Amplitude-dependent Properties Research Articles

Periodic Solutions of Wave Propagation in a Strongly Nonlinear Monatomic Chain and Their Novel Stability and Bifurcation Analyses

Abstract A modified incremental harmonic balance (IHB) method is used to determine periodic solutions of wave propagation in discrete, strongly nonlinear, periodic structures, and solutions are found to be in a two-dimensional hyperplane. A novel method based on the Hill’s method is developed to analyze stability and bifurcations of periodic solutions. A simplified model of wave propagation in a strongly nonlinear monatomic chain is examined in detail. The study reveals the amplitude-dependent property of nonlinear wave propagation in the structure and relationships among the frequency, the amplitude, the propagation constant, and the nonlinear stiffness. Numerous bifurcations are identified for the strongly nonlinear chain. Attenuation zones for wave propagation that are determined using an analysis of results from the modified IHB method and directly using the modified IHB method are in excellent agreement. Two frequency formulae for weakly and strongly nonlinear monatomic chains are obtained by a fitting method for results from the modified IHB method, and the one for a weakly nonlinear monatomic chain is consistent with the result from a perturbation method in the literature.

Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems.

While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing nonlinearizable systems with multiple coexisting steady states have been unavailable. In this paper, we review such a data-driven nonlinear model reduction methodology based on spectral submanifolds. As input, this approach takes observations of unforced nonlinear oscillations to construct normal forms of the dynamics reduced to very low-dimensional invariant manifolds. These normal forms capture amplitude-dependent properties and are accurate enough to provide predictions for nonlinearizable system response under the additions of external forcing. We illustrate these results on examples from structural vibrations, featuring both synthetic and experimental data.This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.

Effect of ultrasonic pretreatment on the emulsification properties of Clanis Bilineata Tingtauica Mell protein

Clanis Bilineata Tingtauica Mell Protein (CBTMP) is a naturally high-quality insect protein resource, while its poor emulsification has limited its application in food industry. In order to change the present situation, in this research, the ultrasonic pretreatment (0 W, 200 W, 400 W, 600 W, and 800 W) method was used to improve the emulsification properties of CBTMP. Results indicated that ultrasound treatment especially at 400 W could significantly change the particle sizes, further increase the content of sulfhydryl group and surface hydrophobicity. The emulsification properties of emulsions were enhanced (from 4.16 ± 1.07 m2/g to 27.62 ± 2.20 m2/g) by sonicated CBTMP solution. Moreover, the physical stability of the emulsions to salt stress and centrifugation treatment was also promoted. Additionally, rheology revealed that a stronger network was formed at 400 W and all samples exhibited frequency-dependent and amplitude-dependent properties. The experiment demonstrated that ultrasound pretreatment was an effective means to improve the emulsification properties of CBTMP and it could provide a promising perspective for the application of CBTMP in food industry.

Effect of Ultrasonic Pretreatment on the Emulsification Properties of Clanis Bilineata Tingtauica Mell Protein

Clanis Bilineata Tingtauica Mell Protein (CBTMP) is a naturally high-quality insect protein resource, while its poor emulsification has limited its application in food industry. In order to change the present situation, in this research, the ultrasonic pretreatment (0 W, 200 W, 400 W, 600 W, and 800 W) method was used to improve the emulsification properties of CBTMP. Results indicated that ultrasound treatment could significantly change the particle sizes, further increase the content of sulfhydryl group and surface hydrophobicity. The emulsification properties of emulsions were enhanced by sonicated CBTMP solution. Moreover, the physical stability of the emulsions to salt stress and centrifugation treatment was also promoted. Additionally, rheology revealed that a stronger network was formed at 400 W and all samples exhibited frequency-dependent and amplitude-dependent properties. The experiment demonstrated that ultrasound pretreatment was an effective means to improve the emulsification properties of CBTMP and it could provide a promising perspective for the application of CBTMP in food industry.

A nonlinear vibration model of fiber metal laminated thin plate with amplitude dependent property

In this paper, a nonlinear vibration model of fiber metal laminated thin plate with amplitude dependent property considering the material nonlinearity is proposed. Based on the Jones-Nelson nonlinear theory and the complex modulus method, the Lagrange energy function has been derived. Then, combining the orthogonal polynomial method and the energy method, the homogeneous linear algebraic equations of the proposed modal are solved. By using the Newton-Raphson iteration method, the nonlinear natural frequencies and responses are obtained. And, the nonlinear modal damping ratios are acquired according to the complex modulus method. As an example to demonstrate the feasibility of the developed model, the experimental test of a TA2/TC500 laminated thin plate is implemented. The calculated and measured results show a good consistency.

