2006
DOI: 10.1016/j.ijsolstr.2006.01.011
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Hamiltonian systems of propagation of elastic waves and localized vibrations in the strip plate

Abstract: In this paper, based on Lagrange-Germanian theory of elastic thin plates, applying the method in Hamiltonian state space, the elastic waves and vibrations when the boundary of the two lateral sides of the strip plate are free of traction are investigated, and the process of analysis and solution are proposed. The existence of all kinds of vibration modes and wave propagation modes is also analyzed. By using eigenfunction expansion method, the dispersion relations of waveguide modes in the strip plate are deriv… Show more

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Cited by 5 publications
(5 citation statements)
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“…where P is the number of zeros of the function h k (•) defined in (18) on (0; 1). For k = k n , n ∈ N * , we have card (Λ ∩ Ri) = 2P − 1 where P is the number of zeros of the function h k (•) on (0; 1).…”
Section: Modal Exponents In the Clamped Casementioning
confidence: 99%
See 1 more Smart Citation
“…where P is the number of zeros of the function h k (•) defined in (18) on (0; 1). For k = k n , n ∈ N * , we have card (Λ ∩ Ri) = 2P − 1 where P is the number of zeros of the function h k (•) on (0; 1).…”
Section: Modal Exponents In the Clamped Casementioning
confidence: 99%
“…In the present paper, for the strip governed by the Kirchhoff-Love model, we introduce radiation conditions and prove that the corresponding scattering problem is of Fredholm type, both in the case of a clamped strip and in the case of a simply supported strip. Let us mention that some analysis of modal solutions in a strip for various boundary conditions have already been conducted (see for example [36,18]). But a rigorous existence and uniqueness analysis of the scattering problem, whatever the boundary conditions, seems not to exist.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, the algebra of real quaternion is used in solving three-dimensional elasticity [2]. The plate theory in elasticity is still a problem worthy of attention in engineering, especially, the non-classical modeling dynamics of the low-dimensional structure [3][4][5][6][7]. The mini-symposium on the topic of the refined theory of plates and shells is held in the 8th European solid mechanics conference [8].…”
Section: Introductionmentioning
confidence: 99%
“…The refined static equation of plate bending was proposed, which yields from the 3-dimensional elasticity by using the operator method [3]. Based on the general solution of elasticity, the refined static equation is extended to transversely isotropic plates [7].…”
Section: Introductionmentioning
confidence: 99%
“…Zhong & Zhang [42] attempted the semi-analytic solutions for rectangular thin plates on foundations, which satisfy the boundary conditions only at two opposite edges. Hu et al [43] investigated the elastic waves and vibrations when the two lateral sides of a strip plate are free of traction. Lim et al [44] presented analytic solutions of rectangular thin plates with two opposite sides simply supported.…”
Section: Introductionmentioning
confidence: 99%