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1.
The problem of wave propagation in shells within the framework of a simplified linear shell theory is treated using the method of Hadamard. Speeds of propagation, wave shape and decay, as well as coupling effects, are obtained for longitudinal, transverse and bending waves. The theory is applied to wave propagation on a spherical shell.
This work was supported in part by funds from the National Research Council of Canada, under Grant Number A 3805. 相似文献
Résumé On traite la problème de la propagation des ondes dans les voiles minces en utilisant la méthode de Hadamard. Les vitesses de la propagation, la forme de l'onde, et aussi les effets d'accouplement sont obtenus pour les onides longitudinales, transversales et fléchissantes. On applique cette théorie à la propagation des ondes dans une coque sphérique.
This work was supported in part by funds from the National Research Council of Canada, under Grant Number A 3805. 相似文献
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The problem of wave propagation in linear elastic membranes is treated using the method of Hadamard. Speeds of propagation, wave shape and decay, as well as coupling effects, are obtained for longitudinal and transverse waves. Examples are considered which illustrate the features of the theory.
This work was supported in part by funds from the National Research Council of Canada, under grant number A3805. 相似文献
Résumé On traite la problème de la propagation des ondes dans une membrane lineare et elastique, utilisant la mèthode de Hadamard. Les vitesses de la propagation, la forme del'onde, et les effets d'accouplement sont obtenus en cas des ondes longitudinales et transversales. Les exemples sont presentés qui demontrent les points essentiales de la theorie.
This work was supported in part by funds from the National Research Council of Canada, under grant number A3805. 相似文献
4.
H. Cohen 《Journal of Elasticity》1976,6(3):245-259
The problem of wave propagation within the framework of a complete linear theory of elastic plates is treated using the method of wave curves. A complete classification of the various extensional and bending waves is obtained, along with the corresponding speeds of propagation. These are shown to correspond to the phase velocities of harmonic waves for infinite wave number. The decay and coupling equations are found, and the problem of waves due to a punch applied to the plate surface is treated.
This work was supported in part by funds from the National Research Council of Canada, under Grant Number A3805. 相似文献
Résumé On a étudié le problème de la propagation des ondes en utilisant la méthode des courbes ondiales et assumant la théorie linéaire et complète des plaques minces. On obtient une classification totale des ondes diverses, de l'extension et de la flexion, avec des vitesses de la propagation. On prouve aussi, que celles-ci correspondent avec des vitesses des phases de la propagation, en cas de nombre infinite des ondes. Les équations de la décadence et de l'accouplement sont derivées, et on a étudié le problème d'une onde, qui est produite par une emporte-pièce appliquée sur la surface d'une plaque.
This work was supported in part by funds from the National Research Council of Canada, under Grant Number A3805. 相似文献
5.
《International Journal of Solids and Structures》2007,44(11-12):3638-3645
Two-dimensional plane wave propagation in an orthotropic micropolar elastic solid is studied. There exist three types of coupled waves in xy-plane, whose velocities depend upon the angle of propagation and material parameters. A problem on reflection of these plane waves from a stress-free boundary is considered. The reflection coefficients of various reflected waves are computed numerically for a particular model of the solid. The effects of anisotropy upon the velocities and reflection coefficients are depicted graphically for different angles of propagation. 相似文献
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Robert S. D. Thomas 《Meccanica》1991,26(2-3):111-115
In this paper, we obtain the modes and velocities of acceleration waves on a thin hyperelastic shell in terms of the second fundamental form, which represents the geometrical properties of the shell, and of seven elastic moduli derived from the velocities in a plate of the same material. Some examples are studied, and approximations obtained in the case of a shallow shell.
Sommario In questo lavoro si ottengono i modi e le velocità delle onde di accelerazione in una volta sottile iperelastica, con riferimento alla seconda forma fondamentale che rappresenta le proprietà geometriche della volta e a sette moduli elastici derivati dalle velocità in una piastra dello stesso materiale. Si studiano alcuni esempi e si presentano soluzioni approssimate nel caso di una volta ribassata.相似文献
8.
