Nonlinear Vibration Characteristics Research Articles

Analysis of nonlinear vibration characteristics in all-composite honeycomb-core sandwich panel with material and geometric nonlinearity

Analysis of nonlinear vibration characteristics in all-composite honeycomb-core sandwich panel with material and geometric nonlinearity

Research on nonlinear dynamic vertical vibration characteristics and control of roll system in cold rolling mill

In order to address the vertical vibration phenomenon of the working roll during the rolling process, taking into consideration the nonlinear factors of the rolling interface and the roll system, this study establishes a nonlinear excitation vertical vibration model based on dynamic rolling force. The impact of nonlinear factors on system stability and vibration characteristics is analyzed. The study reveals that nonlinear damping and linear stiffness exhibit significant effects through time delay characteristics. Nonlinear stiffness has a drastic impact on system stability, while increasing system damping effectively reduces the amplitude and narrows the resonance region. By employing averaging method and singular value theory, the stability of the cold rolling mill roll system is analyzed under non-autonomous and autonomous states. A combined time-delay feedback controller is proposed, which effectively suppresses the system’s large-scale vibration by adjusting the control gain and time delay parameters. MATLAB simulations are conducted to validate the accuracy of the control strategy, providing theoretical support for vibration prediction and system design in rolling mills.

Nonlinear vibration characteristics and damage detection method of blade with breathing fatigue crack

In aero-engine, blades operate under harsh conditions for extended periods, which makes them highly susceptible to fatigue cracks. The localized and nonlinear structural changes caused by blade crack lead to complex vibration characteristics that are not well understood, posing challenges to the identification of these cracks. This paper proposes an approach for identifying breathing fatigue crack in compressor blade, leveraging the nonlinear features induced by the cracks. Crucial sensitive characteristics are extracted and a crack indicator for accurate crack detection is defined. Initially addressing the typical morphology of fatigue breathing cracks, a dynamic model of blade with cracks is developed to analyze their impact on the natural frequencies. Nonlinear contact forces are introduced to characterize the "breathing" effect of the fatigue crack, allowing for the determination of the harmonic distribution patterns in the blade's vibration response under various excitation conditions. A finite element model is then established considering the crack morphology, by adopting the contact element. Based on that, the nonlinear response characteristics associated with the blade's primary, sub-harmonic, and super-harmonic resonances are explored. A crack-sensitive parameter is defined and extracted from the nonlinear responses, under different crack propagation stages. At last, effectiveness and reliability of the defined parameter for identifying cracks is validated through a vibration fatigue test.

Experimental research on nonlinear vibration characteristics of double-layer mining string for deep-sea hydrate extraction under internal and external flow excitation

The vibration mechanism of the deep-sea hydrate mining string is extremely complex due to the combined effects of internal gas–liquid solid multiphase flow, structural contact collision, soil creep effect, and external ocean random load. Based on this, using the principle of similarity, a simulation experimental platform for the vibration of double-layer mining riser in deep-sea hydrate wells under internal and external flow excitation is developed, considering the vortex-induced effect of external flow field on the mining riser in the ocean section (which can simulate a maximum ocean flow velocity of 0.5 m/s), the three-phase flow-induced effect of gas–liquid–solid inside (which can simulate a maximum flow velocity of 2.0 m/s), and the coupling effect of mining string–conductor anchor node (CAN)–seabed. The influence of particle size, phase ratio, three-phase flow, and external flow velocity on the vibration response characteristics and nonlinear behavior of mining string are investigated. It is found that the vibration of vertical string is significantly affected by external ocean currents and internal three-phase currents. The vibration displacement amplitude of the horizontal section (average 0.08 mm) is significantly smaller than those of the vertical section (average 70 mm). The strong vibration positions of the vertical and horizontal sections of the mining string are different, in that the vertical section is mostly located below the middle section (just at 1800–2400 mm), while the horizontal section is mostly located at the three-phase inlet (just at 500 mm). The vertical section of the mining string presents a motion trajectory of oblique straight line, wide oblique straight line, or approximately wide oblique straight line, while the horizontal section is mostly a chaotic trajectory or an “8”-shaped chaotic trajectory. The decrease in particle mesh size and the increase in solid-phase proportion are reflected in the difficulty and accumulation of particle transport, leading to an increase in vibration displacement, as well as a decrease in vibration displacement amplitude and vibration energy. When the particle size set as 50 mesh, the displacement of mining string is largest, just for 110 mm of vertical section and 0.08 mm of horizontal section. The increase in the proportion of gas phase will lead to changes in the flow state of multiphase flow, which will affect the vibration displacement amplitude of the mining string to varying degrees. The increase in three-phase flow velocity further induces vibration of the mining string, and when the flow velocity is between 1.5 and 1.75 m/s, it will resonate with the string system, resulting in a sudden increase in the amplitude of vibration displacement. The research results can effectively guide operations and improve the service life of deep-sea hydrate mining riser.

