The method of reverberation-ray matrix （MRRM） is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within ...The method of reverberation-ray matrix （MRRM） is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within the state space framework. The compatibility of physical variables in local dual coordinates gives the phase relation, from which exponentially growing functions are excluded. The interface and boundary conditions lead to the scattering relation, which avoids matrix inversion operation. Numerical examples are given to show the high accuracy of the present MRRM.展开更多
A general formulation of the method of the reverberation-ray matrix (MRRM) based on the state space formalism and plane wave expansion technique is presented for the analysis of guided waves in multilayered piezoelect...A general formulation of the method of the reverberation-ray matrix (MRRM) based on the state space formalism and plane wave expansion technique is presented for the analysis of guided waves in multilayered piezoelectric structures. Each layer of the structure is made of an arbitrarily anisotropic piezoelectric material. Since the state equation of each layer is derived from the three-dimensional theory of linear piezoelectricity, all wave modes are included in the formulation. Within the framework of the MRRM, the phase relation is properly established by excluding exponentially growing functions, while the scattering relation is also appropriately set up by avoiding matrix inversion operation. Consequently, the present MRRM is unconditionally numerically stable and free from computational limitations to the total number of layers, the thickness of individual layers, and the frequency range. Numerical examples are given to illustrate the good performance of the proposed formulation for the analysis of the dispersion characteristic of waves in layered piezoelectric structures.展开更多
A recursive formulation is proposed for the method of reverberation-ray matrix (MRRM) to exactly analyze the free vibration of a multi-span continuous rectangular Kirchhoff plate, which has two oppo- site simply-suppo...A recursive formulation is proposed for the method of reverberation-ray matrix (MRRM) to exactly analyze the free vibration of a multi-span continuous rectangular Kirchhoff plate, which has two oppo- site simply-supported edges. In contrast to the traditional MRRM, numerical stability is achieved by using the present new formulation for high-order frequencies or/and for plates with large span-to-width ratios. The heavy computational cost of storage and memory are also cut down. An improved recursive formulation is further proposed by modifying the iterative formula to reduce the matrix inversion op- erations. Numerical examples are finally given to demonstrate the effectiveness and efficiency of the proposed recursive formulae.展开更多
With the advent of left-handed magnetic materials, it is desirable to develop high-performance wave devices based on their novel properties of wave propagation. This letter reports the special properties of elastic wa...With the advent of left-handed magnetic materials, it is desirable to develop high-performance wave devices based on their novel properties of wave propagation. This letter reports the special properties of elastic wave propagation in magnetoelastic multilayered composites with negative permeability as compared to those in counterpart structures with positive permeability. These novel properties of elastic waves are discerned from the diversified dispersion curves, which represent the propagation and attenuation characteristics of elastic waves. To compute these dispersion curves, the method of reverberation-ray matrix is extended for the analysis of elastic waves in magnetoelastic multilayered composites. Although only the results of a single piezomagnetic and a binary magnetoelastic layers with mechanically free and magnetically short surfaces as well as perfect interface are illustrated in the numerical examples, the analysis is applicable to magnetoelastic multilayered structures with other kinds of boundaries/interfaces.展开更多
基金supported by the National Natural Science Foundation of China(Nos.10725210,10832009 and 10432030)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20060335107)the Program for New Century Excellent Talents in University(No.NCET-05-05010).
文摘The method of reverberation-ray matrix （MRRM） is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within the state space framework. The compatibility of physical variables in local dual coordinates gives the phase relation, from which exponentially growing functions are excluded. The interface and boundary conditions lead to the scattering relation, which avoids matrix inversion operation. Numerical examples are given to show the high accuracy of the present MRRM.
基金Supported by the National Natural Science Foundation of China (Grant Nos 10725210 and 10832009)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No 20060335107)+1 种基金the National Basic Research Pro-gram of China (Grant No 2009CB623204)the Scientific Research Foundation for Tsuiying Talents of Lanzhou University
文摘A general formulation of the method of the reverberation-ray matrix (MRRM) based on the state space formalism and plane wave expansion technique is presented for the analysis of guided waves in multilayered piezoelectric structures. Each layer of the structure is made of an arbitrarily anisotropic piezoelectric material. Since the state equation of each layer is derived from the three-dimensional theory of linear piezoelectricity, all wave modes are included in the formulation. Within the framework of the MRRM, the phase relation is properly established by excluding exponentially growing functions, while the scattering relation is also appropriately set up by avoiding matrix inversion operation. Consequently, the present MRRM is unconditionally numerically stable and free from computational limitations to the total number of layers, the thickness of individual layers, and the frequency range. Numerical examples are given to illustrate the good performance of the proposed formulation for the analysis of the dispersion characteristic of waves in layered piezoelectric structures.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10725210, 10832009, and 10432030)the National Basic Research Program of China (Grant No. 2009CB623204)+1 种基金 the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060335107)the Program for New Century Excellent Talents in University (Grant No. NCET-05-0510)
文摘A recursive formulation is proposed for the method of reverberation-ray matrix (MRRM) to exactly analyze the free vibration of a multi-span continuous rectangular Kirchhoff plate, which has two oppo- site simply-supported edges. In contrast to the traditional MRRM, numerical stability is achieved by using the present new formulation for high-order frequencies or/and for plates with large span-to-width ratios. The heavy computational cost of storage and memory are also cut down. An improved recursive formulation is further proposed by modifying the iterative formula to reduce the matrix inversion op- erations. Numerical examples are finally given to demonstrate the effectiveness and efficiency of the proposed recursive formulae.
基金supported by the National Natural Science Foundation of China(11372119)partly by the Fundamental Research Funds for the Central Universities(2016XZZX001-05)
文摘With the advent of left-handed magnetic materials, it is desirable to develop high-performance wave devices based on their novel properties of wave propagation. This letter reports the special properties of elastic wave propagation in magnetoelastic multilayered composites with negative permeability as compared to those in counterpart structures with positive permeability. These novel properties of elastic waves are discerned from the diversified dispersion curves, which represent the propagation and attenuation characteristics of elastic waves. To compute these dispersion curves, the method of reverberation-ray matrix is extended for the analysis of elastic waves in magnetoelastic multilayered composites. Although only the results of a single piezomagnetic and a binary magnetoelastic layers with mechanically free and magnetically short surfaces as well as perfect interface are illustrated in the numerical examples, the analysis is applicable to magnetoelastic multilayered structures with other kinds of boundaries/interfaces.
