Analysis Of Nonlinear Coupling Research Articles

Nonlinear thermo-electro-mechanical responses and active control of functionally graded piezoelectric plates subjected to strong electric fields

Functionally graded piezoelectric plates (FGPPs) are often exposed to extreme thermal environments and subjected to large amplitude excitation and strong electric fields. Accurately predicting the nonlinear behaviors of FGPPs under large thermo-electro-mechanical loads remains a considerable challenge. This paper proposes a comprehensive nonlinear coupled analysis model that considers geometric nonlinearity, piezoelectric nonlinearity, and the temperature dependence of piezoelectric parameters. The total Lagrangian incremental finite element equations for FGPPs under thermo-electro-mechanical loads are derived using Hamilton's principle, by employing the first-order shear deformation theory and the von Kármán nonlinear strain-displacement relationship. The accuracy of the model is validated through comparative studies. Based on this multi-nonlinear model, we further investigate the effects of geometric nonlinearity, piezoelectric nonlinearity, and temperature dependence on the nonlinear static bending, dynamic responses, and active control of FGPPs. This study demonstrates that considering these factors enables accurate prediction of the static, dynamic, and active control behaviors of FGPPs.

An Efficient Iterative Method for Vehicle-Track Nonlinear Coupled Dynamic Analysis Based on Explicit and Implicit Algorithms

An Efficient Iterative Method for Vehicle-Track Nonlinear Coupled Dynamic Analysis Based on Explicit and Implicit Algorithms

Study on the Residual Strength of Nonlinear Fatigue-Damaged Pipeline Structures

The heat alternation and bending during the service process of the pipeline structure are the key issues affecting its residual strength. The nonuniform plastic deformation of its cross-section causes nonlinear damage to the structure, which makes it difficult to calculate the residual strength of the overall structure. This study proposed a novel variable-strength material damage model with damage accumulation, which achieved the coupling analysis of structural damage and material fatigue residual strength, making the structural strength of nonlinear damage cross-section computable. Based on this, a theoretical ultimate load model for nonlinear damage cross-section and a finite element analysis model for dynamic material strength with damage accumulation were established. The analysis was conducted on the repeated banding damage to coiled tubing. The results showed that the residual yield strength of nonlinear damaged coiled tubing showed a trend of first rapid decrease and then slow decrease with damage accumulation, and the tensile displacement showed an increasing trend with damage accumulation. The ultimate internal pressure strength of nonlinear damaged structures showed a similar downward trend to the yield strength. The nonlinear damage coupling analysis model proposed in this study has significant practical engineering application value.

A novel view on the canonical ‘stretching-due-to-bending’ nonlinear effect: A slighly curved beam

The analysis of nonlinear coupling between flexural and longitudinal vibrations of ideally straight elastic beams is a classical topic in vibration theory. The boundary conditions usually applied in this analysis are formulated as immobile hinges, which generate the canonical ‘stretching-due-to-bending’ nonlinear effect. The key assumption in formulation of this model is neglecting the longitudinal inertia, which may be referred to as ‘static condensation’. The aims of this work are, first, to re-consider this problem from the viewpoint of a nonlinear theory of curved beams, and, second, employ alternative type of boundary conditions, known as class-consistent ones. A paradoxical difference in nonlinear parts of Duffing equations obtained in the limit of vanishing curvature of an initially curved beam and in the case of an ideally straight beam is demonstrated and explained.

A modified IHB method for nonlinear dynamic and thermal coupling analysis of rotor-bearing systems

