Estimation of flexibility matrix of beam structures using multisensor fusion

A technique is presented for estimating the residual flexibility between nonexcited structural degrees of freedom from experimental structural vibration data. Using this method, one can include the residual flexibility estimated from modal measurements in the computation of measured flexibility for experiments with incomplete reciprocity, i.e., when the response and excitation measurement sensors are not fully collocated. The method can also be used to estimate the unknown entries in the residual flexibility matrix for experimental component mode synthesis when excitations are not provided at all interface degrees of freedom. A general solution is presented that contains an unknown positive semidefinite contribution. The general solution satisfies modal orthogonality in the limit that all of the structural degrees of freedom are instrumented and when the positive semidefinite contribution lies in a nullspace defined by the stiffness matrix and the modal flexibility. With a limited number of measurements, modal orthogonality is shown to be satisfied to the extent that the measured modes are preserved by static condensation. A rank-deficient solution is presented that allows the residual to be used in the computation of the flexibility matrix without further modeling assumptions. Numerical and experimental results that demonstrate the application of the method to both flexibility matrix convergence and experimental component mode synthesis are presented.

Timoshenko beam elements have been the subject of numerous publications. The difficulty was that of arriving at a superconvergent element with four degrees of freedom, as is the case for the Bernuli‐Euler classical beam element. Two different approaches are presented here for the derivation of the shape functions. The first is based on the flexibility matrix, where utilizing the unit load method, including the term that accounts for the shear deformations in the virtual work expression, the stiffness matrix is derived. Then, a second method is presented to derive the exact shape functions, directly from the differential equations of the Timoshenko beam theory. The resulting shape functions are the same in both methods.

Vibration and wave propagation in functionally graded beams with inclined cracks

Summary A problem of elastic structures stress-strain field determination is considered in this article. A theoretical background and computation algorithms of equilibrium finite element method are presented there. The different external effects are estimated, namely: load, prestressing, inicial strains and support settlements. The dual relationships (equilibrium and geometrical equations, stiffness and flexibility equations) of equilibrium element, also the expressions of stiffness and flexibility matrices are given. These relationships describe the stress-strain field of the finite element and allow to transforme the flexibility matrix to the stiffness matrix and on the contrary. There are presented direct and variational formulations of the problem. The algorithms of the forces method and displacements method are made for their solution. Easier is the algorithm of displacements method, because making equations of the forces method needs to solve the system of equilibrium equations. But the formulation and solving of the displacements equations can be changed by direct formulation of global flexibility matrix of the structure. In these cases, when the degree of static indeterminacy of the discrete model of structure is quite less than the number of freedom degrees, suth the change can be effective. The computational results illustrate the high accuracy of equilibrium elements not only with respect to forces, but also to displacements. The direct stiffness method in equilibrium elements makes it possible not only to simplify significantly implementation of the equilibrium element method, but also to include equilibrium elements in libraries of geometrically compatible elements.

An exact approach is proposed for damage identification in statically determinate structures. The contribution of this study is twofold. Firstly, a rigorous disassembly formulation of structural global flexibility matrix is presented based on the matrix spectral decomposition, which can provide an exact relationship between the modifications of structural stiffness parameters and the associated flexibility matrix. Secondly, the static minimum-rank flexibility change is derived to obtain the exact flexibility change before and after damage. The proposed method is economical in computation and is simple to implement. For the statically determinate structures, the proposed method can exactly compute the elemental perturbed stiffness parameter only using a few of incomplete static displacement data. The efficiency of the proposed method is demonstrated by two statically determinate structures.

The diagnosis of structural damage usually belongs to a mathematical inverse problem. This work presents a novel frequency-shift flexibility sensitivity algorithm for structural damage assessment using only the first-order vibration mode to achieve the goal of successfully identifying structural damage with fewer modal parameters. The core idea of the proposed method is to make the first-order vibration mode contribute the most to a structural flexibility matrix through the frequency-shift operation. A high-precision flexibility matrix can be obtained after the frequency-shift operation, which only needs the first mode of structural free vibration. Through this special advantage, structural damage coefficients can be accurately calculated by the frequency-shift flexibility sensitivity equation. Thus, a reliable identification result can be obtained according to the values of the calculated damage coefficients. In some engineering applications, another advantage of the proposed method is that it does not require a complete finite element modeling process, as long as a few lower-frequency vibration modes of the intact structure are measured. A truss structure and a beam structure are used as two numerical examples to demonstrate the proposed approach. The results show that the proposed method has higher calculation accuracy than the ordinary flexibility sensitivity method by using only the first-order vibration mode. The proposed method can overcome possible misdiagnosis of the ordinary flexibility sensitivity method. It also has been shown that the proposed method may have the potential to identify minor damage in a structure. Using the experimental data of a steel frame structure, the effectiveness and reliability of the proposed method have been further verified. The proposed method provides a simple way for structural damage identification with only a few vibration modal data.

