Nonlinear Vibration Analysis Research Articles

Establishment of a multi-clearance coupled 3D floating nonlinear model and vibration analysis for a coaxial reverse closed differential herringbone gear transmission system

Establishment of a multi-clearance coupled 3D floating nonlinear model and vibration analysis for a coaxial reverse closed differential herringbone gear transmission system

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Stability analysis of nonlinear synchronous vibration in an inclined rotor system supported by journal bearing with variational gravity

In vertical rotating shaft-bearing systems, synchronous vibration undergoes destabilization and stabilization owing to the self-excited vibration. Recently, these phenomena have been clarified numerically, experimentally, and analytically based on a newly proposed analytical method. In this method, a two-step linearization of the nonlinear journal bearing (JB) force and generalized eigenvalue analysis are proposed to directly determine the stability of the synchronous orbit. However, this method cannot be used directly for inclined-rotor systems with a large gravitational effect. Moreover, stability changes caused by gravity variations in inclined-rotor systems have not been fully investigated. This study extended the analytical method to one with weighted average dynamic coefficients to efficiently predict the stability changes of synchronous whirling vibrations in inclined rotor systems. The extended analytical method clearly clarifies gravity-induced stability changes in comparison with the numerical (shooting) method. Our analytical method enhances the ability of rotor dynamics software to calculate the stability thresholds of inclined rotor systems with gravity variations.

Nonlinear vibration analysis of multi-support oil-tank system in aero-engine based on asymptotic methods

This article is primarily focused on the complicated nonlinear vibration behavior of an aero-engine lubricating oil-tank system with multiple nonlinear pedestals. First, the rubber damping ring’s nonlinear factors are introduced into a cubic nonlinear dynamic model of lubricating oil-tank system. The nonlinear system parameters are identified by testing a simplified aero-engine lubricating oil-tank structure. Then, the nonlinear dynamic model is solved via asymptotic approach, and results are confirmed using Runge-Kutta numerical analysis approach. The system’s vibration responses and amplitude-frequency curves are also acquired, and influence of system parameters on nonlinearity is analyzed. Finally, an experimental investigation on the simplified oil-tank is performed. The nonlinear vibration characteristics of the rubber damping ring and its vibration reduction mechanism are verified using vibration transmissibility. The experimental results are consistent with numerical results. This paper’s recommended analysis approach has engineering significance for vibration and noise reduction design of aero-engine components.

Nonlinear buckling and free vibration analysis of auxetic graphene origami composite beams under nonuniform thermal environment

This study examines the thermo-mechanical behavior of auxetic metamaterial beams enhanced by graphene origami (GOri) under spatially varying nonuniform temperature distributions (SVTD). Utilizing Timoshenko beam theory considering von-Kármánn type nonlinear strain–displacement relationship, GOri beams are modeled as layered structures. The Ritz method is employed to solve equilibrium equations, analyzing the impact of GOri distribution patterns, content, and folding degree on post-buckling and vibration paths. The effects of five SVTDs, three end conditions, and three GOri distribution patterns on buckling, post-buckling behavior, and nonlinear free vibration characteristics are explored. Findings reveal that the parabolic temperature distribution with peak temperatures at beam ends (P-MAE) results in higher critical temperatures and nonlinear free vibration frequencies. This research provides crucial insights into the design and optimization of GOri-enabled metamaterial structures in complex thermal environments, highlighting the significant influence of nonuniform temperature distributions along the beam’s length.

Nonlinear vibration analysis of sandwich plates with inverse-designed 3D auxetic core by deep generative model

Building on a deep generative model (DGM), this paper introduces an innovative sandwich plate structure featuring an inverse-designed auxetic 3D lattice core and conducts a detailed investigation of its nonlinear vibration characteristics and effective Poisson's ratios under various parameter settings. By incorporating a conditional estimator and quality loss evaluation functions, the enhanced conditional generative adversarial networks are capable of designing 3D truss auxetic topologies that achieve customized negative Poisson's ratios without reliance on subjective experience. Additionally, lattice specimens are created using 3D metal printing, and the mechanical properties of these DGM-based 3D auxetic structures are validated through vibration experiments and finite element models. These structures exhibit significantly superior natural frequencies compared to those obtained through conventional topology optimization methods reported in existing literature. The study also explores the impact of different functionally graded configurations, temperature variations, boundary conditions, and dimensional parameters on the natural frequency, nonlinear vibration response, and effective Poisson's ratio of the inverse designed auxetic sandwich plates.

