Nonlinear Response Characteristics Research Articles

Comparative Analysis of Non-linear Periodic Response of Cross-ply and Angle-ply Laminated Composite Plates

Non-linear periodic response periodic response analysis of laminated structures is necessary for their optimal and safe dynamic design. The present work is intended to explore the influence of lamination scheme and fibre-orientation on the nonlinear forced vibration response of laminated plates. The analysis has been carried out using finite element. In present work, a comparative analysis of forced vibration response between cross-ply and angle-ply laminated composite plates have been explored. The effects of fiber orientation on non-linear forced vibration response characteristics have been analyzed. This finite element analysis has been done using shooting method along with continuation scheme in the time domain. The method employed is capable to get the complete stable and unstable branches past bifurcations. The dynamic behavior is explored using the temporal history of the response and phase plane plots. The method presented in the paper is computationally efficient and does not require apriori assumption on the participating modes, unlike harmonic balance and incremental harmonic balance methods.

Peak ground motions and characteristics of nonlinear site response during the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake

The observed peak ground accelerations and peak ground velocities (PGVs) of the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake generally followed the median values from ground motion prediction equations with reasonable errors at fault distances ≥ 50 km. However, at smaller distances, the equations significantly underestimated the peak ground motions, and it was eminent for PGVs. A comparison of surface-to-borehole spectral ratios of S-waves during the mainshock and other events revealed that the sites at smaller distances experienced various degrees of nonlinear site response. The two most widely known characteristics of nonlinear site response are the weakening of higher-frequency components and shifting of predominant frequencies to lower ones in comparison with the linear site response. At one of the sites that recorded the largest intensity of 7 in JMA scale of 0–7, the latter nonlinear effect was so dominant that the ground motions around the new predominant frequency got intensified by one order of magnitude in comparison with that during the weak-motions. Two sites, which were closely located, recorded vertical peak ground accelerations exceeding 1 g for the up-going motions. The recordings showed asymmetric waveforms and amplitudes characteristics of the nonlinear site response in extreme vertical ground motions recorded during a few earthquakes in the past. Few sites having lower vertical peak ground accelerations were also suspected of being experienced nonlinear site response on vertical motions. These findings suggest taking a cautious approach to enumerate the reduction in amplification at higher frequencies using the single-station horizontal-to-vertical (H-to-V) spectral ratio technique. However, we found that the H-to-V technique was still useful to detect nonlinearity. Finally, an ad hoc equation was derived to correct the nonlinear site amplification in predicting horizontal PGVs with respect to one of the most widely used attenuation models in Japan. The results indicated that the effect was much stronger for a larger input motion than that for a proportional change in the Vs30 values.

Modeling and nonlinear vibration characteristics analysis of symmetrically 3-layer composite thin circular cylindrical shells with arbitrary boundary conditions

Considering the large-deformation hypothesis, the modeling and nonlinear vibration characteristics of symmetrically 3-layer composite thin circular cylindrical shells with arbitrary boundary conditions are analyzed by applying four sets of artificial springs. Firstly, by employing a set of orthogonal polynomials and trigonometric functions, the energy equations of the shells are derived with Donnell's nonlinear thin-shell theory. Then, the arbitrary boundary conditions are simulated by imposing the equivalent elastic constraint to obtain the potential energy of the edges of the shell, which can be universally applicable to all classical boundary conditions. The vibration equation is obtained by using the Lagrange equation method. In order to obtain correct numerical results, several comparisons of linear and nonlinear results are carried out to validate the approach method in the present study; meanwhile, the calculation convergence is checked. At last, the influence of boundary conditions, geometric parameters, symmetrical lamination schemes and damping coefficients on the nonlinear amplitude-frequency characteristics of symmetrically 3-layer composite thin circular cylindrical shells are investigated. The numerical results indicate that the present method is powerful to calculate the nonlinear vibration response characteristics of symmetrically 3-layer composite circular cylindrical thin shells subjected to various boundary conditions.

