Study On Elastic Wave And Vibration Localization In Structures

When elastic waves propagate in structures with obstacles such as cutouts, cracks or interfaces and so on, wave scattering and dynamic stress concentration can occur near these scatterers. As elastic waves propagate through disordered infinite linear periodic structures, localization phenomenon of elastic waves will appear. If the whole size of a periodic structure is not very large, the mode of vibration can not extend all over the whole structure and localization of vibration will arise. Localization is able to destroy the regularity of mode of vibration in periodic structure and aberration of vibration mode occurs. Meanwhile, energy accumulation emerges in structure. It is obvious that both wave scattering and localization can greatly influence structural intensity and working life. Consequently, it is necessary to study elastic wave scattering and vibration localization in structures. The main research contents in this dissertation are as follows: Elastic wave scattering and dynamic stress concentration in circular cylindrical shells with a hole are studied. Due to the effect of curvature of shell, the equation of motion of elastic waves in shell is much more complex than that in plate. The method of operator factorization can't be directly used to solve the equation of motion of elastic waves in shell by reducing it to the second order partial differential equations. Therefore, the boundary-integral equation techniques are put forward to solve this problem and to obtain the approximately analytical solutions of scattered waves on the edge of cutout in shell. Simultaneously, small parameter perturbation methods are employed to transform the problem of elastic wave scattering in cylindrical shell with a cutout into the iterative addition of a series of boundary value problems and to give a semi-analytical method for solving this problem. Multiple wave scattering and dynamic stress concentration in structures with interfacial layers are analyzed and studied to give the analytical method for solving this problem. The unknown mode coefficients of elastic waves are determined by means of the continuous conditions of displacement and stress on the boundary of the interfaces. The expression for calculating dynamic stress concentration factor is presented. The dynamic stress concentration factors near the interfaces in three kinds of fiber-reinforced composite structures are calculated and the influence of different parameters such as distance between two scatterers, material properties, structural size and so forth on the dynamic stress concentration factors is analyzed. The propagation and localization of elastic waves in periodic bar and beam structures are researched. The periodic bar and beam structures are modeled as one-dimensional periodic wave-guides and the expression of transfer matrix of elastic waves is derived. According to the definition of localization factor, the formulation for determining localization factors of mono-coupled periodic wave- guides is obtained. The localization factors in ordered and disordered periodic wave- guides are respectively computed and the effect of several parameters such as the degree of disorder of span-length, the transmission coefficient and the reflection coefficient on the localization factors is analyzed. The propagation and localization of elastic waves in periodic plate structures are studied. By employing the method of transfer matrix, the transfer matrix of the system is obtained in accordance with the continuous conditions between every two spans. According to the definition of localization factor, the method for calculating Lyapunov exponents in continuous dynamical systems by Wolf is used to derive the expression for determining localization factors in multi-coupled periodic rib-stiffened plates. Meanwhile, the localization factors in tuned and mistuned periodic rib- stiffened plates are respectively computed and the effect of the degree of disorder of span-length and the structural parameters of the rib on the localization of elastic waves is analyzed and discussed. A cyclic periodic structure is composed of some identical substructures that arrange along circumferential direction to form an axial symmetrical system. Because of its limited whole structural size, vibration localization in cyclic structure can be investigated based on the viewpoint of vibration mode. By taking example for bladed disk assembly, the localization of vibration mode in cyclic periodic structures is studied. The blades are modeled as cantilever beams fixed on the disk. The equations of motion of the system are derived. The eigenvectors are obtained by solving the eigenvalues of the system and the localized modes of vibration in mistuned systems are further gotten. The influence of degree of disorder of blades, rotating speed of disk and position radius of shroud on the localization of vibration mode is analyzed.