Nonlinear vibrations of three-phase composite truncated conical shells affected by complex factors under 1:1 internal resonance

The investigation into the nonlinear vibrations of the three-phase composite truncated conical shell structure is still in its early stages, which limits its practical implementation. This paper involves calculating equivalent physical property parameters for the three-phase composite materials and establishing a nonlinear dynamic model for the truncated conical shells. The study examines the nonlinear vibration characteristics of the shells under various conditions, considering factors such as temperature, humidity, reinforcement components, and external excitation. It is observed that temperature and humidity changes have significant influences on the structure's resonant responses, with varying effects for the driving mode and accompanying mode. The addition of GPLs or carbon fiber as reinforcement components weakens the resonant response amplitude with an increase in their content. External excitation is identified as a noteworthy energy input source that significantly impacts the nonlinear vibration characteristics of the three-phase composite conical shell structure, thereby amplifying the resonant responses and complicating the nonlinear dynamic behaviors. The findings hold significant value for guiding the design of advanced composite structures in future engineering.

Large-amplitude nonlinear vibrations characteristics of bi-directional functionally graded plate having microstructure defects in hygro-thermal environment

The present article investigates the nonlinear hygro-thermal vibration characteristics of bi-directional functionally graded plates (BFGP) with microstructural defects. The distribution of material properties is anticipated to vary gradually along both thickness and length directions according to the modified power-law distribution. A novel expression has been developed to solve for the nonlinear temperature variation along the thickness of the BFGP. The micro-structural defects in terms of porosity have been incorporated in the formulation using a newly developed porosity model for a BFGP. A refined non-polynomial trigonometric higher-order shear deformation theory (HSDT) with a von Karman sense of geometric nonlinearity has been employed for the vibration response of BFGP. The finite element formulation has been carried out utilizing the C0 continuous Lagrangian quadrilateral element with nine nodes and eight degrees of freedom per node. The equations of motion have been derived using a variational approach. Various validation and comparative studies have been conducted to substantiate the current formulation's authenticity. The effect of the geometric nonlinearity, boundary constraints, volume fraction index along thickness (n) and volume fraction index along length (q), porosity index, temperature, and moisture concentration difference on the vibration frequency ratios (VFR) has been covered in depth. The VFR is more sensitive to the volume fraction indices (VFI) ' n′ than 'q'. Incorporating porosity decreases the VFR of BFGP, but it increases at higher amplitude ratios when BFGP becomes more porous. The VFR of BFGP exhibits nonlinear behavior with increasing moisture concentration and also varies non-linearly with the rise in amplitude ratio due to the hygro-thermal environment.

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 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 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.

Enhancing energy capacity of the car’s hood door under excitation frequency via functionally graded triply periodic minimal surface material: Application of machine learning and mathematical simulation

This study investigates the nonlinear dynamic response and vibration characteristics of a car’s hood door, focusing on its energy capacity under various excitation frequencies. The hood door is modeled using a functionally graded triply periodic minimal surface (FG-TPMS) material, which offers superior mechanical properties and lightweight design. The analysis is conducted using a higher-order shear deformation theory (HSDT), which accounts for shear deformations more accurately than classical theories. The incorporation of von Karman nonlinear terms captures the geometric nonlinearity due to large deformations, providing a realistic simulation of the hood door’s behavior under dynamic loads. To solve the complex equations of motion derived from the HSDT and von Karman terms, a fourth-order Runge–Kutta method is employed. This numerical method ensures accurate time integration and stability of the solution. The dynamic response is further analyzed to determine the energy absorption capacity of the hood door material, crucial for safety and durability in automotive applications. Validation of the numerical model is performed using previous published articles and a hybrid machine learning algorithm, which combines data-driven approaches with traditional physics-based models. This hybrid validation enhances the accuracy and reliability of the predicted responses, ensuring that the proposed model can be effectively used in the design and optimization of car components. The results demonstrate the potential of FG-TPMS materials in automotive applications, offering improved energy absorption and vibration control, which are essential for enhancing vehicle safety and performance.

Nonlinear characteristics in the cylindrical roller bearing with raceway defects

Cylindrical roller bearings (CRBs) are subjected to significant cyclic stress under extreme operating conditions. This leads to the formation of localized wave defects on the raceway surface, such as burn. Thus, a new mathematical model is proposed to consider the local wave defects on the raceway caused by burns in this paper. Further, a dynamic model of CRB incorporating raceway defects is developed based on the contact relationships between components, and the proposed model is verified by measured acceleration responses. The effects of local wave defects on the nonlinear vibration characteristics of the bearings are studied and the results show that an increase in the number of defect waves reduces the additional displacement of rollers passing through the defect area, obscuring signal characteristics induced by the defect. Moreover, the presence of the defect influences the nonlinear interaction between the roller and raceway, which subsequently affects the cage whirling motion. This study of bearing dynamic behavior in this paper can contribute to the condition monitoring of bearings.

Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells

This study utilizes a semi-analytical approach to examine the nonlinear dynamic responses of multilayer functionally graded (MFG) cylindrical shells reinforced by FG spiral stiffeners (FGSSs), which may have symmetric or asymmetric angles, under a thermal condition. It is presumed that the temperature is distributed across the thickness direction. The shell includes three layers: an outer ceramic-rich layer, a middle FG layer, and an inner metal-rich layer. By applying classical shell theory (CST), the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the problem of nonlinear vibrations (NVs) has been addressed. Furthermore, the method of multiple scales (MMSs) is applied to investigate the nonlinear vibrational characteristics of the MFG cylindrical shells reinforced by FGSS, particularly focusing on the 1:2:4 internal resonance and the subharmonic resonance of order 1/2. This study finds that FG spiral stiffeners with symmetric or asymmetric angles and ambient temperature significantly affect the vibrational properties of the MFG cylindrical shells reinforced by spiral stiffeners.

Vibration control of nonlinear viscoelastic systems with displacement delay feedback

In this study, the nonlinear vibration characteristics of a nonlinear Zener model under harmonic excitation, equipped with linear and nonlinear displacement delay feedback control, were investigated. The amplitude–frequency curve of the system’s main resonance was computed using the multi-scale method. Stability conditions for the system were then established based on the Lyapunov stability theory. The influence of several parameters on the system’s dynamic behavior was also analyzed, including time delay, displacement feedback gain coefficient, nonlinear term coefficient, damping coefficient, and external excitation. The findings revealed that the nonlinear displacement feedback gain coefficient was observed to exert a more substantial effect on the system’s amplitude than other factors. Further, the nonlinear displacement delay feedback gain coefficient and time-delay value diminish the amplitude of the vibration, leading all solutions to achieve a stable state. In instances with time-delay control, the impact of the main system parameters on system vibration was significantly diminished. The aim of this study is to provide a theoretical basis for the implementation of displacement delay controllers in nonlinear viscoelastic systems.

Three-dimensional nonlinear vortex-induced vibrations of risers under internal gas-liquid and external shear flows

A novel three-dimensional (3D) dynamic model is proposed to explore the nonlinear vortex-induced vibration (VIV) characteristics of top-tension risers under the combined action of internal gas-liquid two-phase flow and external shear flow. The van der Pol equation is used to evaluate the interaction between the riser and the external shear flow. The nonlinear governing equations are established through Hamilton's principle, and they are discretized by the Galerkin method and solved via the Runge-Kutta method. The VIV responses calculated by the proposed nonlinear dynamic model are compared with the previously experimental and computational fluid dynamics (CFD) results, demonstrating the effectiveness and accuracy of the present theoretical method. The influences of the internal flow effect, the tension and the shear parameter of the external flow on the VIV responses of the riser are analyzed. The results show that when the internal flow effect is not considered, the transition of the external flow from uniform flow to shear flow leads to an increase in excited modes and a decrease in resonance responses of the riser in the cross-flow (CF) direction. Furthermore, with the increase of the external shear flow velocity, resonances at different positions of the riser are not synchronized, which is different from that of the riser in uniform flow. In the case of the riser conveying gas-liquid two-phase flow and being subjected to external uniform or shear flow, the increase in the velocity of the liquid phase leads to an increase in the maximum response amplitudes of the riser in the in-line (IL) and axial directions. When the internal flow changes from single-phase to gas-liquid two-phase, the maximum VIV responses of the riser in the IL and axial directions tend to decrease regardless of whether the riser is in uniform flow or shear flow.

Nonlinear vibration characteristics of all-composite honeycomb-core sandwich panel: Theoretical and experimental investigation

Nonlinear vibration characteristics of all-composite honeycomb-core sandwich panel: Theoretical and experimental investigation

Investigating resonance frequency in advanced composite structures as the main part of bridge construction: a multi-physics simulation approach

This paper investigates the nonlinear vibration characteristics and resonance frequencies of a graphene oxide powders (GOP) reinforced beam structure, which is in contact with fluid, serving as a crucial component in bridge construction. Utilizing a multi-physics simulation approach, this study integrates both mathematical modeling and COMSOL simulations to analyze the behavior of the GOP-reinforced beam. The fluid in the analysis is modeled as incompressible, non-viscous, and irrotational, contributing to the interaction with the beam structure. The isogeometric approach, coupled with the harmonic balance method and the arc-length technique, is employed to solve the complex nonlinear partial differential equations (PDEs). This coupled method ensures the accurate capture of the nonlinear response and resonance frequencies of the beam, which are critical for the safe design and performance of bridge structures. The findings reveal the significant influence of GOP reinforcement on the vibration and stability characteristics of the beam, highlighting its potential to enhance structural performance under dynamic loading conditions. The study also emphasizes the importance of considering fluid-structure interactions in the design process, as the fluid’s presence substantially affects the vibration behavior. This research contributes to the understanding of the dynamic behavior of advanced composite structures in fluid environments, offering valuable insights for the design and analysis of bridge components. The results demonstrate the efficacy of the proposed simulation approach in addressing the complexities of nonlinear vibrations in fluid-structure interaction systems, paving the way for future developments in civil engineering applications.