Nonlinear dynamic response of a spur gear pair based on the modeling of periodic mesh stiffness and static transmission error

• A complete modeling procedure is applied including the modeling of gear mesh stiffness, transmission error and gear pair. • The analytical gear mesh stiffness shows a good agreement with the published result of finite element approach. • The numerical results of proposed dynamic model match well with the published experimental data. • The effects of several essential gear parameters are investigated. • Deeper properties of gear vibration are revealed to guide the actual design and control of gear dynamics. This study is concerned with the nonlinear frequency response characteristics of a spur gear pair system, in which the modeling of time varying mesh stiffness (TVMS) and static transmission error (STE) is stressed. Firstly, a complete modeling procedure is constructed by adopting existing models of TVMS, STE and gear pair, so that the basic gear features and design parameters are contained in the overall gear model. On this basis, a 1 degree-of-freedom (DOF) spur gear pair model is established including the TVMS, STE and nonlinear backlash. Then, to show the validity and reliability, theoretical solutions of the dynamic model are verified by the published numerical results and experimental data. Besides, the stability of the gear system is investigated analytically to obtain the boundaries that separate stable and unstable regions. Finally, parametric studies are conducted to reveal the effects of several key parameters, such as the contact ratio, spacing error, transmitted load and damping ratio. The results show that the modeling of TVMS and STE should be considered and emphasized to obtain precise predictions of system responses and to reveal in depth properties of gear dynamics. Furthermore, the parametric studies and stability analysis offer useful suggestions for researchers and engineers to achieve desirable design and control of dynamic behaviors of gear system.

Characteristics analysis of rotor model with support–foundation looseness fault considering elastic–plastic contact

In this paper, the nonlinear response characteristics of a single degree of freedom lumped mass model with a new support looseness fault are analyzed. In this model, a new nonlinear contact stiffness model between the support and foundation is considered, which considers the elastic–plastic deformation of the contact parts. The nonlinear response of the system is obtained by numerical integration methods. The nonlinear results are compared with an asymmetric model and a piece-wise contact model. By comparing three different looseness fault models, the mechanism of generating multi-frequencies and fractional frequencies is analyzed. The result shows that plastic deformation makes the displacement amplitude increase rapidly; odd harmonics appear in symmetric stiffness model due to the modulation of symmetric shock forces; however, harmonic response appears in asymmetric stiffness model; when the contact number is odd, the frequency components contain odd or even order fractional frequencies at supercritical speeds due to the incompatibility of contacts on the upper and lower surfaces; when the contact number is even, multiple frequency components appear at subcritical frequencies.

Fluorinated Organic Electro‐Optic Quinolinium Crystals for THz Wave Generation

AbstractFluorinated electro‐optic crystals with state‐of‐the‐art second‐order nonlinear optical response and excellent characteristics for terahertz (THz) wave generation are reported. The fluorinated organic ionic crystals consist of optically highly nonlinear fluorinated HM6FQ (6‐fluoro‐2‐(4‐hydroxy‐3‐methoxystyryl)‐1‐methylquinolinium) or HM7FQ (7‐fluoro‐2‐(4‐hydroxy‐3‐methoxystyryl)‐1‐methylquinolinium) cations and 4‐methylbenzenesulfonate (T) counter anions. Compared to benchmark electro‐optic crystals based on nonfluorinated HMQ (2‐(4‐hydroxy‐3‐methoxystyryl)‐1‐methylquinolinium) cations, introducing fluorine substituent on HM6FQ cations creates additional hydrogen bonds (ArF···HC). Such a molecular engineering leads to an enhanced thermal stability and significant modulations of phonon vibrational modes of crystals in THz frequency region, while excellent π–π stacking and space filling characteristics of HM6FQ cations in crystals lead to state‐of‐the‐art diagonal component of the macroscopic nonlinear optical susceptibility, similar to the case of HMQ cations. HM6FQ‐based crystals exhibit a very high optical‐to‐THz conversion efficiency, comparable to benchmark HMQ‐based crystals. In addition, due to additional hydrogen bonds induced by fluorine substituents, the spectral shape of the generated THz wave is remarkably modified; e.g., the largest spectral gap is near 1.5 and 2.0 THz for HM6FQ‐ and HMQ‐based crystals, respectively. The fluorinated cationic engineering on nonlinear optical crystals having benchmark nonlinear optical response is, as far as is known, reported for the first time.