This paper presents a modified incremental harmonic balance (IHB) method to analyze the nonlinear dynamic and thermal coupling characteristics of rotor-bearing systems after thermal balance. The IHB method is modified by tensor contraction and fast Fourier transform (FFT) to efficiently calculate the residual vector and Jacobian matrix. Nonlinear dynamic and thermal full coupling is implemented through the nonlinear part of the Jacobian matrix. The presented method achieves the simultaneous and efficient calculation of the motion and heat balance equations in the frequency domain according to the improvement measures. The effectiveness of the presented method is tested using the vibration response and temperature variation analysis for the coupled thermo-mechanical model of a rotor-ball bearing system. Furthermore, the performance comparisons show the good consistency of results between the presented method and the step-by-step (S-S) method, which is a partitioned iterative solution method for dealing with fully coupled problems in the time domain. The presented method has greater computational efficiency, more accurate temperature prediction, and better recognition of nonlinear phenomena in the system rather than the S-S method. Consequently, the presented method has a broad application prospect in solving fully coupled thermo-mechanical problems of more complex and higher dimensional rotor-bearing systems.

Concurrent multiscale analysis of anti-seepage structures in embankment dam based on the nonlinear Arlequin method

The scales of embankment dam and local anti-seepage structures (core wall or cut-off wall) differ heavily, which poses challenges to analyze both the global and local responses simultaneously. In this study, the nonlinear Arlequin method is introduced to evaluate the behavior of anti-seepage structures in embankment dam within a concurrent multiscale framework. Based on the energy blending approach, the governing equations are deduced, in which the material nonlinearity effect and the Arlequin coupling effect can be separated from each other. Then, a list of subroutines of ABAQUS is used to implement the proposed framework jointly. Multiscale analysis of elasto-plastic cantilever beam demonstrates the effectiveness of the proposed method. The effects of coupling operators are discussed, and constant weighting functions are recommended for nonlinear coupling analysis. The analyses of embankment dams indicate that the uneven settlement pattern and the resulted arching effect between the core and the shell as well as the complicated bending deformation state of cut-off wall can be well captured by the proposed method. It is affirmed that the nonlinear Arlequin method facilitates the increase of computational efficiency without losing much accuracy, showing great merits of modeling local nonlinearity and global response simultaneously under a concurrent multiscale framework.

Geometrically Non-Linear Vibration and Coupled Thermo-Elasticity Analysis with Energy Dissipation in FG Multilayer Cylinder Reinforced by Graphene Platelets Using MLPG Method

Geometrically Non-Linear Vibration and Coupled Thermo-Elasticity Analysis with Energy Dissipation in FG Multilayer Cylinder Reinforced by Graphene Platelets Using MLPG Method

Nonlinear magnetoelectric coupling in magnetostrictive-piezoelectric composites

Two micromechanical formulations are established for analysis of nonlinear magnetoelectric coupling in composite materials with 1-3, 0-3 and 2-2 connectivities. The studied two-phase composites are constructed by magnetostrictive and piezoelectric phases that exhibit significant material nonlinearity when each or all of them are subjected to large driving magnetic or electric fields. The simplified unit-cell model is first formulated followed by a reformulation of the Mori-Tanaka model so that a comparison can be made between two micromechanics models in terms of their mathematical structures and micromechanical predictions. In order to analyze the nonlinear composites, a secant linearization is employed for each constituent, concentration-factor tensors are introduced for bridging microscopic and macroscopic behaviors, and residual vectors are defined for quantitation of the errors resulted from the linearization process. Micromechanical simulations show that 1) magnetoelectric coupling can be modulated by the composite connectivity and constituent proportion, and 2) the field-dependent magnetoelectric responses leads to significant difference between linear and nonlinear predictions.

Understanding the seismic response of electrical equipment subjected to high–frequency ground motions

