1,721,009 research outputs found
Effects of compressive load and support damping on the propagation of flexural waves in beams resting on elastic foundation
No full textThe contributions of compressive load and support damping are included into the formulation of flexural wave motion in beams lying on elastic (Winkler) foundation. The beam is modeled by both Euler-Bernoulli's and Timoshenko's theories. First, dispersion analysis is performed, which reveals that, for a fixed wavenumber, phase velocity decreases as the intensity of the compressive force or the value of the support damping is increased. Secondly, the transverse displacement of a semi-infinite beam excited by a velocity step pulse at its finite end is examined in the transient regime by adopting Laplace transform approach. This latter study sustains the validity of the dispersion analysis outcomes and shows that compressive load and support damping cause an amplification and a diminution, respectively, of the displacement amplitudes at the various positions of the beam
Correction to Bishop’s approximate method for the propagation of longitudinal waves in bars of generic cross-section
No full textPrestress-induced dispersion-like effects on wave propagation in elastic compressible materials
No full textThe paper deals with wave propagation in an elastic homogeneous bar that includes a prestressed segment in it. The prestress in that segment may be due to some distortion forces acting upon the bar. The end surfaces of the segment act as discontinuity surfaces inside the medium. They partially reflect and partially transmit any pressure wave impinging on them. It is found that the coefficients of reflection and transmission are functions both of the prestress of the segment and of the frequency of the wave. This produces a prestress-induced dispersion-like phenomenon, which in principle should be capable of revealing the state of internal stress of the body
Bloch–Floquet waves in flexural systems with continuous and discrete elements
No full textIn this paper we describe the dynamic behavior of elongated multi-structured media excited by flexural harmonic waves. We examine periodic structures consisting of continuous beams and discrete resonators disposed in various arrangements. The transfer matrix approach and Bloch–Floquet conditions are implemented for the determination of different propagation and non-propagation regimes. The effects of the disposition of the elements in the unit cell and of the contrast in the physical properties of the different phases have been analyzed in detail, using representations in different spaces and selecting a proper set of non-dimensional parameters that fully characterize the structure. Coupling in series and in parallel continuous beam elements and discrete resonators, we have proposed a class of micro-structured mechanical systems capable to control wave propagation within elastic structures
Theoretical models to predict the flexural failure of reinforced concrete beams under blast loads
Full text linkThis paper presents two alternative approaches for the study of reinforced concrete beams under blast loads. In the first approach, the beam is modeled by means of Euler–Bernoulli’s theory and its elastic–plastic behavior is expressed through a new nonlinear relationship between bending moment and curvature. In the second approach, instead, the beam is idealized as a single degree of freedom system. The effects of strain rate, which are of paramount relevance in blast problems, are taken into consideration by introducing time-variable coefficients into the equations of motion derived from the two models. The latter are employed to assess the time-history of the maximum deflection of a simply supported beam subjected to a uniformly distributed blast load. By comparing the theoretical results with some experimental findings available in literature and with the solution obtained from a commercial finite element software, it is found that the first approach is capable of accurately evaluating the maximum deflection of the beam at failure; on the other hand, the second approach provides a less precise prediction, however it is simpler to implement in practice because it requires less computational effort
A Dispersive Homogenization Model Based on Lattice Approximation for the Prediction of Wave Motion in Laminates
No full textThe propagation of waves in a periodic laminate is considered. The stratified medium is modeled as
a homogenized material where the stress depends on the strain and additional higher order strain
gradient terms.
The homogenization scheme is based on a lattice model approximation tuned on the dispersive
properties of the real laminate. The long-wave asymptotic approximation of the model shows that,
despite the simplicity of the parameters identification, the proposed approach agrees well with the
exact solution in a wide range of elastic impedance contrasts, also in comparison with different
approximations. In addition, the effect of increasing order of approximation is investigated.
A final example of a finite structure under an impact excitation proves the consistency of the model
in the transient regime
SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects
Full text linkIn this paper, reinforced concrete beams subjected to blast and impact loads are examined. Two single degree of freedom models are proposed to predict the response of the beam. The first model (denoted as “energy model”) is developed from the law of energy balance and assumes that the deformed shape of the beam is represented by its first vibration mode. In the second model (named “dynamic model”), the dynamic behavior of the beam is simulated by a spring-mass oscillator. In both formulations, the strain rate dependencies of the constitutive properties of the beams are considered by varying the parameters of the models at each time step of the computation according to the values of the strain rates of the materials (i.e. concrete and reinforcing steels). The efficiency of each model is evaluated by comparing the theoretical results with experimental data found in literature. The comparison shows that the energy model gives a good estimation of the maximum deflection of the beam at collapse, defined as the attainment of the ultimate strain in concrete. On the other hand, the dynamic model generally provides a smaller value of the maximum displacement. However, both approaches yield reliable results, even though they are based on some approximations. Being also very simple to implement, they may serve as an useful tool in practical applications
Determination of dynamic gradient elasticity length scales
No full textWave dispersion is a widely recognised phenomenon that occurs when elastic waves propagate through a heterogeneous microstructured material; reflection and refraction of higher frequencies leads to an apparent reduction of the wave speed with frequency. Enhanced continua are frequently employed to capture this phenomenon efficiently. Numerical experiments are performed in this paper to establish a procedure for the determination of the length scale parameters used in dynamic gradient elasticity using spectral analysis. Suitable values of the length scale parameters are determined and verified for a one-dimensional laminated bar and for a two-dimensional chequerboard plate
Three-dimensional auxetic porous medium
Full text linkWe propose the design of a novel three-dimensional porous continuous solid exhibiting negative Poisson’s ratio. The shape and periodic distribution of the pores guarantee cubic symmetry, and the directional dependence of the Poisson’s ratio and Young’s modulus shows a moderate degree of anisotropy and multidirectional auxeticity. We demonstrate the auxeticity of the porous solid numerically, solving both a periodic analysis on a unit cell and a boundary value problem on a finite specimen. The numerical results are fully confirmed by experimental results, obtained from Digital Image Correlation data. The final parametric analysis indicates how to modulate the characteristic parameters of the microstructure in order to tune macroscopic properties. The proposed design maintains a relatively high Young’s modulus and it is prone to large-scale industrial production
Dynamic response and localization in strongly damaged waveguides
No full textIn this paper, we investigate the formation of band-gaps and localization phenomena in an elastic strip nearly disintegrated by an array of transverse cracks. We analyse the eigenfrequencies of finite, strongly damaged, elongated solids with reference to the propagation bands of an infinite strip with a periodic damage. Subsequently, we determine analytically the band-gaps of the infinite strip by using a lower-dimensional model, represented by a periodically damaged beam in which the small ligaments between cracks are modelled as ‘elastic junctions’. The effective rotational and translational stiffnesses of the elastic junctions are obtained from an ad hoc asymptotic analysis. We show that, for a finite frequency range, the dispersion curves for the reduced beam model agree with the dispersion data determined numerically for the two-dimensional elastic strip. Exponential localization, boundary layers and standing waves in strongly damaged systems are discussed in detail
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