1,721,045 research outputs found
Explicit Construction of Rods and Beams with Given Natural Frequencies
No full textIn this paper we present a new method for constructing one-dimensional vibrating systems having prescribed values of the first N natural frequencies, under a given set of boundary conditions. In the case of axially vibrating rods, the analysis is based on the determination of the so-called quasi-isospectral rods, that is rods which have the same spectrum as a given rod, with the exception of a single eigenvalue which is free to move in a prescribed interval. The reconstruction procedure needs the specification of an initial rod whose eigenvalues must be close to the assigned eigenvalues. The rods and their normal modes can be constructed explicitly by means of closed-form expressions. The results can be extended to strings and to some special classes of beams in bending vibration. © The Society for Experimental Mechanics 2014
Can the spider hear the position of the prey?
No full textDaily experience shows that a spider that stays in the center of an orb-web is able to orient itself immediately toward the prey, and capture it, by testing the web at the contact points of its eight legs. Although this is one of the key aspects in the study of spider behavior, the prey catching problem still remains a mystery to a large extent, and progress has been limited by the lack of two-dimensional models of wave propagation in the orb-web. Here, we formulate the catching problem as the inverse problem of identifying the region of prey's impact in a continuous membrane model of orb-web from dynamic measurements that mimic those made in Nature by a spider. We provide a mathematically-founded answer to this inverse problem by creating a reconstruction algorithm for the determination of the impact prey's region. We find that the amount of information typically assumed to be available by the spider is enough for an accurate identification of the position of the prey, for different prey and orb-web characteristics
Structural dynamic identification and damage detection
No full textDynamic methods are a powerful tool for studying the behaviour of existing structures and their health conditions. The practical application, however, often raises subtle questions related to the accuracy and completeness of experimental data, the complexity of the mechanical modelling and, ultimately, the inverse nature of the problems that leads to ill-conditioning and non-uniqueness. This chapter addresses some of these aspects, and presents a short overview of the topic, with particular emphasis on dynamic structural identification and damage detection
Classical and advanced theories of thin structures: mechanical and mathematical aspects. CISM courses and lectures n.503
No full textEstimating the area of extreme inclusions in Reissner–Mindlin plates
Full text linkWe derive upper and lower estimates of the area of unknown defects in the form of either cavities or rigid inclusions in Mindlin–Reissner elastic plates in terms of the difference δW of the works exerted by boundary loads on the defected and on the reference plate. It turns out that the upper estimates depend linearly on δW, whereas the lower ones depend quadratically on δW. These results continue a line of research concerning size estimates of extreme inclusions in electric conductors, elastic bodies and plates
Identificazione Dinamica di un Danno nella Connessione di Travi Miste di Acciaio e Calcestruzzo.
No full textDetecting a prey in a spider orb-web
No full textWe consider the inverse problem of localizing a prey hitting a
spider orb-web from dynamic measurements taken near the center
of the web, where the spider is supposed to stay. The actual
discrete orb-web, formed by a finite number of radial and
circumferential threads, is modelled as a continuous membrane. The
membrane has a specific fibrous structure, which is inherited from
the original discrete web, and it is subject to tensile pre-stress
in the referential configuration. The transverse load describing
the prey's impact is assumed of the form g(t)f(x), where g(t)
is a known function of time and f(x) is the unknown term
depending on the position variable x. For axially-symmetric
orb-webs supported at the boundary and undergoing infinitesimal
transverse deformations, we prove a uniqueness result for f(x)
in terms of measurements of the transverse dynamic displacement taken
on an arbitrarily small and thin ring centered at the origin of
the web, for a sufficiently large interval of time. The
theoretical result is illustrated by means of a numerical
implementation of the identification method
Identification of out-of-plane loads over multi-span Timoshenko beams
No full textWe consider a multi-span continuous beam made up elastic elements modeled by the Timoshenko equation occupying Ω=[0,L]⊂R. The supports of the structure are located at the nodes Pn, n=1,...NP. We prove that the loading of the form g(t)Ξ(x) that acts orthogonally to Ω, over the structural system, with known temporal function g:R+→R, g∈C1, g(0)≠0, and Ξ∈H−1(Ω∖∪n=1Njavax.xml.bind.JAXBElement@4f2cfa40Pn), can be identified if the displacement history is known over any segment of the system over an interval of time that is long enough
Closed-form solutions to the static transverse deformation of a spider orb-web
No full textThis paper deals with the study of the Dirichlet and Poisson
problem for the infinitesimal transverse deformation of a spider
orb-web in statical regime. The mechanical model is a pre-stressed
membrane and attention is focused on axially-symmetric webs
formed by radial threads connected with circumferential threads
belonging to concentric circles. The governing equation is an
elliptic scalar equation with variable coefficients having a
singularity at the center of the web. Under suitable assumption on
the tensile pre-stress acting in the referential configuration,
closed-form series representation of the solution to the Dirichlet
and Poisson problem are derived. To the authors's knowledge, these
are the first closed-form solutions to the statical deformation of
a continuous membrane model of spider orb-web. Possible
applications of the obtained results will concern both the
analysis of the most relevant mechanical parameters that rule the
response of the web and the estimate of the initial pre-stress via
approaches of inverse analysis
Inverse Problems for Nanostructures
No full textIn these lectures we review some recent results concerning inverse problems for thin elastic nanostructures. Nanostructures are assumed to be either one-dimensional (nanobeams) or two-dimensional (nanoplates), and are described within a simplified version of the strain gradient linear elasticity theory for isotropic materials. A first group of results concerns the use of nanobeams as mass-resonant sensors to identify an unknown added mass density by the measurement of a finite number of lower resonant frequencies. In the second group of results, we determine constructive upper and lower estimates of the area of an unknown elastic inclusion possibly present in a nanoplate given in terms of the work exerted by force and couple fields applied at the boundary of the nanoplate
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