Wave front analysis in composite materials
01 Sep 1969-Journal of Applied Mechanics (American Society of Mechanical Engineers)-Vol. 36, Iss: 3, pp 497-504
TL;DR: In this article, the propagation of an initially sharp plane pressure pulse through a linear elastic composite medium is analyzed and the reflection and transmission coefficients can be determined for the stress gradient and the higher order derivatives at an arbitrary interface.
Abstract: : The propagation of an initially sharp plane pressure pulse through a linear elastic composite medium is analysed. Wave front and ray theory analogous to geometrical optics is shown to determine the change in shape of the leading wave front and also the stresses immediately behind it. For certain circumstances the stress amplitudes on this front, or the corresponding tensile stresses on its reflection at the free back surface of a slab, may be critical in design. Examples are presented of an initially sharp plane pressure pulse transmitted through an elastic circular cylinder and an elastic spherical inclusion. The method can be applied to more general composite configurations, and can be extended to determine the stress gradient behind the front. For the latter, general formulae are derived by which the reflection and transmission coefficients can be determined for the stress gradient and the higher order derivatives at an arbitrary interface.
Citations
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TL;DR: A review of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations is presented in this paper, where a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials.
Abstract: A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.
288Â citations
TL;DR: It was found that the leading tensile pulse of the reflected longitudinal wave is responsible for the initiation of microcracks in regions inside the phantom where high tensile stresses are produced.
Abstract: Photoelastic and shadowgraph imaging techniques were used to visualize the propagation and evolution of stress waves, and the resultant transient stress fields in solids during shock wave lithotripsy. In parallel, theoretical analysis of the wavefront evolution inside the solids was performed using a ray-tracing method. Excellent agreement between the theoretical prediction and experimental results was observed. Both the sample size and geometry were found to have a significant influence on the wave evolution and associated stress field produced inside the solid. In particular, characteristic patterns of spalling damage (i.e., transverse and longitudinal crack formation) were observed using plaster-of-Paris cylindrical phantoms of rectangular and circular cross sections. It was found that the leading tensile pulse of the reflected longitudinal wave is responsible for the initiation of microcracks in regions inside the phantom where high tensile stresses are produced. In addition, the transmitted shear wave was found to play a critical role in facilitating the extension and propagation of the microcrack.
75Â citations
42Â citations
TL;DR: Experimental results compared favorably to a ray theory analysis of a spherically diverging shock wave striking either concretion or concretion, more closely approximating the wave fields of a clinical extracorporeal lithotripter.
Abstract: Semiconductor strain gauges were used to measure the internal strain along the axes of spherical and disk plaster specimens when subjected to lithotripter shock pulses. The pulses were produced by one of two lithotripters. The first source generates spherically diverging shock waves of peak pressure approximately 1 MPa at the surface of the specimen. For this source, the incident and first reflected pressure (P) waves in both sphere and disk specimens were identified. In addition, waves reflected by the disk circumference were found to contribute significantly to the strain fields along the disk axis. Experimental results compared favorably to a ray theory analysis of a spherically diverging shock wave striking either concretion. For the sphere, pressure contours for the incident P wave and caustic lines were determined theoretically for an incident spherical shock wave. These caustic lines indicate the location of the highest stresses within the sphere and therefore the areas where damage may occur. Results were also presented for a second source that uses an ellipsoidal reflector to generate a 30-MPa focused shock wave, more closely approximating the wave fields of a clinical extracorporeal lithotripter.
39Â citations
TL;DR: In this article, the authors examined fracture and void development in Perspex spheres with bosses (i.e., with cylindrical projections) due to point explosive loading by a detonator using high speed photography.
11Â citations
References
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TL;DR: In this paper, Elastic Waves in Layered Media (ELMW) are used to describe the properties of layered media in a geologiska foreningen i Stockholm Forhandlingar.
Abstract: (1958). Elastic Waves in Layered Media. Geologiska Foreningen i Stockholm Forhandlingar: Vol. 80, No. 1, pp. 128-129.
1,687Â citations
01 Jul 1947
TL;DR: In this article, it was shown that the cyclides of Dupin surfaces of the fourth order can be used to determine all the solutions of the wave equation which are of the simple form where F denotes an arbitrary function.
Abstract: The object of this paper is to determine all the solutions of the wave equationwhich are of the simple formwhere F denotes an arbitrary function. It will be shown that, in addition to the obvious cases of plane or spherical progressive waves, such solutions exist only when the wave frontsare certain algebraic surfaces of the fourth order, the cyclides of Dupin. These include, as degenerate cases, the sphere, the plane, the cylinder, the cone, and the torus.
69Â citations