Current methods of analyzing the response of buried structures to ground shock loads consider the effects of structure response on structure loads, but do not consider the effects of structure motion on the soil flow near the structure and subsequent changes in the structure loads and response. Analyses of the effects of these soil flow changes for a high explosive detonation very close to a structure have not been reported until now. In this paper, dynamic finite-element analyses, including the detonation of high explosives in the soil, are used to determine the changes in soil flow and structure loads. These analyses demonstrate that the soil flow near the structure changes significantly due to structure motion, and neglecting these changes in flow causes the underprediction of late-time loads and structure response.

The object of research is a mathematical model describing the movement of a robot with five degrees of freedom for a warehouse. The work was aimed at analyzing the kinematic structure of the manipulator, on the basis of which the base and local coordinate systems were selected, as well as further formalized recording of the kinematic equations in matrix form. It is noted that one of the most problematic places is that the algorithms for controlling the robot most often contain local rules for the interaction of robots between themselves and the external environment, and emergent behavior is manifested as a result of the application of these rules, which does not have a formal description. Therefore, it is important to modernize the models describing the motion of a robot with five degrees of freedom for a warehouse. Using the matrix method, the sequence of constructing coordinate systems is described and its mathematical description is given, which will make it possible to eliminate this drawback in the future. The computer implementation of the developed algorithms was carried out using methods for processing matrix data structures. The principle of constructing a kinematic model of a robot is presented, with the help of which the main coordinate transformation matrices are obtained for robot with five degrees of freedom, and the possibility of taking into account the size of the gaps in the joints is shown. The resulting model is obtained, which is proposed for use in building control algorithms for a robot with an automatic gap selection, as well as in robot calibration. This is due to the fact that the proposed model has a number of features, in particular, the basic coordinate system and the coordinate system of each link of robot with five degrees of freedom are taken into account. This makes it possible to obtain the values of the indicators for the projection of the robot position vector in the initial state, in the rotation of the fourth link at a well-defined angle and in the case of a vertically straightened manipulator. Compared to similar known studies, this provides advantages such as minimizing errors in position, speed and motion accuracy. The object of research is a mathematical model describing the movement of a robot with five degrees of freedom for a warehouse. The work was aimed at analyzing the kinematic structure of the manipulator, on the basis of which the base and local coordinate systems were selected, as well as further formalized recording of the kinematic equations in matrix form. It is noted that one of the most problematic places is that the algorithms for controlling the robot most often contain local rules for the interaction of robots between themselves and the external environment, and emergent behavior is manifested as a result of the application of these rules, which does not have a formal description. Therefore, it is important to modernize the models describing the motion of a robot with five degrees of freedom for a warehouse. Using the matrix method, the sequence of constructing coordinate systems is described and its mathematical description is given, which will make it possible to eliminate this drawback in the future. The computer implementation of the developed algorithms was carried out using methods for processing matrix data structures. The principle of constructing a kinematic model of a robot is presented, with the help of which the main coordinate transformation matrices are obtained for robot with five degrees of freedom, and the possibility of taking into account the size of the gaps in the joints is shown. The resulting model is obtained, which is proposed for use in building control algorithms for a robot with an automatic gap selection, as well as in robot calibration. This is due to the fact that the proposed model has a number of features, in particular, the basic coordinate system and the coordinate system of each link of robot with five degrees of freedom are taken into account. This makes it possible to obtain the values of the indicators for the projection of the robot position vector in the initial state, in the rotation of the fourth link at a well-defined angle and in the case of a vertically straightened manipulator. Compared to similar known studies, this provides advantages such as minimizing errors in position, speed and motion accuracy.