Ground motion studies in Central and Eastern United States (CEUS) show that the ground motion response spectra exceeds design spectrum of nuclear power plants in high–frequency range. To ensure safe shutdown of nuclear power plants in events where design spectrum is exceeded, the safety–related digital control systems and electrical equipment such as relays must be seismically qualified for high–frequency ground motions. Conventionally, uncoupled linear analysis of building and electrical cabinet is conducted and then seismic demands on equipment are evaluated. The conventional analysis ignores effects of various factors such as geometric nonlinearities, mass interaction between primary (building) and secondary (electrical cabinet) systems, etc. Ignoring such factors leads to unnecessarily high seismic demands on equipment. In this study, the seismic demands on equipment are evaluated by conducting both coupled and uncoupled analysis of linear primary system and linear as well as nonlinear secondary system. Various cases are analyzed where at least one mode of primary system is tuned with one mode of secondary systems. Each case is subjected to both low–frequency and high–frequency ground motions to compare the difference in response to each ground motion. The seismic demands on equipment are compared for coupled and uncoupled analysis as well as for linear and nonlinear systems. The results show reduction in seismic demands on electrical equipment for various nonlinear coupled analysis cases. The high seismic demands evaluated from linear uncoupled analysis may lead to exclusion of some electrical equipment which can be avoided by conducting coupled nonlinear analysis of primary–secondary systems and obtaining the realistic seismic demands on equipment.

Effect of Different Types of Middle Columns on the Seismic Performance of Single-Story Subway Station Structure

In view of the seismic weak component of the single-frame-type subway station structure, the three-dimensional (3D) time-domain nonlinear finite element static-dynamic coupling analysis model of interaction between soil and subway station structure is established by, respectively, using rectangular reinforced concrete (RRC) columns, circular reinforced concrete (CRC) columns, and prefabricated concrete-filled steel tube (CFST) columns with a quick-connection device proposed in this article. This analysis model is further used to investigate the influence of different types of middle columns on the seismic response characteristics of the underground structure, such as the interstory displacement angle, seismic damage, and dynamic response. The results show that, compared with the rectangular columns, the circular columns with the equal moment of inertia suffer less damage in the earthquake and have better seismic performance. The prefabricated CFST columns can effectively ensure that the middle columns of the station structure are not severely damaged and can be replaced quickly after the earthquake, which improves the overall seismic performance of the subway station structure and the rapid recovery ability of the structural function after the earthquake.

Phase tracking with Hilbert transform and nonlinear wave-wave coupling analysis on the HL-2A tokamak

A phase tracking method based on Hilbert transform algorithm is applied to the nonlinear wave-wave coupling analysis on HL-2A tokamak. Synthetic signal analysis is given to show the principle of phase analysis for the detection of nonlinear coupling. If the phase difference between two coherent modes is synchronized with the phase of a third mode, these three modes are nonlinearly coupled, vice versa. The time evolution of the phase of a coherent mode could be computed with Hilbert transform for experimental data, and a phase tracking flowchart is summarized. On HL-2A tokamak, the nonlinear coupling among two Alfvén modes (AMs) and a tearing mode (TM) has been confirmed with bicoherence analysis (Shi et al 2017 Phys. Plasmas 24 042509). With Hilbert transform, it is clearly observed that the phase difference between two AMs Δθ 12 is synchronized with the phase of the TM θ TM. The synchronization is confirmed with normalized cross-correlation. An alternative to check this synchronization is to observe the histogram of the phase difference Δθ 12 − θ TM.

An Enhanced Semi-Coupled Methodology for the Analysis and Design of Floating Production Systems

Abstract This work presents an enhanced hybrid methodology for the analysis and design of floating production systems (FPS). The semi-coupled (S-C) procedure exploits the advantages of coupled and uncoupled models, incorporated into a three-stage sequence of analyses that can be fully automated within a single analysis program, presenting striking reductions of computational costs. The procedure begins by determining, through a full nonlinear static coupled analysis, the mean equilibrium position of the FPS with its mooring lines and risers. Then, it automatically evaluates equivalent six degrees-of-freedom (6DOF) stiffness matrices and force vectors representing the whole array of lines. Finally, these matrices/vectors are transferred to the dynamic analysis, solving the global 6DOF equations of motion restarted from the static equilibrium position. This way, the S-C methodology represents all nonlinear effects associated with the lines and considers their influence on the dynamic behavior of the hull. However, in some situations, it could still overestimate dynamic amplitudes of low-frequency (LF) motions and/or underestimate amplitudes of line tensions. Thus, to improve the overall accuracy, enhanced procedures are incorporated to better represent damping and inertial contribution of the lines. Results of case studies confirm that this methodology provides results adequate for preliminary or intermediary design stages.

