Transfer Influence Coefficient Method Research Articles

탄성지지된 티모센코 호의 면외 자유진동 해석

Arcs have widely been used as structural elements in many mechanical, aerospace, and civil engineering applications. The authors previously analyzed the in-plane free vibration of Timoshenko arcs with elastic supports by using the transfer influence coefficient method. The basic concept of this method is based on the transfer of influence coefficient. In this study, the transfer influence coefficient method is applied to the out-of-plane vibration of Timoshenko arcs. The authors formulate a computational algorithm to analyze the out-of-plane free vibration of the arcs with elastic supports by using the transfer influence coefficient method. The reliability of the transfer influence coefficient method is confirmed by comparing both the numerical results of the transfer influence coefficient method and those of other researchers. The authors verify that the transfer influence coefficient method is more effective than the transfer matrix method in analyzing an arc with a hinged point at its intermediate.

Free Vibration Analysis of a Structure with Closed Loops by the Transfer Influence Coefficient Method

The Transfer Influence Coefficient Method (TICM), which was developed by the authors, is effective in analyzing dynamic responses of structures. The TICM has the advantages of computational speed and accuracy compared with conventional methods. However, the TICM has not been available for the structures with closed loops, such as truss and rahmen structures. In this paper, a new algorithm of the TICM applicable to such truss and rahmen structures is presented. The algorithm presented here is provided for in-plane free vibration analyses of two-dimensional frame structures to aid in clarifying the fundamental procedure. The validity of the newly presented algorithm is demonstrated through some numerical computations. The present algorithm has a remarkable advantage in terms of computational speed compared with a conventional algorithm.

Vibrations of probe used for the defect detection of helical heating tubes in a fast breeder reactor: Part 2. Vibration analysis and numerical simulations

A detection of a defect of a helical heating tube installed in the fast breeder reactor “Monju” in Japan is done by a feeding of an eddy current testing (ECT) probe with magnetic sensor into the tube. An undesirable vibration of the ECT probe always happens under a certain condition and makes the inspection difficult. Several characteristics of the vibration have been made clear by some experiments using a mock-up, but the essential factor of the vibration is still unclear. In this paper, a numerical simulation of the vibration is implemented on the assumption that the vibration is caused by Coulomb friction. An analytical model, which is obtained as a lumped mass model, is a large-scale non-linear vibration system and many computational costs are ordinarily required to carry out the simulations. The Transfer Influence Coefficient Method is applied so that the simulation is efficiently carried out. The results of simulation qualitatively agree well with the experimental results. It confirms the validity of the assumption that the vibration is caused by Coulomb friction.

Sensor Noise Caused by Vibrations of Flaw Detection Probe Generated in Helical Heating Tubes in a Fast Breeder Reactor and Its Countermeasures (2nd Report, Numerical Simulations of Probe Vibration)

A diagnosis of a helical heating tube installed in a fast breeder reactor is operated by an insertion of an eddy current testing (ECT) probe with magnetic sensor into the tube. An undesirable vibration of the ECT probe always happens under a certain condition and makes the diagnosis difficult. The cause of the vibration has not been clear. Numerical simulation of the vibration is implemented on the assumption that the vibration is caused by the Coulomb's friction. An analytical model is derived as a large scale nonlinear vibration system and a lot of computational costs are ordinarily required to carry out the simulations. The Transfer Influence Coefficient Method is applied so that the simulation is efficiently carried out. The results of simulation qualitatively agree well with the experimental results. It confirms the validity of the assumption that the vibration is caused by the Coulomb's friction.