Nonlinear bending and vibration analysis of a variable-width piezoelectric nanoplate with flexoelectric effects

Nonlinear bending and vibration analysis of a variable-width piezoelectric nanoplate with flexoelectric effects

Nonlinear dynamic modeling and vibration analysis for early fault evolution of rolling bearings

In rotating machinery, the condition of rolling bearings is paramount, directly influencing operational integrity. However, the literature on the fault evolution of rolling bearings in their nascent stages is notably limited. Addressing this gap, our study establishes an innovative nonlinear dynamic model for early fault evolution of rolling bearings based on collision impact. Firstly, considering the fault evolution characteristics, the influence of the rolling element and fault structure, the dynamic model of early fault evolution between the rolling element and the local fault is established. Secondly, according to the Hertzian contact deformation theory, a nonlinear dynamic model of rolling bearings expressed as mass-spring is established. Thirdly, the energy contribution method is used to integrate the fault evolution model and the nonlinear dynamic model of the rolling bearing. A nonlinear dynamic model of early fault evolution of the rolling bearing is proposed by using the Lagrangian equation. Comparing the simulation results of the nonlinear dynamic with the experimental results, it can be seen that the numerical model can effectively predict the evolution process and vibration characteristics of the fault evolution of rolling bearings in the early stage.

Analysis of nonlinear vibration of lateral-torsional coupling for drill string in deviated well

To clarify the motion characteristic of the drill string in deviated well, the nonlinear dynamic model of lateral-torsional coupling for drill string system is established by the Lagrange equation. This model incorporates the contact between the drill string and borehole wall, torque dissipation, and borehole trajectory effects. Additionally, the contact behavior using linear elastic contact model is simulated. Meanwhile, the torque transfer law in the drill string system is described by a discrete torque-drag model. Finally, numerical simulations are employed to determine the dynamic properties of the drill string system. The results reveal that friction losses in drill string systems are increased with higher well inclination angles. The motion of BHA along the x direction is predominantly concentrated near the wellhole center at inclination angle of 65°, while in the y direction it primarily focuses on the low side of the wellhole. An increase in inclination angle leads to a more prominent occurrence of stick-slip motion in the drill string. When inclination angle more than 25°, there is a slightly higher collision frequency observed between the BHA and the low side of the borehole wall compared to that with the upper side. When increasing the WOB (weight on bit) to 160 kN, stick-slip motion becomes more pronounced within the drill string. Through parametric dynamics analysis of the drill string system, the rotary speed can be controlled in range from 40 to 70 r/min, and the WOB should be restricted in range from 20 to 40 kN in well depth 5000 m.

Analytical model of curvic coupling and application in nonlinear vibration analysis of a squeeze film damper - rolling bearing - rotor system

The curvic coupling has been extensively employed in the rotor system of aero-engine. Effects of the radical slip of the teeth and damping are usually neglected in the traditional models of the curvic coupling. Additionally, there are only a few researches on the vibration characteristics of the rotor system with curvic coupling, squeeze film damper (SFD) and rolling bearing. In this paper, an analytical model of the curvic coupling is proposed. The nonlinear vibration analysis of a SFD - rolling bearing - rotor system with curvic coupling is furtherly carried out. The Jenkins element is adopted to simulate the dynamic behaviors of the curvic coupling in the model. The hysteresis curves of the analytical model show good agreement with the results of the three-dimensional (3D) finite element (FE) simulation. After that, the dynamic equation of a SFD - rolling bearing - rotor system with curvic coupling is formulated. Subsequently, detailed parametric analyses, including preload, number of teeth and pressure angle, are conducted to investigate the vibration characteristics of the rotor system. Results show that the curvic coupling mainly produces stiffness loss and damping at the interface of the curvic coupling. The motion stability of the rotor system can be enhanced by increasing the preload, number of teeth at multiple curvic couplings and pressure angle. Moreover, the vibration level of the rotor system initially decreases and then increases as the number of the teeth and pressure angle increase. Finally, the numerical results are validated to be reasonable by an experimental study.