Modeling of amplitude-dependent damping characteristics of fiber reinforced composite thin plate

A damping model of fiber reinforced composite thin plate with consideration of amplitude-dependent property is established using the Jones–Nelson nonlinear theory in conjunction with the classical laminated plate theory, polynomial fitting method and strain energy method. In this model, the elastic moduli are expressed as the function of strain energy density and the loss factors in the longitudinal, transverse and shear directions are expressed as the functions of excitation amplitude. Moreover, three TC300 carbon/epoxy composite plates are taken as research objects to carry out a case study. One of them is used to determine the amplitude-dependent coefficients of loss factors in fiber reinforced composites by combining the least square method with polynomial fitting method, and the other two plates are used to verify the correctness of the theoretical model. The results of the developed model considering amplitude dependence and experimental test show a good consistency. It is discovered that the viscoelastic effect of epoxy resin materials will contribute to the increased degree of damping. So, if such plate structures exhibit more pronounced viscoelastic characteristics, there will be more significant in the nonlinear degree of amplitude-dependent damping phenomenon.

A numerical study of tuned liquid damper based on incompressible SPH method combined with TMD analogy

Tuned liquid dampers (TLDs) are economical dynamic vibration absorbers which are increasingly being used for structural response control. Nevertheless, a thorough understanding of the sloshing behavior inside the TLD is essential for efficient design. In this paper, a truly incompressible smoothed particle hydrodynamics (ISPH) method is employed to circumvent the difficulties regarding the simulation of fully nonlinear sloshing motion induced by large amplitude excitations. The behavior of the TLD with damping screens is studied numerically over a wide range of excitation frequencies and amplitudes. It is found through comparison with the existing experimental data that the ISPH model is a powerful tool for accurate predictions of the TLD behavior. The amplitude-dependent properties of an equivalent tuned mass damper (TMD) model, which is capable of reproducing the energy dissipation characteristics of the TLD, are derived from the simulations results. Good agreement between the numerical and experimental results is indicative of the equivalent model’s ability to predict the response of structure–TLD systems, suggesting that the ISPH model can properly simulate the TLD behavior. The effect of screen placement on the performance of structure–TLD systems is also investigated. Findings reveal that improved performance of TLD can be realized under high amplitude excitations by placing the damping screens in the locations corresponding to the higher sloshing modes.

A new nonlinear vibration model of fiber-reinforced composite thin plate with amplitude-dependent property

In this paper, the material nonlinearity is introduced in the dynamic modeling of fiber-reinforced composite thin plates, and a new nonlinear vibration model of such composite plate structures with amplitude-dependent property is established with the consideration of the nonlinear stiffness and damping characteristics, which is observed and confirmed in the nonlinear vibration characterization experiment. In this new model, the elastic moduli and loss factors are expressed as the function of strain energy density on the basis of Jones–Nelson material nonlinear model. By using the identified parameters under different excitation amplitudes, these elastic moduli and loss factors are characterized as the function of the maximum dimensionless strain energy density. Then, the power function fitting technique is used to determine the nonlinear stiffness and damping parameters in the model, and the nonlinear natural frequencies, vibration responses and damping ratios of a TC300 carbon/epoxy composite thin plate are calculated and measured in a case study. The comparisons between the theoretical and experimental results show that the maximum calculation error of natural frequencies with consideration of amplitude-dependent property is less than 4.3%, and the maximum calculation errors of resonant response and damping results are no more than 12.5 and 9.6% in the 3rd mode and the 6th mode, respectively. Therefore, the practicability and reliability of the proposed model have been verified.

A novel amplitude-independent crack identification method for rotating shaft

The shaft crack is one of the most common and serious malfunctions in rotating machines and may lead to catastrophic failure if undetected in time. However, the conventional crack identification methods are amplitude-dependent and thus can be only applied to the crack identification under some specific conditions. In this paper, a novel amplitude-independent crack identification method (AiCIM) is significantly proposed to eliminate the amplitude-dependent property and promote the effectiveness of the crack identification. First and foremost, a fast time-varying vibration phenomenon of the cracked-rotor system is newly found. Through the theoretical analysis, the fast time-varying vibration mechanism of the cracked-rotor system is revealed for the first time. It is indicated that the vibration signal of the cracked-rotor system is modulated by the fast-oscillated instantaneous frequency, which is independent of the amplitude of the vibration signal. AiCIM is then put forward on the basis of the fast time-varying vibration mechanism and matching time–frequency analysis theory. Specially, the amplitude-independent instantaneous frequency of the vibration signal is extracted via the matching time–frequency analysis theory, and the time–frequency representation energy-concentration is enhanced along the instantaneous frequency trajectory. Since instantaneous frequency of the vibration signal carrying the critical fault information is employed to identify the shaft crack, AiCIM is only relevant to the phase of the vibration signal, i.e. amplitude independent. As a result, AiCIM successfully eliminates the dependence on the signal amplitude and is more sensitive to the weak crack. Both the numerical and experimental results demonstrate that AiCIM behaves best to extract the fast-oscillated feature of the fast time-varying vibration induced by the shaft crack in comparison with other time–frequency analysis methods, and AiCIM effectively suppress the effect of noises on the instantaneous frequency estimation because of its amplitude-independent property. Influences of the crack parameters on the nonlinear instantaneous frequency are finally discussed with AiCIM. This study provides a potential way to the online crack identification.

