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The article deals with the modeling of stiffness properties of the rotors flange joints, which largely determine overall dynamics. Research is conducted on the example of the standard compressor shaft flange connection and the disk of the high-pressure turbine in the gas generator of the gas turbine engine (GTE). It is noted that the bending stiffness of the flange connection is a nonlinear function of the bending moment, whose both experimental and analysis magnitude is related to the rotor deflection from the unbalanced forces. It is shown that the value of the bending stiffness essentially depends not upon the flange connection geometry but on the bolts tightening force, the axial force, the tensile joint, the contact strain of the flange surfaces. Analysis of the effect obtained in different models of the flange connection of the bending stiffness values on the overall dynamics of the rotor showed the necessity of taking into account the entire set of factors acting in the joint.
An elastic-plastic B spline finite strip method is proposed to investigate the continuous plate straightening process in this paper. First, the B spline displacement function that satisfies the boundary conditions of simply supported end and free end of the strip element is established, and then the stress-strain matrix is established. Second, the set method of total stiffness matrix based on B spline finite strip method for plate straightening problem is proposed, and the influence of nodal line number and strip elements number on the sparsity of total stiffness matrix is analyzed. Third, the loads on the strip elements are taken as linear uniform distribution, and the transformation matrix between the equivalent linear load and the actual load of the strip element is established. At last, the plate straightening simulation of 11 rolls straightening machine is made based on the elastic-plastic B spline finite strip method, the calculated results agree with the measured results, which approves that the elastic-plastic B spline finite strip method established can be applied to the plate straightening process.
When the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.
There has been considerable interest in stratospheric airships as a cost-effective alternative to earth orbit satellites for sightseeing, aerial photography, communication and carrying weapons, etc. Many countries have plans to develop the airship owing to its greatly expected usage. The suspended curtain plays a vital role in force transmission in stratospheric airships but lacks attention. In this paper, the relationship between the optimal shape of suspended curtain and load conditions was studied through CAE Abaqus and Isight. Firstly, by using secondary development function of Abaqus, parametric FEA models of suspended curtains and envelopes have been established, several parameters were used to describe the shape of suspended curtains. Secondly, parameters of the suspended curtain shape were optimized under different loading conditions by means of the genetic algorithm. Lastly, through the analysis of the results, some conclusions are summarized: The relationship between n1(n2) and nb was found to be linear when the suspended curtain is subjected to vertical load. The stress transfer law of suspended curtain and inflatable membrane structure under the inclined load were also obtained, which are valuable for the structural engineering design of stratospheric airships..
Due to the high brittleness, cracks, holes, and other defects that are easily generated in quasi-crystal structures can affect safe applications in serious cases. For guided wave non-destructive testing, the propagation of Lamb and SH waves in functionally graded one-dimensional hexagonal quasi-crystal plates are investigated. Governing equations of wave motion in the context of Bak’s model are deduced and solved by the Legendre orthogonal polynomial method. Dispersion curves, phonon and phason displacement, and stress distributions are illustrated. The convergence of the present method applied to functionally graded quasi-crystal plates is verified. Moreover, the influences of the phonon-phason coupling effect and graded fields on wave characteristics are analyzed. Some new results are obtained: angular frequencies of phason modes always decrease as phonon-phason coupling coefficients, Ri, increase; and phonon and phason displacements of Lamb and SH waves at high frequencies are mainly distributed in the region that contains more quasi-crystal material with a smaller elasticity modulus and less rigidity. The obtained results establish the theoretical foundation of guided wave non-destructive testing for functionally graded quasi-crystal plates.
In this study, a spherical indenter mounted on an atomic force microscope (AFM) was used to compress a Nannochloropsis oculata (N. oculata) cell on a poly-l-lysine coated slide. A mathematical model of the cell, which was derived by considering a fluid-filled spherical shell with axisymmetric compression between a sphere and an infinite flat plate, is proposed. In the construction of this mathematical model, the spherical shell was assumed to be a homogenous, isotropic, and elastic material. Thin-film theory was applicable to the spherical shell because the thickness of the shell was nearly negligible compared with its diameter. The governing equations of the contact and noncontact regions were converted from a boundary condition problem to an initial value problem. Then, the fourth-order Runge–Kutta method was applied to solve the transformed governing equations. The force curve obtained from the compression experiment was compared with the theoretical results derived from the proposed model. Furthermore, the numerical solution of the proposed model was verified to be consistent with the experimental data. The mechanical properties of cell walls were confirmed by applying the least square error method. Subsequently, the contact radius, inner pressure and tension distribution of the cell wall could be determined using the proposed model. The models proposed in other studies are suitable for analyzing the compression characteristics of cells whose size is of the order of tens of micrometers and millimeters. By contrast, the model proposed in this study can analyze the compression characteristics of N. oculata, which is only a few micrometers in diameter. Furthermore, a force curve that accurately describes the deformation behavior of N. oculata under strain levels of 25% was established.