Response Spectrum Analysis (RSA) and modal combination techniques are widely used to estimate the peak response of structures subjected to earthquake vibrations. This paper presents the numerical modeling and seismic analysis of structures. The response spectra based on Eurocode 8 is implemented for a five storey moment-resisting 3D structure to estimate peak response to earthquake-induced vibration. Eigenvector analysis is carried out to determine undamped free vibration mode shapes and frequencies. The lumped mass matrix, stiffness matrix of the full 3D structure is derived and natural periods, modal shapes, modal participation factors, and effective modal mass ratios are calculated. The structural response in different modes is combined to estimate the total dynamic response. The Square Root of Sum of Squares (SRSS), Complete Quadratic Combination (CQC), and Absolute Sum (AbsSum) rules are discussed and compared. The results of the SRSS and CQC rule for the examined building are almost identical as all cross-correlation coefficients are approximately equal to zero, and the responses of the individual modes are completely uncorrelated. CQC rule is appropriate when the natural frequencies are close to each other. AbsSum method shows an upper bound estimate of the total response since it assumes that all modal peaks occur at the same time. The simulation for numerical modeling and response spectrum analysis (RSA) is implemented in MATLAB® software.

The test rig of the A-frame which is used more at home and abroad is carried out kinematic analysis. The offsets of slip angle,camber angle and the tire trace center are discovered when the test rig is in the composite posture of slip angle and camber angle. The offset formula is deduced by the method of space analytic geometry based on the tire coordinate system defined in ISO.The results showed that each offset can't be ignored in a large complex attitude angle. In order to effectively solve the phenomenon,a novel structure of six degrees of freedom(DOF) tire test rig is proposed. The length of six electric cylinders is calculated when the new test rig is in different postures by the Euler angles of rotation method. The control precision of attitude angle of the tire is analyzed and six DOF platform electric cylinders are space rearranged. The results showed that each physical quantity is with no offset when the new structure six DOF tire test rig is in the composite posture and the tire posture can be arbitrarily controlled. As the same time,a new program of six power cylinder arrangement improves the control precision of tire attitude angle.

Guidelines for seismic performance evaluation of existing structures have been published by FEMA and the European Commission. Additionally, these organizations have presented frameworks for strengthening the resilience of society and industry. These frameworks require countermeasures for early recovery after natural disasters. For rapid post-earthquake recovery, it is necessary to assess the structural integrity and implement repairs. To achieve this, the utilization of structural health monitoring is essential. In structural damage assessment, loads and response displacements are important physical quantities, but these are difficult to obtain directly from structures. Therefore, in structural health monitoring, structural integrity is evaluated using measured accelerations. However, the superposition of uncertainties related to seismic motion and structures can sometimes complicate the setting of thresholds for structural integrity evaluation. To detect structural anomalies caused by earthquakes rapidly and with high accuracy, structural health monitoring methods incorporating deep learning have begun to be researched. Additionally, by extracting features from measured data using deep learning, prior setting of evaluation thresholds becomes unnecessary. Generally, training deep learning models requires large amounts of training data. However, since it is difficult to acquire anomaly data from existing structures, seismic response analysis is utilized. Typically, to represent real phenomena, analytical models require many degrees of freedom. In frequency domain response analysis, the frequency response function is defined as the ratio of the Fourier spectra of the structural seismic response to the seismic motion. By modeling the frequency response function, the seismic response of structures can be calculated. In this paper, we develop a method to calculate structural seismic responses by modeling the frequency response function with an AR model. This eliminates the need to set parameters such as degrees of freedom, mass, and stiffness of the analytical model. Furthermore, we propose a structural health monitoring method that uses this approach for training deep learning models. Verification of this method using experimental data from a full-scale steel building demonstrated that anomaly detection was possible from limited observational data only.

This article is concerned with the experimental validation of a structural health monitoring methodology for damage detection and identification. Three different data-driven multivariate algorithms are considered here to obtain the baseline pattern. These are based on principal component analysis, independent component analysis and hierarchical non-linear principal component analysis. The contribution of this article is to examine and compare the three proposed algorithms that have been reported as reliable methods for damage detection and identification. The approach is based on a distributed piezoelectric active sensor network for the excitation and detection of structural dynamic responses. A woven multilayered composite plate and a simplified aircraft composite skin panel are used as examples to test the approaches. Data-driven baseline patterns are built when the structure is known to be healthy from wavelet coefficients of the structural dynamic responses. Damage is then simulated by adding masses at different positions of the structures. The data from the structure in different states (damaged or not) are then projected into the different models by each actuator in order to generate the input feature vectors of a self-organizing map from the computed components together with squared prediction error measures. All three methods are shown to be successful in detecting and classifying the simulated damages. At the end, a critical comparison is given in order to investigate the advantages and disadvantages of each method for the damage detection and identification tasks.

An Evaluation Method for New Energy Power Prediction Based on Flexibility Matrix and TOPSIS Method

Kinematic analysis and error modeling of TAU parallel robot

Computation of the homogenized nonlinear elastic response of 2D and 3D auxetic structures based on micropolar continuum models