Mechanical properties of multifunctional structure with viscoelastic components based on FVE model

Based on the models of Lion and Kardelky (2004) and Hofer and Lion (2009), a finite viscoelastic (FVE) constitutive model, considering the predeformation-, frequency- and amplitude-dependent properties, has been proposed in our earlier paper [1]. FVE model is applied to investigating the dynamic characteristics of the multifunctional structure with the viscoelastic components. Combing FVE model with the finite element theory, the dynamic model of the multifunctional structure could be obtained. Additionally, the parametric identification and the experimental verification are also given via the frequency-sweep tests. The results show that the computational data agree well with the experimental data. FVE model has made a success of expressing the dynamic characteristics of the viscoelastic materials utilized in the multifunctional structure. The multifunctional structure technology has been verified by in-orbit experiments.

Electromechanical nonlinearities and losses in piezoelectric sonar transducer materials

Next-generation sonar projectors rely on piezoelectric single crystals such as lead magnesium niobate-lead titanate to induce mechanical strain and generate ever greater acoustic output, but the performance of these materials under high-power operation is not well understood. As the electrical driving force increases, the linear piezoelectric relationships give way to nonlinear, amplitude-dependent properties. Such behavior is impossible to predict solely from small signal, linear measurements. This work has characterized the behavior of single crystals by examining the dynamic relaxation from initial strain levels of 0.1 to 0.2%. Strain-dependent values of the mechanical quality factor and resonance frequency are reported for single crystals, and these properties are compared with conventional high-power piezoceramics.

A literature review of automotive vehicle engine mounting systems

The ideal engine mount system should isolate engine vibration caused by engine disturbance force in engine speed range and prevent engine bounce from shock excitation. This implies that the dynamic stiffness and damping of the engine mount should be frequency- and amplitude-dependent. The development of engine mounting systems has mostly concentrated on improvement of frequency- and amplitude-dependent properties. The conventional elastomeric mounts do not meet all the requirements and can only offer a trade-off between static deflection and vibration isolation. Passive hydraulic mounts can provide a better performance than elastomeric mounts especially in the low frequency range. Semi-active techniques are usually used to further improve performance of hydraulic mounts by making them more tunable. The active engine mounting system can be very stiff at low frequency and be tuned to be very soft at the higher frequency range to isolate the vibration. The active engine mounts have been considered as the next generation of engine mounts. The optimization of engine mounting systems is quite desirable. The current work on the optimization of the engine mount systems shows some limitations.

Review of automotive vehicle engine mounting systems

The ideal engine mount system should isolate engine vibration caused by engine disturbance force in engine speed range and prevent engine bounce from shock excitation. This implies that the dynamic stiffness and damping of the engine mount should be frequency and amplitude dependent. The development of engine mounting systems has mostly concentrated on improvement of frequency and amplitude dependent properties. The conventional elastomeric mounts do not meet all the requirements and can only offer a trade-off between static deflection and vibration isolation, but there is still some room for improving the properties of elastomeric mounts. Passive hydraulic mounts can provide a better performance than elastomeric mounts especially in the low frequency range. Semi-active techniques are usually used to further improve performance of hydraulic mounts by making them more tunable. The active engine mounting system can be very stiff at low frequency and be tuned to be very soft at the higher frequency range to isolate the vibration. The active engine mounts have been considered as the next generation of engine mounts. The optimisation of the engine mounting system is quite useful both in terms of speed and more effective design. The current work on optimisation of the engine mount systems shows some limitation. Further work is needed to consider the nonlinear variations in properties of different types of mounting systems.

Automotive Vehicle Engine Mounting Systems: A Survey

This study divided into three portions to provide performance requirements; overview and development of various engine mounts; and the optimization of engine mount systems. The first part provides an insight about the ideal engine mount system that should isolate vibration caused by engine disturbance force in various speed range and prevent engine bounce from shock excitation. This implies that the dynamic stiffness and damping of the engine mount should be frequency and amplitude dependent. Therefore, the development of engine mounting systems has mostly concentrated on improvement of frequency and amplitude dependent properties. The second part starts discussion on the conventional elastomeric mounts that offer a trade-off between static deflection and vibration isolation. The next level, passive hydraulic mounts can provide a better performance than elastomeric mounts especially in the low frequency range. Subsequently, semi-active and active techniques are used to improve performance of hydraulic mounts by making them more tunable. The active engine mounting system can be very stiff at low frequency and be tuned to be very soft at the higher frequency range to isolate the vibration. The final part is about the optimization of engine mounting systems. An overview of the current work on this optimization shows some limitations. Further study is needed to consider the nonlinearities and variations in properties of different types of mounting systems.