Amares Chattopadhyay Volker Michel 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,75(2-3):113-124
We study a spherical wave propagating in the radial and latitude directions and oscillating in the longitude direction in
the case of fibre-reinforced linearly elastic material. A function system solving Euler's equation of motion in this case
and depending on certain Bessel and associated Legendre functions is derived. 相似文献
9.
The propagation of longitudinal and flexural waves in axisymmetric circular cylindrical shells with periodic circular axial curvature is studied using a finite element method previously developed by the authors. Of primary interest is the coupling of these wave modes due to the periodic axial curvature which results in the generation of two types of stop bands not present in straight circular cylinders. The first type is related to the periodic spacing and occurs independently for longitudinal and flexural wave modes without coupling. However, the second type is caused by longitudinal and flexural wave mode coupling due to the axial curvature. A parametric study is conducted where the effects of cylinder radius, degree of axial curvature, and periodic spacing on wave propagation characteristics are investigated. It is shown that even a small degree of periodic axial curvature results in significant stop bands associated with wave mode coupling. These stop bands are broad and conceivably could be tuned to a specific frequency range by judicious choice of the shell parameters. Forced harmonic analyses performed on finite periodic structures show that strong attenuation of longitudinal and flexural motion occurs in the frequency ranges associated with the stop bands of the infinite periodic structure. 相似文献
10.
S.D. Akbarov E.R. Agasiyev A.D. Zamanov 《European Journal of Mechanics - A/Solids》2011,30(3):409-422
The extensional and flexural Lamb waves in a sandwich plate with finite initial strains made from compressible highly elastic materials is investigated. It is assumed that the initial strains are caused by the uniformly distributed normal compression forces acting on the face planes of the plate. The cases where the compression forces are “dead” (Case 1) and “follower” (Case 2) are considered. The investigations are carried out within the scope of the piecewise homogeneous body model with the use of the 3D linearized theory of elastic waves in initially stressed bodies. Numerical results for the dispersion of the extensional and flexural Lamb waves on the influence of the initial strains and on the influence of the character of the external compression forces are presented and discussed. 相似文献
11.
This paper reports the results of an investigation into the characteristics of wave propagation in carbon nanotubes embedded
in an elastic matrix, based on an exact shell model. Each of the concentric tubes of multi-walled carbon nanotubes is considered
as an individual elastic shell and coupled together through the van der Waals forces between two adjacent tubes. The matrix
surrounding carbon nanotubes is described as a spring element defined by the Winkler model. The effects of rotatory inertia
and elastic matrix on the wave velocity, the critical frequency, and the amplitude ratio between two adjacent tubes are described
and discussed through numerical examples. The results obtained show that wave propagation in carbon nanotubes may appear in
a critical frequency at which the wave velocity changes suddenly; the elastic matrix surrounding carbon nanotubes debases
the critical frequency and the wave velocity, and changes the vibration modes between two adjacent tubes; the rotatory inertia
based on an exact shell model obviously influences the wave velocity at some wave modes. Finally, a comparison of dispersion
solutions from different shell models is given. The present work may serve as a useful reference for the application and the
design of nano-electronic and nano-drive devices, nano-oscillators, and nano-sensors, in which carbon nanotubes act as basic
elements. 相似文献
12.
Fan He 《International Journal of Computational Fluid Dynamics》2013,27(3):164-172
In this paper, a fluid–wall interaction model, called the elastic tube model, is introduced to investigate wave propagation in an elastic tube and the effects of different parameters. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic, isotropic and incompressible. A fluid–wall interaction scheme is constructed using a finite element method. The results demonstrate that the elastic tube plays an important role in wave propagation. It is shown that there is a time delay between the velocity waveforms at two different locations and that the peak velocity increases while the low velocity decreases in the elastic tube model, contrary to the rigid tube model where velocity waveforms overlap each other. Compared with the elastic tube model, the increase of the wall thickness makes wave propagation faster and the time delay cannot be observed clearly, however, the velocity amplitude is reduced slightly due to the decrease of the internal radius. The fluid–wall interaction model simulates wave propagation successfully and can be extended to study other mechanical properties considering complicated geometrical and material factors. 相似文献
13.