Numerical analysis of fractional nonlinear vibrations of a restrained cantilever beam with an intermediate lumped mass

This paper focuses on the numerical investigation of the fractional nonlinear oscillator for a restrained cantilever beam with an intermediate lumped mass. A numerical approach based upon the fractional complex transformation and the global residue harmonic balance method (FCT-GRHBM) is suggested for approximately solving this fractional oscillation system of fifth-order nonlinearity. The approximated fractional periodic solutions and frequencies are provided by FCT-GRHBM, which are not touched in the existing literature. Numerical results and sensitive analysis with respect to different parameters are shown to confirm its efficiency.

A nested non-intrusive stochastic isogeometric method for nonlinear thermal vibration of FGM plates under random loading

This paper introduces an adaptive nested non-invasive dynamic SIGA method based on RBFNN for the nonlinear thermal vibration analysis of FGM plates under random loading. This method is robust and accurate in high-dimensional input spaces regardless of the sample sequence, addresses the low convergence rate of QMCS, and solves the stochastic dynamic response probability density function under random loading. Firstly, the multidimensional input space for random loading is constructed based on several mutually independent random variables via the stationary Gaussian stochastic process simulation technique. The nonlinear FGM plate model subjected to random loading in the thermal environment is modeled using HSDT with von Kármán strain-displacement relation within the IGA framework. Subsequently, a nested non-invasive dynamic response surface analysis method, SIGA-RBFNN, is proposed based on the RBFNN technique. Analysis of the FGM plate response under random loading demonstrates that SIGA-RBFNN, compared to tensor-product-based SIGA methods, is less affected by sample sequence types. It effectively addresses high-dimensional stochasticity and offers significant advantages in robustness, accuracy, and efficiency. Finally, SIGA-RBFNN compensates for the low convergence speed of QMCS and successfully solves the FGM plate displacement response statistics and probability density function under random loading.

Nonlinear free vibration analysis of the rectangular conductive elastic plate in magnetic field based on homotopy perturbation method

AbstractThis article tries to investigate the nonlinear free vibrations of the rectangular conductive elastic plate in uniform magnetic fields under the classic plate theory considering nonlinear strain‐displacement. The formulation of the governing equations integrates the electromagnetic forces arising from the motion of the plate. The nonlinear motion equations are dimensionless, which takes the effect of in‐plane inertia into account. The equations are solved by the Galerkin method and homotopy perturbation method (HPM). The effectiveness of the solution is verified. According to the solutions by HPM, the effects of the initial conditions, length‐to‐thickness ratio, and magnetic induction intensity on the nonlinear free vibrations behavior of conductive elastic plates are discussed.

Nonlinear free vibration analysis of imperfect cylindrical panels with discontinuous unilateral elastic base

In this work, the nonlinear free vibration analysis of the imperfect cylindrical panels in contact with discontinuous unilateral elastic base are conducted, evaluating the influence of the type of contact, unilateral or bilateral, and the contact area of the elastic base on the natural frequencies and nonlinear frequency-amplitude relations. For that, the structural cylindrical panel model considers the Donnell's nonlinear shallow shell theory to obtain the partial differential equilibrium equation and the compatibility and continuity equation. To represent the unilateral capability of the elastic base, a signum function is inserted in the reaction force of the elastic base to describe its dependence of the transversal displacement field of the cylindrical panel. To apply the elastic base in certain subdomain of the cylindrical panel, a Heaviside-type function is also inserted into elastic base's reaction forces. The nonlinear equilibrium equation is discretized by the Galerkin method, using a consistent transversal displacement field that it was obtained from a perturbation technique. The discretized set of equilibrium equations is employed to obtain the natural frequencies and the nonlinear frequency-amplitude relations, evaluating the influence of the unilateral contact and the contact region of the elastic base on these results. Depending on the signal of the imperfection's magnitude and the type of contact of the elastic base, the imperfect cylindrical panel can display an initial gap between the cylindrical panel and the elastic base, and this possibility is also investigated in this work. From the numerical results, it is observed that the unilateral elastic base applies less structural stiffness than the bilateral elastic base, decreasing the natural frequencies for the same imperfect cylindrical panel. The localization of the elastic base in the cylindrical panel also affects the natural frequencies, increasing or decreasing them depending on the modifications on the structural stiffness. The frequency-amplitude relations are strongly influenced by both unilateral contact of elastic base and the type of the contact consideration between the cylindrical panel and elastic base, exhibiting an intricated nonlinear behavior.

