Linear Bending Stiffness Research Articles

Rub-impact dynamic analysis of a dual-rotor system with bolted joint structure: Theoretical and experimental investigations

Large gas turbines often utilize dual-rotor structures to improve efficiency. To facilitate manufacture and maintenance, the large rotor systems are typically constructed by connecting components made from different materials together through the bolted joint. In this work, a dynamic model of a dual-rotor system with bolted joint included in the high-pressure (HP) rotor is established based upon the finite element theory of Timoshenko beam element, as well as taking into account the bearing forces and fixed-point rubbing fault. To evaluate the influence of rubbing faults on the dynamic behavior of a dual-rotor system, this study analyzed the response characteristics of the rotor under the cases of the LP rotor and the HP rotor subjected to the rubbing fault, respectively. In order to further reveal the effect of bolted joint structure on the system response while rubbing fault occurs, piecewise linear bending stiffness is also considered in this study. The nonlinear vibration responses of the bolted joint dual rotor-bearing system are studied through numerical simulation. Effect of rotor–stator contact stiffness and the occurrence of rubbing faults at the low-pressure (LP) rotor and the HP rotor are investigated through frequency-amplitude curves, waterfall diagrams, time-domain responses, and bending stiffness of the bolted joint. The results indicate that the presence of rubbing faults, whether occurring at the LP rotor or the HP rotor, leads to a decrease in the critical speed. Furthermore, under a rubbing fault, the bending stiffness of the bolted joint enters the stiffness softening region earlier and exhibits a wider range, which is exacerbated with increased contact stiffness. This phenomenon is considered one of the main causes of system response instability. Finally, the experimental studies are carried out on a bolted joint dual-rotor test rig to validate the numerical simulation results.

Analysis of construction parameters of outriggers in the mega column-core tube-outrigger structure based on seismic reliability

The design of outriggers is one of the hot issues in mega column-core tube-outrigger structures (MCCTOS). Therefore, the analysis of the parameters of the outriggers is of great practical significance. In this paper, based on the generalized probability density evolution theory, the reliabilities of MCCTOS with different outrigger parameters are investigated by absorbing boundary condition method and extreme-value distribution method, respectively. Based on the consideration of the randomness of the structural parameters and earthquake, the influence of the linear bending stiffness ratio of the outrigger-to-core tube, the number and position of the outriggers on the MCCTOS are analyzed by quantitative reliability. By comparing the results, it is found that for one-outrigger structure and two-outrigger structure, the reliability of the structure will reach a stable stage when the linear bending stiffness ratio of the outrigger-to-core tube is taken as 0.5 and 0.7 respectively. It indicates that the difference in the number of outriggers leads to the different reasonable values of the linear bending stiffness ratio of the outrigger-to-core tube. In addition, the reasonable locations of the outriggers can maximize the overall reliability of the structure and make the distribution of the reliability of each storey more uniform. The analysis of construction parameters of outriggers from the perspective of reliability can more comprehensively describe the influence of outriggers on the seismic capacity of the structure. The investigation on the seismic reliability of MCCTOS can more objectively evaluate the safety of structure. Moreover, the analysis of different construction parameters of outriggers in the MCCTOS based on seismic reliability can provide more objective suggestions for the design of outriggers.

Seismic performance of the concrete-encased CFST column to RC beam joints: Analytical study

A finite element analysis (FEA) model is established to investigate the concrete-encased concrete-filled steel tubular (CFST) column to reinforced concrete (RC) beam joints under cyclic loading. The feasibility of the FEA model is verified by a set of test results, consisting of the failure modes, the exposed view of connections, the crack distributions and development, and the hysteretic relationships. The full-range analysis is conducted to investigate the stress and strain development process in the composite joint by using this FEA model. The internal force distributions of different components, as well as the deformation distributions, are analyzed under different failure modes. The proposed connections are investigated under dimensional and material parameters, and the proper constructional details of the connections are recommended. Parameters of the beam-column joints, including material strength, confinement factor, reinforcement ratio, diameter of steel tube to sectional width ratio, beam to column linear bending stiffness ratio and beam shear span ratio are evaluated. Furthermore, the key parameters affecting the failure modes and the corresponding parameters ranges are proposed in this paper.