Philippe G. Ciarlet Véronique Lods Bernadette Miara 《Archive for Rational Mechanics and Analysis》1996,136(2):163-190
We consider as in Part I a family of linearly elastic shells of thickness 2?, all having the same middle surfaceS=?(?)?R 3, whereω?R 2 is a bounded and connected open set with a Lipschitz-continuous boundary, and?∈l 3 (?;R 3). The shells are clamped on a portion of their lateral face, whose middle line is?(γ 0), whereγ 0 is any portion of?ω withlength γ 0>0. We make an essential geometrical assumption on the middle surfaceS and on the setγ 0, which states that the space of inextensional displacements $$\begin{gathered} V_F (\omega ) = \{ \eta = (\eta _i ) \in H^1 (\omega ) \times H^1 (\omega ) \times H^2 (\omega ); \hfill \\ \eta _i = \partial _v \eta _3 = 0 on \gamma _0 ,\gamma _{\alpha \beta } (\eta ) = 0 in \omega \} , \hfill \\ \end{gathered}$$ where $\gamma _{\alpha \beta }$ (η) are the components of the linearized change is metric tensor ofS, contains non-zero functions. This assumption is satisfied in particular ifS is a portion of cylinder and?(γ 0) is contained in a generatrix ofS. We show that, if the applied body force density isO(? 2) with respect to?, the fieldu(?)=(u i (?)), whereu i (?) denote the three covariant components of the displacement of the points of the shell given by the equations of three-dimensional elasticity, once “scaled” so as to be defined over the fixed domain Ω=ω×]?1, 1[, converges as?→0 inH 1(Ω) to a limitu, which is independent of the transverse variable. Furthermore, the averageζ=1/2ts ?1 1 u dx 3, which belongs to the spaceV F (ω), satisfies the (scaled) two-dimensional equations of a “flexural shell”, viz., $$\frac{1}{3}\mathop \smallint \limits_\omega a^{\alpha \beta \sigma \tau } \rho _{\sigma \tau } (\zeta )\rho _{\alpha \beta } (\eta )\sqrt {a } dy = \mathop \smallint \limits_\omega \left\{ {\mathop \smallint \limits_{ - 1}^1 f^i dx_3 } \right\} \eta _i \sqrt {a } dy$$ for allη=(η i ) ∈V F (ω), where $a^{\alpha \beta \sigma \tau }$ are the components of the two-dimensional elasticity tensor of the surfaceS, $$\begin{gathered} \rho _{\alpha \beta } (\eta ) = \partial _{\alpha \beta } \eta _3 - \Gamma _{\alpha \beta }^\sigma \partial _\sigma \eta _3 + b_\beta ^\sigma \left( {\partial _\alpha \eta _\sigma - \Gamma _{\alpha \sigma }^\tau \eta _\tau } \right) \hfill \\ + b_\alpha ^\sigma \left( {\partial _\beta \eta _\sigma - \Gamma _{\beta \sigma }^\tau \eta _\tau } \right) + b_\alpha ^\sigma {\text{|}}_\beta \eta _\sigma - c_{\alpha \beta } \eta _3 \hfill \\ \end{gathered} $$ are the components of the linearized change of curvature tensor ofS, $\Gamma _{\alpha \beta }^\sigma$ are the Christoffel symbols ofS, $b_\alpha ^\beta$ are the mixed components of the curvature tensor ofS, andf i are the scaled components of the applied body force. Under the above assumptions, the two-dimensional equations of a “flexural shell” are therefore justified. 相似文献
14.