Free Vibration Analysis of a Structure with Closed Loops by the Transfer Influence Coefficient Method

The Transfer Influence Coefficient Method (TICM), which was developed by the authors, is effective in analyzing dynamic responses of structures. The TICM has the advantages of computational speed and accuracy compared with conventional methods. However, the TICM has not been available for the structures with closed loops, such as truss and rahmen structures. In this paper, a new algorithm of the TICM applicable to such truss and rahmen structures is presented. The algorithm presented here is provided for in-plane free vibration analyses of two-dimensional frame structures to aid in clarifying the fundamental procedure. The validity of the newly presented algorithm is demonstrated through some numerical computations. The present algorithm has a remarkable advantage in terms of computational speed compared with a conventional algorithm.

Vibration Analysis of a Structure with Closed Loops by the Transfer Stiffness Coefficient Method

The transfer stiffness coefficient method, which was developed in the previous report by introducing the concept of the substructure synthesis method into the computation process of the transfer influence coefficient method, is applied to a structure with closed loops in the system. Such a structure can not be analyzed easily by the transfer influence coefficient method. However, the transfer stiffness coefficient method becomes applicable to such a structure, since the cross-dynamic stiffness coefficient matrix is introduced to represent the relationship between the state variables of substructure. As a typical example of the structure with closed loops, an algorithm based on the transfer stiffness coefficient method is formulated for the free and forced vibration analyses of a framework structure constructed from some uniform beams. In the analysis, both the truss and rahmen structures are treated. The validity of the present algorithm concerning the computation efficiency and the computational accuracy is confirmed by comparing the numerical computational results obtained by the transfer stiffness coefficient method with those obtained by applying the finite element method and the transfer matrix method.

341 軸力を考慮した伝達影響係数法による自由振動解析

341 軸力を考慮した伝達影響係数法による自由振動解析

340 伝達影響係数法による二次元トラス構造物の面内自由振動解析 : ピン接合の取り扱い

340 伝達影響係数法による二次元トラス構造物の面内自由振動解析 : ピン接合の取り扱い

Forced Vibration Analysis of a Straight-Line Beam Structure with Nonlinear Support Elements. 1st Report. Suggestion of Incremental Transfer Stiffness Coefficient Method.

The incremental transfer stiffness coefficient method is developed in order to analyze the periodic steady-state vibrations of a large-scale structure having locally strong nonlinear elements. The present method is based on the concepts of the method of harmonic balance, the transfer stiffness coefficient method and the incremental method. Firstly, in the present method, the structure treated is separated into the linear parts and the nonlinear elements, and the inner degrees of freedom of the linear parts are eliminated from the process of successive approximation for the solution by applying the transfer stiffness coefficient method. Secondly, the computation technique as the transfer influence coefficient method is applied to the above process to reduce the computation cost remark-ably. As a fundamental example, an algorithm based on the present method is formulated to analyze the in-plane flexural forced vibration of the straight-line beam structure supported by the nonlinear base support elements.

Time Historical Response Analysis of Nonlinear Vibration Systems by the Step-by-Step Integration Scheme Utilizing the Transfer Influence Coefficient Method.

The authors have been presented a method of time historical response analysis for a large-scaled structure and remarkably improved the computational efficiency and accuracy of the analysis by applying some merits of the transfer influence coefficient method to linear structures. There exist many nonlinear elements in actual structures and in many cases the nonlinearities are found in the base support elements. Therefore, they present a method of nonlinear time historical response analysis for a large-scaled structure. They formulate an algorithm on the assumption that the nonlinearities exist only in the base support elements and they take piecewise linear spring, Coulomb's friction and cubic nonlinear spring into account as nonlinear elements. The time historical response of a three-dimensional tree structure is treated and the validity of the present method is demonstrated by some numerical computational results.

Forced Vibration Analysis of a Nonlinear Structure Connected in Series. (Stability Analysis Based on the Argument Principle).