Nonlinear thermo-mechanical coupled analysis of high temperature effect on strength, contact stress and ultimate torque of tool joint

In this study, a NC35 tool joint with double shoulder is considered as the research object and studied by finite element method (FEM) using nonlinear thermo-mechanical coupled model and implicit & explicit conversion method. Von mises stress field, temperature field, contact stress, and ultimate working torque of tool joint under different axial loads at high temperatures are calculated and compared with those at normal atmospheric temperature. High temperature doesn't change the stress and contact stress distribution under make-up torque condition but reduces the value of stress and contact stress due to material properties decline. Ultimate working torque decreases with the increase of temperature under the same axial load. Coupled influence of axial load and temperature on shoulder contact state is analyzed. Furthermore, failure modes of tool joint under different temperatures and axial loads are discussed. According to the results of calculation, a guiding diagram considering safety factor is presented which can provide a safe operating range at normal atmospheric temperature and high temperature. It can help engineers choose appropriate operating parameters under different conditions.

Chiral constrained stent: Effect of structural design on the mechanical and intravascular stent deployment performances

The high mortality of atherosclerosis-caused cardiovascular disease has promoted the requirement of designing novel intravascular stents with comprehensive robust mechanical performances, which is critical for re-constructing the blocked artery and recovering the biomechanical functions of artery vessels during vascular interventional therapy procedures. In this study, a chiral constrained structure with zero/negative Poisson's ratio and robust expansion transformation ability is proposed through combining the axial constraint effect of tetrachiral element and the good stretchability of oscillating wave element along circumferential direction. Afterwards, through applying the theoretical prediction, experimental tests and finite element analysis, the mechanical properties and stenting performances of the chiral constrained structure are explored. The modified tetrachiral topology shows strong orthotropic after integration of oscillating wave strut profile, indicating its capability of handling radial loads without great longitudinal recoil (foreshortening). Finally, stent deployment performances have been evaluated through a highly nonlinear coupling analysis of the stenosed vessels system, in terms of transformation characteristics, dogboning, radial recoil, foreshortening, and plaque prolapse ratio, etc. Especially, remarkable non-conventional performances of anti-dogboning and anti-foreshortening are identified in chiral constrained stent. Synthetically index is generated to compensate the competing behaviors among the above terms, and to improve the comprehensive mechanical performances of chiral constrained stent. These results show the potential in generating a new family of the intravascular stent with chiral mechanical metamaterials and provide a promising clinical application in curing atherosclerosis.

Optimization of double-layer stress grading system for high voltage rotating electrical machines by electric field and thermal coupled analysis

Silicon carbide particle-loaded semi-conductive materials with electric field-dependent conductivity have been used for end-turn stress grading (SG) systems of high voltage rotating electrical machines for decades. Particularly, high voltage class turbogenerators use double-layer SG systems, at which two SG materials with different conductivities are applied, to reduce power dissipations within the SG materials. To prevent the excessive local heating of the SG material and resulting flashover, the field-dependent conductivities of the two SG materials, as well as length of the SG layer in the longitudinal direction along a coil, were optimized, by a nonlinear transient electrical field and thermal coupled analysis. The field-dependent conductivities of the SG materials were adjusted to the suitable ones by changing the average diameter of silicon carbide particles. Then, the appropriate length of the SG layer was selected to minimize the temperature rise in the system. As a result, the newly optimized double-layer SG system showed a 20% lower temperature rise, and more than 15% higher flashover voltage than the conventional ones. Therefore, the effectiveness of the optimized double-layer SG system is successfully confirmed.