A non-local, ordinary state-based, peridynamic elastoplastic model is formulated to numerically simulate the fracture of reinforced concrete materials. Several basic definitions are first discussed to avoid confusion; and then, a detailed derivation of the force vector state is presented, leading to a unified expression of force state for one-, two- and three-dimensional elasticity problems. Furthermore, an ordinary state-based peridynamic (OSB PD) elastoplastic analysis approach is developed for both plastic compressible and incompressible materials, including the constitutive relationship, the yield function, the consistency condition and the plasticity flow rule. The peridynamic predictions of a quasi-static deformation of the steel rods are in good agreement with the analytical solution. Moreover, the OSB PD plasticity is verified by analyzing a square plate with or without a central hole suffering different loading-unloading paths. Finally, a two dimensional reinforced concrete clamped beam subjected to impact loading is simulated with the proposed OSB PD elastoplasticity, demonstrating its capability in capturing the damage characteristics and structural failure behavior. Simulation results show good accuracy of the peridynamics in simulating elastoplastic problems.
The mechanical characterization of rocks is important in engineering design and analysis of rock-related structures. In the current researches, rocks are classified as heterogeneous materials with anisotropic behavior, and advanced methods such as combined experimental-numerical approach are developed to characterize the behavior of rocks. In this study, the nanoindentation experiment in conjunction with the generalized means method is used to determine the Young’s modulus and hardness of eight different polycrystalline granite rocks. In the first step, the Young’s modulus and hardness of granites’ constituents are determined through nanoindentation tests on pure granite minerals. Then, the properties of granites are determined using generalized means method by considering the mechanical properties of minerals, their volume fractions and an empirical constant called the microstructural coefficient. Accurate results with less than 3% error are obtained for 62.5% of the granite samples. The generalized means is introduced as a simple and effective method to characterize the mechanical properties of heterogeneous polycrystalline rocks.
Empirical Mode Decomposition (EMD) and its approaches are powerful techniques in signal processing especially for the diagnosis of rotating machinery running in non-stationary regime. We are interested in this paper to the dynamic behavior of a defected one stage gearbox equipped with an elastic coupling and loaded under acyclism regime generated by a combustion engine. Actually, we adopt an approach to the EMD method called Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) as a technique to perform the diagnosis of the studied system. Since the obtained signals are modulated, all obtained Intrinsic Mode Functions (IMFs) are modulated and are processed and shown by the Wigner-Ville distributions (WVD) as well as the spectrum of their envelope in order to detect defects such as cracked tooth defect in the wheel of the spur gearbox and eccentricity defect in the gear.
This paper investigates the electromechanical behavior of functionally graded piezoelectric composite beams containing axially functionally graded (AFG) beam and piezoelectric actuators subjected to electrical load. The mechanical properties of the AFG beam are assumed to be graded along the axial direction. Employing the electromechanical coupling theory and load simulation method, the expression for the simulation load of the piezoelectric actuators is obtained. Based on Euler-Bernoulli beam theory and the obtained simulation load, the differential governing equation of the piezoelectric composite beams subjected to electrical load is derived. The integration-by-parts approach is utilized to solve the differential governing equation, and the expression for the deflection of the piezoelectric composite beams is obtained. The accuracy of the proposed method is validated by the finite element method. The bending response of the functionally graded piezoelectric composite beams is investigated through the proposed method. In the numerical examples, the effects of electrical load, actuator thickness, AFG beam thickness and AFG beam length on the electromechanical behavior of the functionally graded piezoelectric composite beams are studied.