It is a very difficult problem to determine the stability of the periodic steady-state vibrations generated in a large-sized nonlinear system with multi-degree-of-freedom.In order to overcome such difficulty, a new pratical method to accurately analyze the stability of the periodic solutions obtained from the method of harmonic balance is developed for a nonlinear structure connected in series.The present method is mainly based on the argument principle and is applicable to the stability analysis of any multi-degree-of-freedom system excited parametrically.By introducing the same treatment as that of the incremental transfer influence coefficient method into the computation process of the present method, the computation speed is improved and the memory size required in the computation is considerably reduced.The validity of the present method is confirmed by the results of numerical computation for some examples.

Transfer Stiffness Coefficient Method Combined with Concept of Substructure Synthesis Method. (Linear Free and Forced Vibration Analyses of a Straight-Line Beam Structure).

The transfer stiffness coeficient method was developed in order to improve the computation efficiency and extend the applicability of the transfer influence coefficient method through introduction of the concept of the substructure synthesis method. In the new method, the structure to be analyzed is divided into substructures, each of which is divided into a number of identical fundamental elements. Each substructure is reconstructed by connection of the fundamental elements and the computation cost is markedly reduced by elimination of the degrees of freedom at the inner nodes of substructures in the process of reconstruction. In addition, the computation procedure, which is the same as that in the transfer influence coefficient method, is applied to the entire structure reconstructed from the substructures, for even greater improvement of the computation efficiency. As the most fundamental example of use of the present method, an algorithm is formulated for free and forced vibration analyses of a straightline beam structure. The validity of the present method is confirmed by the results of numerical computation.

Time Historical Response Analysis of Large-scaled Structures. Improvement of Computational Efficiency and Numerical Stability by Applying the Transfer Influence Coefficient Method.

A method of time historical response analysis for large-scale structures is presented. This method is derived from a combination of the transfer influence coefficient method and the Newmark-β or Wilson-θ method, and it improves the computational efficiency and accuracy of the transient response analysis remarkably by means of several advantages of the transfer influence coefficient method. The present method is free of the numerical instabilities which often occur in using the Newmark-β or Wilson-θ method combined with the transfer matrix method or the Runge-Kutta-Gill method. An algorithm for the transient response is formulated for the three-dimensional three structure which is mainly found in pipeline systems. We regard the tree structure as a lumped mass system here. The validity of the present method compared with other methods for transient analysis is demonstrated through various numerical computations.

Transfer Stiffness Coefficient Method Combined with the Concept of Substructure Synthesis Method. Linear Free and Forced Vibration Analyses of a Straight-line Beam Structure.

The transfer stiffness coefficient method is developed in order to improve the computation efficiency and the applicability of the transfer influence coefficient method with the introduction of the concept of the substructure synthesis method. In the new method, the structure to be analyzed is divided into substructures, each of which is equally divided into fundamental elements. Each substructure is reconstructed by connecting the fundamental elements and the computation cost is markedly reduced by eliminating the degrees of freedom at the inner nodes of substructures in the process of reconstruction. In addition, the computation procedure, which is the same as that of the transfer influence coefficient method, is applied to the entire structure reconstructed from the sub-structures in order to improve the computation efficiency even more. As the most fundamental example of the present method, an algorithm is formulated for the free and the forced vibration analyses of a straight-line beam structure. The validity of the present method is confirmed by the results of numerical computation.

Application of Transfer Influence Coefficient Method to Inverse Iteration Method.

The inverse iteration method is one of the most effective methods of eigenvalue analysis and is suited for both vibration and structural analyses. It can compute eigenvalues in the order of increasing absolute value, the convergence of iterative computation can be accelerated by applying the technique of origin shift. However, the inverse iteration method must be able to solve a large-sized simultaneous linear algebraic equation in every iterative process. In order to improve the computation accuracy and the computation speed of the inverse iteration method, we introduce the concept of the transfer influence coefficient method into the iterative process. The transfer influence coefficient method is advantageous in that it can solve simultaneous linear algebraic equations, and the memory size required in the computation is extremely decreased. The present method is applied to both the undamped and the damped systems.

Linear Forced Vibration Analysis of Two- and Three-dimensional Tree Structures by the Transfer Influence Coefficient Method.