Nonlinear response analysis for an aero engine dual-rotor system coupled by the inter-shaft bearing

This paper focuses on the nonlinear response characteristics of an aero engine dual-rotor system coupled by the cylindrical roller inter-shaft bearing. The motion equations of the system are formulated considering the unbalance excitations of the two rotors, vertical constant forces acting on the rotor system and the gravities. By using numerical calculation method, the motion equations are solved to obtain the nonlinear responses of the dual-rotor system. Accordingly, complex nonlinearities affected by the bearing radical clearance, the vertical constant force and the rotating speed ratio are discussed in detail. The jump phenomenon, hard resonant hysteresis characteristics are shown for a relatively large bearing clearance, and the soft resonant hysteresis characteristics can be observed for a relatively large vertical constant force. Moreover, the super-harmonic frequency components and the combined frequency components caused by the inter-shaft bearing are observed for both rotors. But the corresponding frequency components for the low-pressure rotor are more complex than that for the high-pressure rotor in same condition. These results would be helpful to recognize the nonlinear dynamic characteristics of dual-rotor bearing system.

Nonlinear response characteristics of bridges with hysteretic dampers between the abutment and the deck subjected to severe ground motions

Nonlinear response characteristics of bridges with hysteretic dampers between the abutment and the deck subjected to severe ground motions

Theoretical analysis of vibration energy harvesters with nonlinear damping and nonlinear stiffness

Theoretical analysis of the vibration energy harvesters with nonlinear damping and nonlinear stiffness is provided to reveal their physical mechanism. Both the method of multiple scales and the method of averaging are employed to derive the theoretical solutions of the output voltage and power of the harvesters. The corresponding theoretical solutions are verified by direct numerical simulations. The nonlinear response characteristics are conducted by combining the stability analysis and the classification of the theoretical solutions. Especially, the dynamical hysteresis criterion which is used to determine the softening or hardening property is derived for enhancing energy harvesting performance. Meanwhile, the backbone curve is obtained. In addition, the influence of the excitation amplitude, the stiffness, the damping exponent, and the electromechanical coupling coefficient on the output power of the harvesters is explored. Overall, the physical mechanism of the harvesters is revealed and a framework for the optimization of maximizing the output power is provided.

Local defect modelling and nonlinear dynamic analysis for the inter-shaft bearing in a dual-rotor system

