodic array of cracks

Abstract In the context of wave propagation in damaged (elastic) solids, an analytical approach for normal penetration of a plane wave through a doubly periodic array of cracks is developed. Using a uniform approximation in a one-mode range previously obtained, we give explicit representations for the wave field throughout the structure (including reflection and transmission coefficients) and for the relevant dispersion equation.

Well posedness theorems for linear elastic materials with voids

Abstract In the context of a well known theory for porous elastic materials, some theorems of uniqueness and continuous dependence on data are proved for both the dynamic and the static (linear) problems. The material is allowed to fill an unbounded domain of the physical space.

Fundamental Solutions in the Theory of Thermoelasticity for Solids with Double Porosity

In this article, the linear theory of thermoelasticity for solids with double porosity is considered. The fundamental solutions for the systems of steady vibrations (including quasi-static case) and equilibrium equations are constructed by means of elementary functions; the basic properties of such solutions are also established.

Minimum principles for the bending problem of elastic plates with voids

In the context of a linear theory for the bending of porous elastic plates, we explore minimum properties of suitable functionals for homogeneous and non-homogeneous mixed problems.

In-plane problem for wave propagation through elastic solids with a periodic array of cracks

SummaryIn the context of wave propagation in damaged (elastic) solids, an analytical method previously introduced for scalar problems, is now applied to study the (vector) problem for normal penetration of a longitudinal plane wave into a periodic array of collinear cracks. Reduced the problem to an integral equation holding over the openings, an approximation of one-mode type leads to analytical solutions and then to explicit representations for the wave fields and the scattering parameters. Some graphs will finally compare our results with the numerical ones by other authors.

Wave propagation through a periodic array of inclined cracks

Abstract In the frame of wave propagation in damaged (elastic) solids, an analytical approach for normal penetration of a plane wave through a periodic array of inclined cracks is developed. The problem is reduced to an integral equation holding over the length of each crack; approximated forms (of one-mode and low-frequency types) are then given to the kernel, so as to derive explicit formulas for the reflection and transmission coefficients. Numerical resolution of the relevant equations finally provides some graphs that are compared.

Explicit Analytical Representations in the Multiple High-Frequency Reflection of Acoustic Waves from Curved Surfaces: The Leading Asymptotic Term

In the context of wave propagation through a three-dimensional acoustic medium, we develop an analytical approach to study high-frequency diffraction by multiple reflections from curved surfaces of arbitrary shape. Following a previous paper (of one of us) devoted to two-dimensional problems, we combine some ideas of Kirchhoffs physical diffraction theory with the use of (multidimensional) asymptotic estimates for the arising diffraction integrals. Some concrete examples of single and double reflection are treated. The explicit formulas obtained by our approach are compared with known results from classical geometrical diffraction (or Ray-) theory, where this is applicable, and their precision is tested by a direct numerical solution of the corresponding diffraction integrals.

Minimum problems in the dynamics of viscous fluids with memory

Abstract A minimum principle and its converse are stated for a viscoelastic incompressible fluid. We involve suitable (Reiss type) functions in the minimizing functional, so that minimum properties are preserved in passing from Laplace-transform domain to original time domain.

Theorems of continuous dependence in elasticity for exterior domains

Nel presente lavoro si dimostrano alcuni teoremi di dipendenza continua in elasticità per il problema dei piccoli spostamenti sovrapposti ad una deformazione finita. Si suppone che il corpo elastico occupi un dominio esterno dello spazio fisico. I teoremi vengono stabiliti con il metodo della «funzione peso».