1,721,156 research outputs found
Spatial behaviour of the states of bending in microstrech elastic plates
No full textIn this paper we study the spatial behavior of the states of bending in a microstretch elastic plate. We show that, for fixed time t, in that part of the plate where the distance to the support of data is greater tha ct (c is a material constant), the state of bending is vanishing. While for the part of the plate where the distance to the support is less than ct an appropriate measure associate with the state of bending decays exponentially with that distance. As a consequence, a uniqueness theorem is presented for an infinite plate with no apriori conditions at infinity
On a generalized biharmonic equation in plane polars with applications to functionally graded material
No full textIn this paper we consider a generalized biharmonic equation modelling a two–dimensional inhomogeneous elastic state in the curvilinear rectangle a ≤ r ≤ b, 0≤θ≤α, where (r, θ) denote plane polar coordinates. Such an arch–like region is maintained in equilibrium under self–equilibrated traction applied on the edge θ = 0, while the other three edges r = a, r = b and θ = α are traction free. Our aim is to derive some explicit spatial exponential decay bounds for the specific Airy stress function and its derivatives. Two types of smoothly varying inhomogeneity are considered: (i) the elastic moduli vary smoothly with the polar angle, (ii) they vary smoothly with the polar distance. Such types of smoothly varying inhomogeneous elastic materials provide a model for technological important functionally graded materials. The results of the present paper prove how the spatial decay rate varies with the constitutive profile
Problemi di Omogeneizzazione: Formule di Rappresentazione, Domini Perforati.
No full textSunto della tesi di dottorato di Ricerca in Analisi Matematica e Calcolo delle Probabilita
A mathematical study of the spatial behaviour of the time-harmonic oscillations in a thermoelastic rectangular plate
No full textThe present paper is concerned with the linear thermoelastic plate model based on a Mindlin-type assumption on the displacements. The bending of a Mindlin-type thermoelastic rectangular (semi-in ̄nite) plate is studied when the boundary end data are time-harmonic with angular frequency ɷ and the lateral sides are clamped and thermally insulated and su±cient time has elapsed for the system to have reached a steady-state.
A line-integral cross-sectional measure is associated with the amplitude of the resulting harmonic oscillation and then a first-order differential inequality is established in terms of the measure, provided that the angular frequency ɷ is lower than of an explicit critical frequency ɷm. An integration leads to a spatial estimate describing the spatial exponential decay of the amplitude with the distance to the excited end
Convexity considerations and spatial behavior for the harmonic vibrations in thermoelastic plates
No full textIn this paper we study the spatial behavior of the steady-state solutions for the approach of thin thermoelastic plates developed by Lagnese and Lions [J.E. Lagnese, J.-L. Lions, Modelling, Analysis and Control of Thin Plates, Collection RMA, vol. 6, Masson, Paris, 1988]. The model leads to a coupled complex system of partial differential equations, one of fourth order in terms of the amplitude of the vertical deflection and the other of second-order in terms of the amplitude of temperature field. Coupling in an appropriate way the two equations in an integral identity we are able to identify some cross-sectional line integral measures associated with the amplitudes of the vertical deflection and temperature vibrations, provided that the exciting frequency is less than a certain critical frequency. Furthermore, we are able to establish a second-order differential inequality whose integration furnishes a Saint-Venant type decay estimate for a bounded strip and an alternative of Phragmen-Lindelof type for a semi-infinite strip. The critical frequency is individuated by means of the use of some Wirtinger and Knowles inequalities
Plane harmonic waves in the theory of thermoviscoelastic materials with voids
No full textIn this article we analyze the behavior of plane harmonic waves in the entire space filled by a linear thermoviscoelastic material with voids. We take into account the effect of the thermal and viscous dissipation energies upon the corresponding waves and, consequently, we study the damped in time wave solutions. There are five basic waves in an isotropic and homogeneous thermoviscoelastic porous space. Two of them are shear waves, while the remaining three are dilatational waves. The shear waves are uncoupled, damped in time with decay rate depending only on the viscosity coefficients. The three dilatational waves are coupled and consist of a predominantly dilatational damped wave of Kelvin–Voigt viscoelasticity, other is predominantly a wave carrying a change in the void volume fraction and the third takes the form of a standing thermal wave whose amplitude decays exponentially with time. The explicit form of the dispersion equation is obtained in terms of the wave speed and the thermoviscoelastic homogeneous profile. Furthermore, we use numerical methods and computations to solve the secular equation for some special classes of thermoviscoelastic materials considered in literature
How Learning Mathematics Can Be Made More Enjoyable
No full textNew information technologies have to act as a Trojan
horse offering activities that will require deep changes in
the teaching-learning process. Computer aided learning
applications are able to offer advanced students the
opportunity to improve their skill and to maintain their
motivation. In the spirit of “learning by doing”, they are
encouraged to discover principles by themselves. In this
paper, a friendly package implemented in MathematicaTM
was developed with the aim of killing the old idea that
Mathematics and its teaching are tedious! It was designed
in order to closely connect the expositive component, i.e.
material that describes the theoretical background of the
subject, and the active component for exercises
Search for customers in a finite capacity queueing system with phase-type distributions of interarrival and service times
No full textWith the rapid spread of new technologies many efforts have been addressed towards the
modelling of telecommunications systems. Since actual statistics shows that queueing systems characterized
by Poisson flows of customers with exponentially distributed service times are not good models
for multimedia flows, queueing systems with distributions different from traditional ones have to be
investigated. In this paper we deal with a single-server queueing system in which the server requires
a search for customers allocated in a finite buffer. Queueing systems with the server searching for
customers can be used to evaluate performance of telecommunication systems in which the processor
must spend a random time to choose the next item to be processed. We assume PH-distributions for
the probability distribution functions of interarrival times, service times and search times. The solution
of the equilibrium equations of the underlying Markov process is obtained in a matrix-geometric form.
Numerical examples are presented and some system performance indices are computed
Vertex flow models for vehicular traffic on networks
No full textSome models of flow on a network are discussed. Assuming a macroscopic approach on
each arc of the network, we consider a system of conservation laws and various possible
choices to describe the evolution at vertices are discussed. A general framework proposed
in recent literature is presented, then some new solutions for the scalar case are proposed
and analyzed
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