A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different ...A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.展开更多
To explore the approaches of combined toughening and strengthening of the Al_3Ti-based L1_2 intermetallic alloys, multiphase Al_3Ti alloys formed by combining with reinforcement or by second phase precipitation are be...To explore the approaches of combined toughening and strengthening of the Al_3Ti-based L1_2 intermetallic alloys, multiphase Al_3Ti alloys formed by combining with reinforcement or by second phase precipitation are being studied. The interface reactions between Al_(66)Fe_9Ti_(25)matrix and SiC reinforcement were investigated. It is determined that SiC is chemically incompatible with the Al_(66)Fe_9Ti_(25)matrix, Al_2O_3 barrier coating on SiC by sol-gel process was developed to minimize the interfacial reactions. On the other hand, a new type of Al_3Ti-based alloy having a L1_2 matrix with second phase precipitation has been developed. The quaternary alloys based on Al_(66)Fe_9Ti_(25)and modified with Nb additions, consist of a L1_2 matrix and D0_(22) second phase in the annealed state ,but the second phase can be dissolved by solution treatment and precipitated during high temperature aging.展开更多
Cement bond model wells （1：10 scaled-down） were made with a gradually degrading cement annulus for cement bond evaluation of the first interface （between the casing and the cement annulus） and the second interfa...Cement bond model wells （1：10 scaled-down） were made with a gradually degrading cement annulus for cement bond evaluation of the first interface （between the casing and the cement annulus） and the second interface （between the cement annulus and the formation）. Experimental simulation on cement bond logging was carried out with these model wells. The correlation of acoustic waveforms, casing wave energy and flee casing area before and after cement bonding of the second interface was established. The experimental results showed that the arrival of the casing waves had no relationship with the cement bonding of the second interface, but the amplitude of the casing head wave decreased obviously after the second interface was bonded. So, cement bonding of the second interface had little effect on the evaluation of the cement bond quality of the first interface by using casing head wave arrivals. Strong cement annulus waves with early arrivals were observed before the second interface was bonded, while obvious ＂formation waves＂ instead of cement annulus waves were observed after the second interface was bonded.展开更多
We present a parallel Cartesianmethod to solve elliptic problems with complex immersed interfaces.This method is based on a finite-difference scheme and is second-order accurate in the whole domain.The originality of ...We present a parallel Cartesianmethod to solve elliptic problems with complex immersed interfaces.This method is based on a finite-difference scheme and is second-order accurate in the whole domain.The originality of the method lies in the use of additional unknowns located on the interface,allowing to express straightforwardly the interface transmission conditions.We describe the method and the details of its parallelization performed with the PETSc library.Then we present numerical validations in two dimensions,assorted with comparisons to other related methods,and a numerical study of the parallelized method.展开更多
文摘A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.
文摘To explore the approaches of combined toughening and strengthening of the Al_3Ti-based L1_2 intermetallic alloys, multiphase Al_3Ti alloys formed by combining with reinforcement or by second phase precipitation are being studied. The interface reactions between Al_(66)Fe_9Ti_(25)matrix and SiC reinforcement were investigated. It is determined that SiC is chemically incompatible with the Al_(66)Fe_9Ti_(25)matrix, Al_2O_3 barrier coating on SiC by sol-gel process was developed to minimize the interfacial reactions. On the other hand, a new type of Al_3Ti-based alloy having a L1_2 matrix with second phase precipitation has been developed. The quaternary alloys based on Al_(66)Fe_9Ti_(25)and modified with Nb additions, consist of a L1_2 matrix and D0_(22) second phase in the annealed state ,but the second phase can be dissolved by solution treatment and precipitated during high temperature aging.
基金supported by the National Natural Science Foundation of China(Grant No.10534040 and No.40574049)key laboratory of well logging of China National Petroleum Corporation(CNPC).
文摘Cement bond model wells （1：10 scaled-down） were made with a gradually degrading cement annulus for cement bond evaluation of the first interface （between the casing and the cement annulus） and the second interface （between the cement annulus and the formation）. Experimental simulation on cement bond logging was carried out with these model wells. The correlation of acoustic waveforms, casing wave energy and flee casing area before and after cement bonding of the second interface was established. The experimental results showed that the arrival of the casing waves had no relationship with the cement bonding of the second interface, but the amplitude of the casing head wave decreased obviously after the second interface was bonded. So, cement bonding of the second interface had little effect on the evaluation of the cement bond quality of the first interface by using casing head wave arrivals. Strong cement annulus waves with early arrivals were observed before the second interface was bonded, while obvious ＂formation waves＂ instead of cement annulus waves were observed after the second interface was bonded.
文摘We present a parallel Cartesianmethod to solve elliptic problems with complex immersed interfaces.This method is based on a finite-difference scheme and is second-order accurate in the whole domain.The originality of the method lies in the use of additional unknowns located on the interface,allowing to express straightforwardly the interface transmission conditions.We describe the method and the details of its parallelization performed with the PETSc library.Then we present numerical validations in two dimensions,assorted with comparisons to other related methods,and a numerical study of the parallelized method.