We consider a family of linearly elastic shells with thickness 2?, clamped along their entire lateral face, all having the same middle surfaceS=φ(?ω) ?R 3, whereω ?R 2 is a bounded and connected open set with a Lipschitz-continuous boundaryγ, andφ ∈l 3 ( $\overline \omega$ ;R 3). We make an essential geometrical assumption on the middle surfaceS, which is satisfied ifγ andφ are smooth enough andS is “uniformly elliptic”, in the sense that the two principal radii of curvature are either both>0 at all points ofS, or both<0 at all points ofS. We show that, if the applied body force density isO(1) with respect to?, the fieldtu(?)=(u i(?)), whereu i (?) denote the three covariant components of the displacement of the points of the shell given by the equations of three-dimensional elasticity, one “scaled” so as to be defined over the fixed domain Ω=ω×]?1, 1[, converges inH 1(Ω)×H 1(Ω)×L 2(Ω) as?→0 to a limitu, which is independent of the transverse variable. Furthermore, the averageξ=1/2ε ?1 1 u dx 3, which belongs to the space $$V_M (\omega ) = H_0^1 (\omega ) \times H_0^1 (\omega ) \times L^2 (\omega ),$$ satisfies the (scaled) two-dimensional equations of a “membrane shell” viz., $$\mathop \smallint \limits_\omega a^{\alpha \beta \sigma \tau } \gamma _{\sigma \tau } (\zeta )\gamma _{\alpha \beta } (\eta ) \sqrt \alpha dy = \mathop \smallint \limits_\omega \left\{ {\mathop \smallint \limits_{ - 1}^1 f^i dx_3 } \right\}\eta _i \sqrt a dy$$ for allη=(η i) εV M(ω), where $a^{\alpha \beta \sigma \tau }$ are the components of the two-dimensional elasticity tensor of the surfaceS, $$\gamma _{\alpha \beta } (\eta ) = \frac{1}{2}\left( {\partial _{\alpha \eta \beta } + \partial _{\beta \eta \alpha } } \right) - \Gamma _{\alpha \beta }^\sigma \eta _\sigma - b_{\alpha \beta \eta 3} $$ are the components of the linearized change of metric tensor ofS, $\Gamma _{\alpha \beta }^\sigma$ are the Christoffel symbols ofS, $b_{\alpha \beta }$ are the components of the curvature tensor ofS, andf i are the scaled components of the applied body force. Under the above assumptions, the two-dimensional equations of a “membrane shell” are therefore justified. 相似文献
15.
Franz Ziegler 《International Journal of Solids and Structures》1977,13(4):293-305
A powerful complex transfer matrix approach to wave propagation perpendicular to the layering of a composite of periodic and disordered structure is worked out showing propagating and stopping bands of time-harmonic waves and the singular cases of standing waves. A state ratio of left- and right-going plane waves is defined and interpreted geometrically in the complex plane in terms of fixed points and flow lines. For numerical considerations and extension of the approach to higher dimensional problems a continued fraction expansion of the state ratio mapping is presented. Impurity modes of wave propagation in composites with widely spaced impurity cells of different elastic materials are discussed. Stopping bands in the frequency spectrum of global waves in fully disordered composites are found to exist in the range of frequencies corresponding to common gaps in the spectrum of cnstituent regular periodic composites which are constructed from the cells of the disordered system. For those frequencies, waves propagate only a (short) finite distance and are therefore strongly localized modes in a composite of fairly large extent. 相似文献
16.