Nonlinear vibration characteristics of rotor-bearing system with disc-shaft insufficient interference and flexible coupling misalignment fault

Abstract For the traditional rotor system, the looseness fault caused by disc-shaft insufficient interference is always ignored. Aimed at the disc-shaft looseness caused by insufficient interference, a novel dynamic model of rotor-bearing system in the presence of coupling misalignment is established in this paper to make an investigation on the fault characteristics of disc-shaft looseness fault. Due to the nonlinearity of contact model between disc-shaft, the iterative solving of kinetic equations can be obtained by the combination of Newmark-β and Newton-Raphson methods. The vibration characteristics of the rotor-bearing system with and without the disc-shaft looseness caused by insufficient interference are compared and analyzed. The comparison results show that the slight collision between disc-shaft can be caused in the disc-shaft early looseness fault, and the beat vibration of system is appeared when the disc-shaft looseness become severe. Considering the effect of coupling misalignment, the vibration responses of system under different coupling misalignment are further discussed and parallel misalignment is proved to have a significant effect on the disc-shaft looseness. It is expected that the research results provide a useful reference for the identification and diagnosis of the looseness fault caused by disc-shaft insufficient interference.

Nonlinear Vibrations of Composite Cylindrical–Cylindrical Shells with Bolt Loosening Connection

The nonlinear vibrations of composite cylindrical–cylindrical shells with bolt loosening connections are investigated. First, a theoretical model of such a combined shell is developed, with a multisegmental virtual material ring technique being adopted to replicate the partial bolt looseness in the bolted connection zone of two single shells. Furthermore, to consider the nonlinear vibration issue of such a bolted connection zone affected by external excitation amplitude, the equivalent Young’s modulus of the virtual material is defined, and the equation of motion is derived to solve nonlinear vibration parameters. Finally, three single composite cylindrical shells are connected with 12 bolts to form two combined shell specimens, and experimental tests are carried out to validate the model and examine the nonlinear vibration characteristics of such combined shells. Also, the impact of partial bolt loosening parameters on the nonlinear vibration behaviors is investigated with some important findings being summarized. The analysis methods, modeling techniques, test methods and important conclusions proposed in this study provide a useful reference for the study of the vibration issues of bolted composite shells.

Experimental study of nonlinear vibration characteristics of a two-rotor turbofan engine system with an intershaft support

Experimental study of nonlinear vibration characteristics of a two-rotor turbofan engine system with an intershaft support

Nonlinear Vibrations of the Piezoelectric-Laminated Composite Cantilever Rectangular Plate Subjected to the Transverse and Parametric Excitation

The intelligent structure will be the key to the industrial manufacturing field in the future, piezoelectric materials are the most commonly used active materials in many mechatronic and vibration control systems. In this paper, we illustrated the nonlinear vibration behaviors of the piezoelectric-laminated composite cantilever rectangular plate subjected to transverse and parametric excitation. Two piezoelectric layers are attached to the upper and lower surfaces of graphite/epoxy composite laminated plate. The nonlinear dynamic equations are derived via the classical laminated plate theory, von Karman large deformation theory, the constitutive equation of the piezoelectric materials, and the Hamilton principle. Considering the Galerkin method, the nonlinear ordinary differential equations for the two-order vibration mode of the piezoelectric laminated composite cantilever rectangular plate are achieved. The multiple scale method is applied to obtain the average equations to study the nonlinear vibration characteristic of the stable motion. The primary resonance and the 1:1 internal resonance of the piezoelectric laminated composite cantilever rectangular plate are investigated. The amplitude-frequency response curves, force-amplitude response curves, time histories, phase curves, and bifurcation diagrams are given to investigate the nonlinear dynamic characteristic of the piezoelectric laminated composite cantilever rectangular plate. The detailed parametric analyses show that bubble response curves are separated from the amplitude-frequency response curves with the continuous increase of the external excitation due to the internal resonance. In addition, the results reveal the energy transform between the various order vibration modes of the system. This work is expected to provide theoretical guidance for the nonlinear vibration of the smart piezoelectric laminated composite structure.