High-frequency nonlinear vibration analysis through low-frequency stereo-camera systems

This paper describes a new methodology that expands the capabilities of low-frame, high-resolution stereo-camera systems in studying the dynamic behavior of components in the presence of nonlinear phenomena. A new downsampling technique called the Smoothed Harmonics Analysis (SHA) is proposed. This technique addresses the limitations due to the low-frame rate cameras for the study of high-frequency periodic steady-state nonlinear oscillations. SHA enables accurate reconstruction of downsampled signals, thus opening up numerous potential applications. The feasibility of this technique is demonstrated by analyzing the motion of a beam with nonlinear behavior. The nonlinearity is caused by intermittent contact while the beam is subjected to harmonic excitation.

Nonlinear forced vibration analysis of doubly curved shells via the parameterization method for invariant manifold

Nonlinear forced vibration analysis of doubly curved shells via the parameterization method for invariant manifold

Nonlinear free vibration analysis of moderately thick sandwich plates with viscoelastic core using finite strip method

Nonlinear free vibration analysis of moderately thick sandwich plates with viscoelastic core using finite strip method

Nonlinear dynamic modeling and vibration analysis for flexible tethered satellite systems under large deformations

The escalating threat posed by space debris necessitates innovative approaches for its removal. This article presents a comprehensive mathematical modeling and dynamic analysis of a flexible tethered satellite system (FTSS) in the post-capture phase, taking into account nonlinear strain effects for the flexible appendages. The FTSS consists of a rigid central body satellite, two identical flexible panels, and a towing mass that manipulates the satellite through a tether. We develop a detailed dynamic model that accurately represents the system’s three-dimensional motion, incorporating the rigid body’s 6 degrees of freedom (DOF), the tether’s 3 DOF motion, and two modal generalized coordinates for each panel. The extended Hamilton method is employed to derive this model, enabling us to investigate the conditions under which nonlinear strain considerations become critical. The findings of this article reveal that nonlinear strain effects can profoundly impact the system’s dynamics under certain geometric and forcing conditions, often overlooked in previous studies. In these scenarios, the panel strains exceed the linear regime, necessitating the use of nonlinear models for accurate representation. This work emphasizes the importance of incorporating nonlinear strain terms in the dynamic analysis of FTSSs, particularly when dealing with large deformations and high-amplitude vibrations encountered in debris removal applications.

Application of bilateral iterative displacement control method to nonlinear free vibration analysis of dual-FG nanocomposite circular plates

This paper studies the geometrically nonlinear free vibration of a novel nanocomposite circular plate. The matrix of the nanocomposite structure is made of functionally graded (FG) polymer, and the distribution of graphene platelets (GPLs) as the reinforcement is assumed based on the five various linear FG models. Therefore, this novel nanocomposite is called dual-FG. The Voigt rule of mixture and Halpin-Tsai method are employed to homogenize FG polymer, and distribution of the GPLs within the matrix, respectively. Moreover, the whole structure is fixed on a nonlinear Kerr elastic foundation. The displacements of the plate are estimated by means of the first-order shear deformation theory (FSDT). Von-Kármán type of geometrically nonlinear relations expresses the plate's strains. The generalized differential quadrature (GDQ) technique, bilateral iterative displacement control method (BIDCM), and the weighted residual Galerkin procedure are implemented to extract the free vibration characteristics of the structure. The developed structure is validated with those reported in the open literature. A comprehensive parametric study is conducted to illustrate the effect of various parameters on the dynamic response of the dual-FG nanocomposite circular plate. It will be observed that the influence of the volume fraction and distribution model of GPL is more pronounced on the vibration frequency in the FG matrix. It was noted that the volume fraction of graphene platelets (GPL) and the power-law index of the matrix exhibit a direct and inverse relationship, respectively, with the natural frequency of the structure. Furthermore, the V-GPL model exhibits the highest percentage growth in nonlinear frequencies, while the Λ-GPL model shows the least growth. This observation is particularly pronounced for plates with hinged boundary conditions.

Nonlinear Vibration Analysis of Specially Orthotropic Micro-plates with Partial Crack and Varying Thickness Submerged in Fluid

Nonlinear Vibration Analysis of Specially Orthotropic Micro-plates with Partial Crack and Varying Thickness Submerged in Fluid