Baljeet Singh 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(4):253-258
The boundary conditions at free surface of an incompressible, transversely isotropic elastic half-space are satisfied to obtain
the reflection coefficients for the case when outer slowness section is re-entrant. Two quasi-shear waves will be reflected
for an angular range of direction of incident wave. The numerical illustrations of reflection coefficients are presented graphically
for three arbitrary materials. 相似文献
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We consider as in Parts I and II a family of linearly elastic shells of thickness 2?, all having the same middle surfaceS=?(?)?R 3, whereω?R 2 is a bounded and connected open set with a Lipschitz-continuous boundary, and? ∈ ?3 (?;R 3). The shells are clamped on a portion of their lateral face, whose middle line is?(γ 0), whereγ 0 is a portion of?ω withlength γ 0>0. For all?>0, let $\zeta _i^\varepsilon$ denote the covariant components of the displacement $u_i^\varepsilon g^{i,\varepsilon }$ of the points of the shell, obtained by solving the three-dimensional problem; let $\zeta _i^\varepsilon$ denote the covariant components of the displacement $\zeta _i^\varepsilon$ a i of the points of the middle surfaceS, obtained by solving the two-dimensional model ofW.T. Koiter, which consists in finding $$\zeta ^\varepsilon = \left( {\zeta _i^\varepsilon } \right) \in V_K (\omega ) = \left\{ {\eta = (\eta _\iota ) \in {\rm H}^1 (\omega ) \times H^1 (\omega ) \times H^2 (\omega ); \eta _i = \partial _v \eta _3 = 0 on \gamma _0 } \right\}$$ such that $$\begin{gathered} \varepsilon \mathop \smallint \limits_\omega a^{\alpha \beta \sigma \tau } \gamma _{\sigma \tau } (\zeta ^\varepsilon )\gamma _{\alpha \beta } (\eta )\sqrt a dy + \frac{{\varepsilon ^3 }}{3} \mathop \smallint \limits_\omega a^{\alpha \beta \sigma \tau } \rho _{\sigma \tau } (\zeta ^\varepsilon )\rho _{\alpha \beta } (\eta )\sqrt a dy \hfill \\ = \mathop \smallint \limits_\omega p^{i,\varepsilon } \eta _i \sqrt a dy for all \eta = (\eta _i ) \in V_K (\omega ), \hfill \\ \end{gathered}$$ where $a^{\alpha \beta \sigma \tau }$ are the components of the two-dimensional elasticity tensor ofS, $\gamma _{\alpha \beta }$ (η) and $\rho _{\alpha \beta }$ (η) are the components of the linearized change of metric and change of curvature tensors ofS, and $p^{i,\varepsilon }$ are the components of the resultant of the applied forces. Under the same assumptions as in Part I, we show that the fields $\frac{1}{{2_\varepsilon }}\smallint _{ - \varepsilon }^\varepsilon u_i^\varepsilon g^{i,\varepsilon } dx_3^\varepsilon$ and $\zeta _i^\varepsilon$ a i , both defined on the surfaceS, have the same principal part as? → 0, inH 1 (ω) for the tangential components, and inL 2(ω) for the normal component; under the same assumptions as in Part II, we show that the same fields again have the same principal part as? → 0, inH 1 (ω) for all their components. For “membrane” and “flexural” shells, the two-dimensional model ofW.T. Koiter is therefore justified. 相似文献
19.
A. C. Pipkin 《Journal of Elasticity》1976,6(2):179-193
The general theory of linear constraints in linear elasticity theory is outlined. For problems that are ill-posed in constraint theory although well-posed in the absence of any constraint, a modified form of constraint theory is proposed.
Resume Les grandes lignes de la théorie générale des contraints en élasticité linéaire sont exposées. Une forme modifiée de la théorie des contraints est proposée pour les problèmes mal posés en présence de contraints quoique bien posés en l'absence de contraints.相似文献
20.
A generalization of the simpler microstructure theory developed earlier for elastic laminates by Sun, Achenbach and Herrmann is used to analyze steady state plane wave propagation. This new version incorporates higher-order thickness variations in the displacement functions and includes restrictions on both displacement and stress at the laminate interfaces.To assess the potential of a second-order microstructure theory for accurate modeling of mechanical processes in laminates, dispersion results and especially mode shape data for both displacements and stresses are obtained and compared to corresponding solutions obtained by the theory of elasticity. The comparisons indicate that while dispersion results may be nearly identical, extremely significant differences may be observed in the mode shapes. 相似文献