Linear μ-bending method for the measurement of the residual stress of surface-micromachined MEMS

This study introduces a simple and reliable strategy, called ‘linear μ-bending method’, to measure the residual stress of surface-micromachined micro-electro-mechanical systems (MEMS). The basic theory of the linear μ-bending method relies on the fact that not only the geometry and the material, but also the residual stress contribute much to determine the linear bending stiffness of MEMS. In a reverse way, this study identifies the residual stress after obtaining the linear bending stiffness of MEMS through experimental procedure. In a first step, bending tests for the surface-micromachined cantilevers are performed so that the bending rigidity and the anchor stiffness, which play important role in altering the stiffness of suspending MEMS, are obtained as pre-data. Secondly, the bending stiffness of the surface-micromachined bridge is measured through bending tests. And, as the last step, the residual stress is achieved by putting the obtained data from the bending tests – ‘linear bending stiffness’, ‘the anchor stiffness’, and ‘the bending rigidity’ – into the analytic model presented in this study. The results from the tests about the surface-micromachined poly-silicon structures with various residual stresses demonstrate that the linear μ-bending method is reliable. The output from the linear μ-bending method is that the residual stress of as-deposited poly-silicon film is 142.7 MPa (compressive) with the standard deviation of 3.5% and that the residual stress of the poly-silicon film decreases as the annealing effect grows.

The nonlinear vibration analysis of a clamped-clamped beam by a reduced multibody method

The nonlinear response characteristics for a dynamic system with a geometric nonlinearity is examined using a multibody dynamics method. The planar system is an initially straight clamped-clamped beam subject to high frequency excitation in the vicinity of its third natural mode. The model includes a pre-applied static axial load, linear bending stiffness and a cubic in-plane stretching force. Constrained flexibility is applied to a multibody method that lumps the beam into N elements for three substructures subjected to the nonlinear partial differential equation of motion and N-1 linear modal constraints. This procedure is verified by d'Alembert's principle and leads to a discrete form of Galerkin's method. A finite difference scheme models the elastic forces. The beam is tuned by the axial force to obtain fourth order internal resonance that demonstrates bimodal and trimodal responses in agreement with low and moderate excitation test results. The continuous Galerkin method is shown to generate results conflicting with the test and multibody method. A new checking function based on Gauss' principle of least constraint is applied to the beam to minimize modal constraint error.

Finite element analysis of rotating disks

A finite element formulation is presented for the analysis of rotating disks in either a body-fixed or a space-fixed co-ordinate system. The in-plane stress distribution resulting from the in-plane body force due to rotation is determined first by a plane stress finite element analysis. This stress distribution is then used in calculating the out-of-plane geometric stiffness which in turn is added to the linear bending stiffness. In the space-fixed co-ordinate system, inertia and a viscous type damping also contribute to the out-of-plane stiffness, even in the steady state case. The formulation presented here places no restrictions on the disk geometry if the problem is solved in a body-fixed co-ordinate system, although only disks of axisymmetric geometry may be considered in the space-fixed co-ordinate system. A direct method of determining the critical speeds through an eigenvalue analysis in space-fixed co-ordinates is presented. Then the undamped steady state response to a space-fixed transverse point load is examined. The effects of a viscous type damping are also presented.

屋根型円筒トラスシェルの座屈解析 : その 2 剛接度をバネ剛性で評価したトラスモデルによる非線形挙動の解析

In the previous paper, we presented an accurate analytical method for reticulated cylindrical shells using finite element method and showed several characteristic features of buckling behavior. In this paper, we lead a simplified analytical method which deals bending rigidity as rotational spring stiffness of member joints in accordance with the result that nonlinear terms due to bending have a little influence on the buckling behavior. Summary of results obtained may be as follows. (1) Due to linear bending stiffness, the geometrical stiffness matrix is explicitly obtained and the computation time is reduced. (2) Good accuracy is obtained even in large deformation region when the bending stress is considered to be secondary stress compared with the axial one. (3) According to this method, nonlinear behavior which alters due to joint rigidity is grasped. (4) Lowering of joint rigidity may cause a reduction of buckling load and buckling mode comes near to that of dimple buckling.