Research on the dynamic hammering method for identifying weak parts in cantilever structures

Identification of the vulnerabilities in the structural stiffness is one of the most crucial issues in improving this property of machine tools. In this paper, the Flexibility Matrix Diagonal element method, based on hammer testing, is proposed as an effective approach to identifying the stiffness weakness of cantilever structures. To verify the proposed method, the element stiffness weakening is used to simulate the weak parts regarding stiffness. Several scenarios, with single and multiple weakness points, including various noise levels, are studied, using finite element simulations. Next, a novel method, to measure the accuracy of the algorithm and quantify the weakness level, under noise conditions, is proposed. The advantage of this method, compared to the ones based on Flexibility Difference Method, is the higher identification accuracy under noise interference. Finally, the cantilever beam with elastic support is experimentally studied. The natural frequencies and modal shapes are obtained, according to the singular value decomposition method, to establish the flexibility matrix. In addition, using only the lowest three modes, a series of numerical examples and experiments are provided, to illustrate the validity and the considerable practical engineering value of the method.

Solving Systems of Linear Algebraic Equations with the Use of an Selective Regularization

The solution of systems of linear algebraic equations, which matrices can be poorly conditioned or singular is considered. As a solution method, the original matrix is decomposed into triangular components by Gauss or Chole-sky with an additional operation, which consists in increasing the small or zero diagonal terms of triangular matrices during the decomposition process. In the first case, the scalar products calculated during decomposition are divided into two positive numbers such that the first is greater than the second, and their sum is equal to the original one. In further operations, the first number replaces the scalar product, as a result of which the value of the diagonal term increases, and the second number is stored and used after the decomposition process is completed to correct the result of calculations. This operation increases the diagonal elements of triangular matrices and prevents the appearance of very small numbers in the Gauss method and a negative root expression in the Cholesky method. If the matrix is singular, then the calculated diagonal element is zero, and an arbitrary positive number is added to it. This allows you to complete the decomposition process and calculate the pseudo-inverse matrix using the Greville method. The results of computational experiments are presented.

A Truncated Matrix Completion Algorithm Using Prior Information for Wind Turbine Clutter Suppression

The conventional matrix completion (MC) regularizes each singular value equally, and thus the rank cannot be well approximated, which greatly limits the flexibility and accuracy of MC usage. In this paper, a truncated MC algorithm using prior information to determine the threshold while generating the target rank is proposed for the wind turbine clutter suppression of weather radar. During the singular value shrinking process, an appropriate threshold is selected to obtain the optimal approximation of the sampling matrix. Specifically, the mean value of the diagonal element in the recovered weather matrix is calculated to improve the robustness of the recovery result effectively. Simulation results demonstrate that the proposed algorithm reduces the computational complexity as well as further improves the MC accuracy and realizes the effective suppression of the wind turbine clutter.

Stressed state of webbed framing joints with diagonal element

In most of cases, webbed beams of ship grillages intersect at the right angle. The intersections at arbitrary angle lead to structural and technological challenges, whereas the welds too close to each other bring about high stress concentrations and high welding stresses. Beam intersections at sharp angles are hard to weld. This paper discusses the beam joint with diagonal element suggested and patented by the authors, as well as the results of stressed-state study for this joint.

Pola Keruntuhan Jembatan Rangka Menerus Tipe Waren

Bridge damage often occurs, as a result of damage to the bridge causing financial aspects losses and can also cause fatalities. The causes of the damage various factor, one of which is the bridge structure experiencing fatigue. This fatigue caused the strength of the structure of the bridge to decrease. Bridge damage due to a decrease in the strength of this bridge structure can impact the bridge to collapse. To minimize bridge damage due to a decrease in the strength of the structure of the bridge there is a need for bridge maintenance and to make it easier in terms of maintenance it is necessary to know the pattern of collapse of the existing bridge. In the analysis of this collapse pattern, a waren type steel continous bridge will be modeled with a span length of 120 meters. This analysis is carried out by giving a static vertical load at a reference point on the bridge frame, where the load is increased by multiplying until the structure is demage. The results of the study show that in the waren type continuous steel truss bridge failure occurs at the final portal diagonal element in the 2 middle positions. Based on FEMA 356 displacement target, the level of structural performance shows the bridge model under IO conditions and based on SNI 2833-2008, the actual ductility that occurs has met the requirements.