• A force model for the inter-shaft bearing with a local defect on surface of the outer or inner race. • The system may resonant in some non-critical-speed region due to the local defect. • Parameters affecting the resonant frequencies and vibration amplitudes of the abnormal resonances. • A comprehensive parametric analysis is carried out to show the nonlinear resonant response characteristics. This paper presents a force model for the inter-shaft bearing with a local defect on the surface of the outer race or the inner race, and the nonlinear dynamic characteristics of a dual-rotor system affected by the local defect are investigated. A simplified dual-rotor system is presented with the consideration of the inter-shaft bearing's nonlinearities such as the Hertzian contact force and the radial clearance. The local defect is considered as a regular dent with a constant depth, thus the radial clearance will increase when rolling elements go through the range of the local defect. The motion equations of the system with eight degrees of freedom are formulated by using the Lagrange's equation. The nonlinear vibration responses of the dual-rotor system affected by the local defect are obtained using numerical method. The results show that there exist four abnormal resonances on the amplitude frequency curves of the system due to the effect of the local defect, apart from the couple of primary resonances excited by the unbalance excitations of the two rotors. With the aid of the characteristic defect frequency analysis, it is revealed that one pair of the abnormal resonances are excited by the characteristic defect frequency, and the other pair of the abnormal resonances are excited by the combination frequency. Furthermore, a comprehensive parametric analysis is carried out to give an insight into the nonlinear resonant response characteristics affected by parameters such as the depth and the span of the defect, the rotation speed ratio, the unbalances of two rotors, the stiffness and the damping of the linear elastic spring, and the radial clearance, the stiffness and the roller number of the inter-shaft bearing. The results show that the vibration amplitudes for the abnormal resonances are mainly determined by the depth and the span of the defect, while the resonant frequencies for the abnormal resonances are mainly influenced by the rotation speed ratio and the roller number of the inter-shaft bearing. However, the rotors’ unbalances mainly affect the corresponding primary resonance rather than the abnormal resonances. The obtained results will contribute to a better understanding of the nonlinear resonant response characteristics of dual-rotor systems with a local defect on the inter-shaft bearing, which are helpful for the fault diagnostics of the inter-shaft bearing in a dual-rotor system.

Nonlinear Dynamic Analysis of a Skyhook-Based Semi-Active Suspension System With Magneto-Rheological Damper

Response characteristics of a magneto-rheological suspension with a modified skyhook control scheme, focusing directly on the command current, were analyzed considering hysteresis nonlinearities. Suspension performance and its dynamic stability were investigated under harmonic excitation at frequencies up to 50 Hz to illustrate highly nonlinear influences of the excitation frequency and magnitude. The nonlinear response characteristics of the system, attributed to damper hysteresis and on–off control, were thoroughly analyzed considering the bifurcation diagrams, Lyapunov exponent spectra, phase portraits, and the Poincare maps. These, invariably, showed the presence of quasi-periodic, multiperiodic, and chaotic responses of the system under mid- as well as high-frequency excitations. The conducted electromagnetic interference (EMI) due to high frequency variations in the drive current, caused by the nonlinear system responses, was further evaluated using the method described in EN 55022 for the first time. The assessments using the GB9254 guidelines showed that the EMI levels exceed the recommended limits. The chaos-induced EMI may thus be detrimental to the electronic control systems of the automobile and cannot be ignored. This work is considered to serve as a theoretical foundation for future studies on EMI reduction and nonlinear control of intelligent semi-active suspensions.

Guiding Ketogenic Diet with Breath Acetone Sensors.

Ketogenic diet (KD; high fat, low carb) is a standard treatment for obesity, neurological diseases (e.g., refractory epilepsy) and a promising method for athletes to improve their endurance performance. Therein, the level of ketosis must be regulated tightly to ensure an effective therapy. Here, we introduce a compact and inexpensive breath sensor to monitor ketosis online and non-invasively. The sensor consists of Si-doped WO3 nanoparticles that detect breath acetone selectively with non-linear response characteristics in the relevant range of 1 to 66 ppm, as identified by mass spectrometry. When tested on eleven subjects (five women and six men) undergoing a 36-h KD based on the Johns Hopkins protocol, this sensor clearly recognizes the onset and progression of ketosis. This is in good agreement to capillary blood β-hydroxybutyrate (BOHB) measurements. Despite similar dieting conditions, strong inter-subject differences in ketosis dynamics were observed and correctly identified by the sensor. These even included breath acetone patterns that could be linked to low tolerance to that diet. As a result, this portable breath sensor represents an easily applicable and reliable technology to monitor KD, possibly during medical treatment of epilepsy and weight loss.