The butterfly plastic zone theory based on Mohr Coulomb criterion has been widely used in coal mine production. In order to verify the universality of the theory, it is necessary to compare the distribution of plastic zone under different strength criteria. Based on the elastic-plastic mechanics, the principal stress distribution function around the circular tunnel is deduced in the paper, and the boundary and radius of the plastic zone under different strength criteria are calculated. The results show that the change laws of the plastic zone around the circular tunnel under different strength criteria has the following commonness: firstly, with the increase of the lateral pressure coefficient, the shape of the plastic zone presents the change laws of “circle ellipse butterfly”; Secondly, with the increase of the lateral pressure coefficient, the radius of the plastic zone is exponential distribution, while the characteristic value is different when the radius of the plastic zone is infinite. At same time, it shows that the butterfly plastic zone has a low sensitivity dependence on the strength criterion, no matter which strength criterion is adopted, and the butterfly plastic zone will inevitably appear in the surrounding rock mass of circular tunnel in the high deviator stress environment; The plastic zone with butterfly shape is highly sensitive to the stress change, and the small stress change may promote the expansion of the plastic zone. This result is significant for us to understand and prevent rock engineering disasters and accidents.
The basic constitutive equations of theory of mixtures obtained for a mixture of two linear elastic solids can be used as an alternative way to describe the mechanical behavior of binary composite materials. Determining the load ratios carried by each constituent solid of a binary composite is one of challenges of this theory. In this study, the results of directly calculating the ratios of external load carried by each constituent solid for the case of perfectly bonded interface between binary mixture constituents are discussed. Thus, the effects of loading type and volume fraction of the constituent solids to the load ratios carried by each constituent solid are investigated by using three different loading cases and three different volume fractions. Finally, displacement, stress and diffusive force results of two constituent solids using the calculated load ratios are given.
To evaluate the dynamic properties of a coupled structure based on the dynamic properties of its substructures, this paper investigates the dynamic substructuring issue from the perspective of response prediction. The main idea is that the connecting forces at the interface of substructures can be expressed by the unknown coupled structural responses, and the responses can be solved rather easily. Not only rigidly coupled structures but also resiliently coupled structures are investigated. In order to further comprehend and visualize the nature of coupling problems, the Neumann series expansion for a matrix describing the relation between the coupled and uncoupled substructures is also introduced in this paper. Compared with existing response prediction methods, the proposed method does not have to measure any forces, which makes it easier to apply than the others. Clearly, the frequency response function matrix of coupled structures can be derived directly based on the response prediction method. Compared with existing frequency response function synthesis methods, it is more straightforward and comprehensible. Through demonstration of two examples, it is concluded that the proposed method can deal with structural coupling problems very well.
For a vibration system, the best designed spring is compliant to a desired vibration mode while it is robust to other undesired modes. There are several types of spring design for displacing the proofmass along the x and y axes, however, very few designs of spring compliant to the z axis are introduced. Therefore, we propose a z axis microactuator in which the suspending spring is designed so that it is only compliant to vibration along the z axis. The suspending spring consists of straight beam stages mechanically coupled with each other via frames which are symmetrically designed around a center plate. The operation characteristics of the microactuator is investigated by theoretical expresses and numerical simulation. The frequency split between the z axis mode and undesired modes can obtain more than 45%. The operation frequency can be modified in a wide range, from 68 kHz to 400 kHz, by changing the dimensional parameters of spring beams. The spring beams can be lengthened to increase displacement in the z axis while the mode cross-talk is still suppressed. Compared to the previously reported researches, the current microactuator shows robustness to undesired vibration modes, which is potential for integration in low mode cross-talk multi-axis micro-stages and low-noise mechanical sensors.
The edge surface warping defect seriously affect the surface quality of strips. In this paper, a technology for diagnosis of warping defects in hot-rolled strip based on data-driven methods is studied. Based on the mechanism analysis of the warping defects, the process parameters affecting the warping defects were sorted out and used as the original input parameters of the defect diagnosis model. Firstly, a diagnostic model that combines the deep belief network and contribution plots of each dimensionality reduction layer is proposed. The deep belief network that integrates each dimensionality reduction layer can predict product defects more accurately and stably than the traditional deep belief network. Meanwhile, on the basis of the pre-judgment model, the method of contribution plot is further introduced to trace the defects, and the comprehensive diagnosis function of model pre-judgment and traceability is realized. Finally, collected the production data from a hot rolling production line for a period of time. Tested the model and predicted a hit rate of 85%. The main influencing factors of edge surface warping defects were determined that the rate of defect decrease with the increase of furnace temperature. When the heating temperature of the second stage of the heating furnace is higher than 1160°C, the incidence of defects is significantly reduced. Defect rate is relatively low within 240min of total furnace time. With the first and third pass phosphorus removal equipment turned on, the incidence of defects was relatively low.