Criteria for H-Matrices Based on γ−Diagonally Dominant Matrix

In this paper, we present a new practical criteria for H-matrix based on γ-diagonally dominant matrix. In order to make the judgment conditions convenient and effective, we give two new definitions, one is called strong and weak diagonally dominant degree, the other is called the sum of non-principal diagonal element for the matrix. Further, we obtain a new practical method for the determination of the H-matrix by combining the properties of γ-diagonally dominant matrix, constructing positive diagonal matrix, and adding the appropriate parameters. Finally, we offer numerical examples to verify the validity of the judgment conditions, corresponding numerical examples compared the new criteria and the existing results are presented to verify the advantages of the new determination method.

A Method for Multidisciplinary System Analysis Based on Minimal Feedback Variables

As modern engineering design usually involves dependence of one discipline on another, multidisciplinary system analysis (MDSA) plays an important role in the multidisciplinary simulation and design optimization on coupled systems. The paper proposes an MDSA method based on minimal feedback variables (MDSA_MF) to enhance the solving efficiency. There are two phases in the method. In phase 1, design structural matrix (DSM) is introduced to represent a coupled system, and each off-diagonal element is denoted by a coupling variable set; then an optimal sequence model is built to obtain a reordered DSM with minimal number of feedback variables. In phase 2, the feedback in the reordered DSM is broken, so that the coupled system is transformed into one directed acyclic graph; then, regarding the inputs depending on the broken feedback as independent variables, a least-squares problem is constructed to minimize the residuals of these independents and corresponding outputs to zero, which means the multidisciplinary consistence is achieved. Besides, the MDSA_MF method is implemented in a multidisciplinary platform called FlowComputer. Several examples of coupled systems are modeled and solved in the platform using several MDSA methods. The results demonstrate that the proposed method could enhance the solving efficiency of coupled systems.

Active control of structures and sound radiation modes and its application in vehicles

This paper presents computation of structural sound power and sound radiation modes, combined with structural dynamic equations to obtain the coupling relationship between sound and structures. As a result, the relationship between sound radiation modes of structures and structural vibration modes is established. The influence of the number and position of optimal secondary force sources on control of sound radiation modes is considered. Results show that sound radiation efficiency of sound radiation modes at the first order was more than that of sound radiation modes at other orders. The main diagonal element of coupling matrix between modes and sound radiation impedances was more than elements at other positions. Sound radiation modes at the first order were dominant sound radiation modes. When the number of secondary force sources was 4, the sound radiation power of structures was the lowest. Four force sources were taken as the basis to conduct on the related experiments in the anechoic chamber and compare with the computational result. Their results had a good consistency, which showed that the mentioned theory method was effective. Finally, the control strategy was applied to roofs of the vehicle. Experiments verified that sound pressure level of the driver in the low frequency was obviously improved, which remedied the defect of other optimization strategies for solving noises in the low frequency.

An improvement of H. Wang preconditioner for L-matrices

In this paper, we improve the preconditioner, that introduced by H. Wang et al [6]. The H. Wang preconditioner \(P\in R^{n\times n}\) has only one non-zero, non-diagonal element in \(P_{n1}\) or \(P_{1n}\) , when \(a_{1n}a_{n1}\ne 0\) . But the new preconditioner has only one non-zero, non-diagonal element in \(P_{ij}\) or \(P_{ji}\) if \(a_{ij}a_{ji}\ne 0\), so the H. Wang preconditioner is a spacial case of the new preconditioner for L-matrices. Also we present two models to construct a better \(I+S\) type preconditioner for the \(AOR\) iterative method. Convergence analysis are given, numerical results are presented which show the effectiveness of the new preconditioners.