Side-Slither Data-Based Vignetting Correction of High-Resolution Spaceborne Camera with Optical Focal Plane Assembly

Optical focal plane assemblies are increasingly being used in high-resolution optical satellite systems to enhance the width of the image using linear push-broom imaging. With this system, vignetting occurs in the area of overlap, affecting image quality. In this paper, using the characteristics of the side-slither data, we propose side-slither data-based vignetting correction of a high-resolution spaceborne camera with an optical focal plane assembly. First, the raw side-slither data standardization is used to ensure that each row has the same features. Then, with the spatial correlation of a gray-level co-occurrence matrix, the gray-level co-occurrence matrix is proposed to identify the uniform regions, to extract the sample points. Finally, due to the characteristics of compatible linear response and non-linear response, the power-law model was used to fit, and the Levenberg–Marquardt algorithm was used to fit the model. In the experiment, polynomial fitting, laboratory coefficients and on-orbit coefficients were used for comparison with the proposed method. The side-slither data can be treated as a uniform scene due to their characteristics, and the side-slither image that was corrected using the proposed method showed less than 1% change in mean value, a root-mean-square deviation value better than 0.1%, and the average streaking metrics were superior to 0.02. The results showed that the proposed method performs significantly better in the vignetting area.

Dynamic response analysis for the aero-engine dual-rotor-bearing system with flexible coupling misalignment faults

This paper focuses on the nonlinear response characteristics of an aero-engine dual-rotor-bearing system with flexible coupling misalignment faults in the low-pressure rotor system (rotor 2). The motion equations of the system are formulated by using finite element method, in which the excitations induced by the misalignment faults, the dual-unbalance excitations of the two rotors (the high-pressure rotor system-rotor 1 and the low-pressure rotor system-rotor 2), the gravities, and the nonlinear force induced by the inter-shaft bearing are all considered. By using numerical calculation method, the motion equations are solved to obtain the nonlinear responses of the system. Then, the nonlinear responses for the alignment dual-rotor-bearing system are analyzed, the hardening type hysteresis characteristics with jump phenomenon are shown. Accordingly, the nonlinear responses affected by the amount of parallel misalignment and angular misalignment are discussed in detail. The results show that, with the increase of by the amount of parallel misalignment (angular misalignment), the frequency components 2 times rotational speed of rotor 2 appear, and the amplitudes of the responses at the super-harmonic frequency components and combined frequency components get larger for not only rotor 2 but also rotor 1, which indicates that the vibration characteristics of misalignment faults in rotor 2 can be transmitted to the rotor 1 and can be used to diagnose the misalignment faults. The results obtained in this paper will contribute to the response analysis for the aero-engine dual-rotor-bearing system with flexible coupling misalignment faults.

An efficient signal conditioning circuit to piecewise linearizing the response characteristic of highly nonlinear sensors

To obtain the solutions to the problem of linearization of the sensor characteristics is a matter of investigations for a long time. This paper presents a new and simple piecewise linearizing circuit to compensate the nonlinearity of highly nonlinear sensor. It is having a mixed signal conditioning circuit, employing a 2-bit flash ADC, a (4×1) multiplexer and the Op amp-based signal conditioning units. The circuit was initially simulated using SPICE software and then hardware implemented for linearizing the nonlinear response characteristic of two sensors. One of the sensors is a graphene oxide capacitive humidity sensor with nearly 46% nonlinearity and the other is a thermistor-based temperature sensor with 16.4% nonlinearity. The humidity sensor is fabricated and characterized to measure humidity in the range of 2–85% RH. The maximum nonlinearity of the humidity and temperature sensors of the hardware implemented circuit after compensation was 1% and 1.5% respectively. The circuit is simple and requires few hardware components for implementation and applicable for any nonlinear sensor. The circuit is CMOS compatible for ASIC implementation.