An algorithm for free vibration analysis of a tree structure formulated in the previous reports by applying the transfer influence coefficient method is extended in order to analyze forced vibration of a tree structure which is mainly found in pipeline systems. The tree structure has some crooked parts and subsystems but has no closed loop in the systems. It is modeled as a distributed mass system with consideration of structural damping, and the present algorithm is formulated for both two- and three-dimensional tree structures. It is theoretically confirmed that some merits of the transfer influence coefficient method for free vibration analysis, for example, excellence in both computation accuracy and speed are also realized for the forced vibration analysis. Moreover, the present algorithm enables us to easily analyze a vibrating system excited by forced displacement by changing the corresponding spring constants conveniently.

Forced Vibration Analysis of a Nonlinear Structure Connected in Series. Stability Analysis Based on the Argument Principle.

It is a very difficult problem to determine the stability of the periodic steady-state vibrations generated in a large-sized nonlinear system with multiple degrees of freedom. In order to overcome such difficulty, a new practical method to accurately analyze the stability of the periodic solutions obtained from the method of harmonic balance is developed for a nonlinear structure connected in series. The present method is mainly based on the argument principle, and is applicable to the stability analysis of any multi-degree-of-freedom system excited parametrically. By introducing the same treatment as that of the incremental transfer influence coefficient method into the computation process of the present method, the computation speed is improved and the memory size required in the computation is considerably reduced.

Free Vibration Analysis of a Tree Structure by the Transfer Influence Coefficient Method (2nd Report, Treatment of a Three-Dimensional Tree Structure and Numerical Computational Results).

An algorithm for a two-dimensional tree structure formulated in the previous report by applying the transfer influence coefficient method is extended in order to analyse the longitudinal, flexural and torsional coupled free vibration of a three-dimensional tree structure. Moreover, adequate selection of a nonzero state variable as an initial standard value in the computation of characteristic modes and the problem of false roots which occur in the analysis for a structure with subsystems by applying the transfer matrix method are also discussed. The superiority of the present method over the transfer matrix method in the computational accuracy and the computation speed is confirmed by the numerical computation for typical models of both two-and three-dimensional tree structures.

Free Vibration Analysis of a Tree Structure by the Transfer Influence Coefficient Method (1st Report, Formulation for a Two-dimensional Tree Structure).

The authors apply the transfer influence coefticient method to a two-dimensional tree structure, and formulate a general algorithm to analyse in-plane longitudinal and flexural coupled free vibration. The tree structure, which is mainly found in the F-shaped structure of machine tools, pipeline systems and so on, has some crooked parts and subsystems but has no closed loop in the system. It is modeled as a distributed mass system in the present algorithm. It is theoretically confirmed that some merits of the transfer influence coefficient method also hold for the two-dimensional tree structure; that is, boundary conditions are easily controlled by the spring constants, and false roots in the use of the bisection method as a solution to the frequency equation can readily be eliminated by using the values obtained in the computational process. The occurrence mechanism of false roots is discussed in detail.

Forced Vibration Analysis of a Nonlinear Structure Connected in Series. 1st Report. Suggesting the Incremental Transfer Influence Coefficient Method.

The incremental transfer influence coefficient method is developed in order to analyze the periodic steady-state vibrations of a nonlinear system with a multi-degree-of-freedom system on a personal computer, combining the concepts of both the method of harmonic balance and the transfer influence coefficient method through the incremental method. The present method has some merits, that is, high computation speed, high numerical computational accuracy, applicability to the various types of nonlinearity and so on. For the stability problem, general and simplified methods are suggested in order to determine the stability of the periodic solutions from the behavior of the solutions of the corresponding variational equation, which is described as a multi-degree-of-freedom system with parametric excitations. The former is applicable to the variational equation in general and with high accuracy. The latter gives the sufficient condition for certain main unstable regions of the variational equation.