Static tension test and the finite element analysis of constant resistance and large deformation anchor cable

Compared to the traditional anchor cable, the constant resistance and large deformation anchor cable (constant resistance and large deformation anchor cable) has good applications in many fields of geotechnical engineering. Through the indoor static tension test, this study reveals the variation law of constant resistance, axial strain, the outer diameter of the sleeve, and the thermal effect of constant resistance and large deformation anchor cables during static tension. The ANSYS software was used for the first time to establish the nonlinear thermomechanical coupling analysis model of the finite element structure of constant resistance and large deformation anchor cables for the numerical calculation and analysis of static tension mechanical properties of constant resistance anchor cables. The experimental results that the average elongation of this batch of constant resistance anchor cables is 905 mm with an average elongation rate of 45.2% and an average constant resistance of 650 kN prove that constant resistance anchor cables are characterized by good constant resistance and large deformation, which can meet the requirements of deep soft rock roadway support and advanced landslide monitoring. The numerical simulation results show that the elongation of this type of anchor cables is 902 mm with an elongation rate of 45.1% and a constant resistance of 660 kN, which are basically consistent with the experimental results, indicating that numerical simulation is relatively accurate for testing the mechanical property of constant resistance and large deformation anchor cables, and the combination of the indoor test and numerical simulation provides the reference for engineering practice and design optimization of constant resistance and large deformation anchor cables.

A numerical model for non-linear coupled analysis of the seismic response of liquefiable soils

A simplified model to reproduce the pore pressure build-up until liquefaction under seismic shear loads is implemented in a one-dimensional code for loosely coupled site response analysis of effective stress. One-dimensional consolidation relationships are also integrated into the formulation to simulate both the generation and dissipation of excess pore water pressure. The performances of the code are evaluated by analysing an ideal soil profile, a centrifuge model test and an instrumented test site. The comparisons between records and simulations highlight that notwithstanding the simplicity of the proposed approach, the code provides reliable predictions.

Geometrically nonlinear coupled analysis of thin-walled $$\hbox {Al/Al}_{2}\hbox {O}_{3}$$ Al/Al 2 O 3 FG sandwich box beams with single and double cells

In this study, a geometrically nonlinear coupled analysis of thin-walled $$\hbox {Al/Al}_{{2}}\hbox {O}_{{3}}$$ functionally graded (FG) sandwich box beams with single and double-cell sections is presented. The material properties such as Young’s modulus and Poisson’s ratio are continuously graded through the thickness of wall. The geometric nonlinearity is considered in the von Karman sense, and the analysis model includes the effects of elastic coupling and restrained warping. The nonlinear governing equations are derived and solved by the Newton–Raphson method. The displacement-based one-dimensional finite element model using the Hermite cubic interpolation polynomials is employed with the scope to discretize the nonlinear governing equations. Numerical results are obtained for $$\hbox {Al/Al}_{{2}}\hbox {O}_{{3}}$$ FG sandwich box beams with single- and double-cell sections. Three types of material distributions are considered to investigate the effects of geometric nonlinearity, gradient index, thickness ratio of ceramic, material ratio, span-to-height ratio, and boundary conditions on the nonlinear coupled responses of $$\hbox {Al/Al}_{{2}}\hbox {O}_{{3}}$$ FG sandwich box beams. Numerical results show that above-mentioned effects play an important role on the nonlinear behavior of FG sandwich box beams.

Influence of the modulation format on the nonlinear impairments in space division multiplexed systems

This paper is focused on the analysis of nonlinear mode coupling in space division multiplexed communication systems with linear mode coupling. Simultaneous propagation of modulated mode channels is simulated by numerical solving of the system of generalized coupled nonlinear Schroedinger equations. Different types of modulation format are simulated and corresponding nonlinear impairments are presented. We shown that QAM-modulated signal is more robust for increasing of nonlinear impairments due to the linear mode coupling than NRZ-coded signal.

Statistical analysis of nonlinear coupling in a WDM system over a two mode fiber.

We study the effect of nonlinear coupling in a WDM configuration over a two-mode fiber. A statistical analysis is presented that takes into account the effect of the random phase-sensitive amplification or depletion. Our results show high nonlinear coupling between the modes. We have quantified the channel power fluctuations, due to the wave phase random variations, at the output of the fiber. We also investigate the effect of random linear mode coupling on the nonlinear mode coupling.