Nonlinear stiffness and dynamical response characteristics of an asymmetric X-shaped structure

Abstract Nonlinearity is more and more shown to be very beneficial to various engineering practice, including vibration control, vibration energy harvesting and structural health monitoring, etc. An X-shaped structure has been investigated recently for its special and beneficial nonlinear stiffness and damping characteristics in passive vibration isolation and suppression. In this study, a novel n-layer vertically-asymmetric X-shaped structure is systematically studied for its generic modelling, nonlinear stiffness/damping features and dynamic response in vibration isolation. It is shown that, (a) micro-gravity environment can reduce the linear natural frequency and it can improve the vibration isolation performance in the vertical direction (good for micro-gravity environment vibration control), and an optimal assembly angle α1 and rod-length ratio s1 can be designed to achieve the minimum natural frequency when the gravity acceleration is not equal to zero for the best vibration isolation performance; (b) the asymmetric structure can produce lower natural frequency than that of symmetric counterparts (i.e. s1 = 1/s2 = 1) by properly adjusting rod-length ratio s1 (or s2), and the developed generic model can be used freely to study the structure response under different asymmetric settings; (c) the transmissibility of the asymmetric X-shaped structure can be tuned to have much lower transmissibility than that of the symmetric counterpart, which is very beneficial for vibration isolation; (d) the structure in the horizontal direction demonstrates very special dynamic response characteristics which can well explain a linear damper in the horizontal direction much better for vibration energy absorption for a much wider frequency range compared with the vertical direction. It should be noticed that instead of direct modeling of the vibration system in vertically direction, the dynamical equation is established with an intermediate variable, due to vertical asymmetry of the structure. The results provide new understanding on the X-shaped structures including its modelling, gravity effect, asymmetric ratio and nonlinear response in both vertical and horizontal directions, which can help practical applications of this class of structures.

Pressure Re-Impulse Diagram of the FLNG Tanks Under Sloshing Loads

Sloshing impact loads can cause severe structural damage to cargo tanks in liquefied natural gas floating production storage offloading units (LNG-FPSOs or FLNGs). Studies of sloshing can be classified into two types, namely, hydrodynamics-related and structural mechanics-related studies. This study is a sequel to the authors’ previous studies (Paik et al. 2015; Lee et al. 2015), but is more related to issues of structural mechanics. In this study, a new method for probabilistic sloshing assessment, which has been previously developed by the authors, is briefly explained. The nonlinear impact structural response characteristics under sloshing impact loads are examined by a nonlinear finite element ANSYS/LS-DYNA method. An iso-damage curve, representing a pressure-impulse diagram, is derived for the self-supporting prismatic-shape IMO B type LNG cargo containment system of a hypothetical FLNG. The insights developed from this work can be useful for the damage-tolerant design of cargo tanks in FLNGs.

Eardrum and columella displacement in single ossicle ears under quasi-static pressure variations

Although most birds encounter large pressure variations during flight, motion of the middle ear components as a result of changing ambient pressure are not well known or described. In the present study, motion of the columella footplate and tympanic membrane (extrastapedius) in domestic chickens (Gallus gallus domesticus) under quasi-static pressure conditions are provided. Micro-CT scans were made of cadaveric heads of chickens under positive (0.25 kPa, 0.5 kPa, 1 kPa, and 1.5 kPa) and negative (−0.25 kPa, −0.5 kPa, −1 kPa, and −1.5 kPa) middle ear pressure. Both extrastapedius and columella footplate displacements show a non-linear S-shaped curve as a function of pressure indicating non-linear response characteristics of the middle ear components. The S-curve is also seen in mammals, but unlike in mammals, the lateral piston-like displacement of both the columella footplate and extrastapedius, which is caused by an increased middle ear pressure are smaller than the medial piston-like displacements, caused by a decreased middle ear pressure of the same magnitude. Columella footplate piston displacements are always smaller than the extrastapedius piston displacements, indicating the flexibility of the extracolumella. The cone-shape of the avian tympanic membrane with inverted apex in comparison to the mammalian tympanic membrane can cause the inverted shape of the pressure response curve.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Nonlinear vibration response characteristics of high-speed flexible rotor system

Nonlinear vibration response characteristics of high-speed flexible rotor system