In order to maintain the no-slip condition and the divergence-free property simultaneously, an iterative scheme of immersed boundary method in the finite element framework is presented. In this method, the Characteristic-based Split scheme is employed to solve the momentum equations and the formulation for the pressure and the extra body force is derived according to the no-slip condition. The extra body force is divided into two divisions, one is in relation to the pressure and the other is irrelevant. Two corresponding independent iterations are set to solve the two sections. The novelty of this method lies in that the correction of the velocity increment is included in the calculation of the extra body force which is relevant to the pressure and the update of the force is incorporated into the iteration of the pressure. Hence, the divergence-free properties and no-slip conditions are ensured concurrently. In addition, the current method is validated with well-known benchmarks.
Convective Heat Transfer Coefficient (CHTC) is a determining factor in building energy simulation (BES) tools for building thermal calculations. The accuracy of CHTC calculation has a direct effect on building energy analysis.This study aims to assess the impact of multiple parameters, namely temperature difference, wind speed, and wind direction on CHTC of building exterior surfaces. Then the overall high accuracy correlation based on these parameters for CHTC is provided. According to the specified values for temperature and velocity, Richardson’s number range from 0.1 to 10, representing a mixed heat transfer. The simulated results are compared with a wind tunnel experiment for validation. The standard k-epsilon model is used for turbulence simulation. Several cases are numerically simulated, considering various velocities, wind directions, and temperature differences. Results indicate that the studied parameters could be ranked as velocity, building orientation, and temperature difference in the order of effectiveness. All of the correlations used in EnergyPlus software for the exterior surface of the building are compared with the presented correlation and simulated data. The comparison shows that the proposed expression could predict CHTC for various angles, velocities, and temperature differences with an error of below 3%.
The performance of the solid fuel ramjet is accurately predicted using full part simulation of this propulsion system, where the flow fields of the intake, combustion chamber, and the nozzle are numerically studied all together. The conjugate heat transfer is considered between the solid phase and the gas phase to directly compute the regression rate of the fuel. The finite volume solver of the compressible turbulent reacting flow is utilized to study the axisymmetric three dimensional flow fields, and two blocks are used to discretize the computational domain. It is shown that the combustion chamber's pressure is changed due to the fuel flow rate's increment which must be taken into account in predictions. The results demonstrate that omitting the pressure dependence of the regression rate and also the effect of the combustor's inlet profile on the regression rate, which specially exists when simulating the combustion chamber individually, under-predicts the solid fuel burning rate when the regression rate augmentation technique is applied to improve the performance of the solid fuel ramjets. It is also illustrated that using the inlet swirl to increase the regression rate of the solid fuel augments considerably the thrust level of the considered SFRJ, while the predictions without considering all parts of the ramjet is not accurate.
A new derivation considering the non-linear terms has been proposed to calculate stiffness and damping coefficients for short hydrodynamic journal bearings lubricated with pseudo-plastic fluids. The proposed method has relaxed the constraint of small perturbation method applicable to only small values of non-Newtonian factor α. An analytical solution is also given. The non-linear Reynolds equation is solved with a more reasonable boundary condition ∂p*/∂z* = 0 at the location of z*=0 while the analytical pressure distribution is obtained by seven-point Gauss-Legendre integral formula. When the non-dimensional non-Newtonian factor α is small, the stiffness and damping coefficients of computed by the proposed method can agree well with those from small perturbation method, which could verify the proposed derivation. As for large non-dimensional non-Newtonian factor α, the stiffness coefficients
as well as the damping coefficients
decrease with the increasing of non-dimensional non-Newtonian factor α. The significance of the derivation is that it can relax the constraint of small α and simplify the computation process.
Battery-casing sealing is the key factor for secure travel of new energy vehicles. We constructed a relatively accurate mechanical-simulation model by selecting a constitutive model, analyzing the influence of thermal elongation, verifying the grid-independence and comparing numerically by the pressure-measurement film on the basis of studying the physical performance of a certain type of sealing material that had been used in battery-casings after aging. Based on a porous-media model and combined with changes of macroscopic and microscopic contact characteristics of materials at different times after aging, the evolution rule of sealing performance with time was analyzed quantitatively by calculating the leakage. By analyzing the structure of circular arc bulge on the surface of sealing material, the radius of circular arc bulge with better sealing performance was obtained, which could reduce the leakage of sealing structure during the material’s lifecycle.