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The purpose of this study is to provide some references about applying the semi-active particle damper to enhance the stability of the pipe structure.

This paper establishes the dynamical models of semi-active particle damper based on traditional dynamical theory and fractional-order theory, respectively. The semi-active particle damping vibration isolation system applied in a pipe structure is proposed, and its analytical solution compared with G-L numerical solution is solved by the averaging method. The quantitative relationships of fractional-order parameters (a and kp) are confirmed and their influences on the amplitude-frequency response of the vibration isolation system are analyzed. A fixed point can be obtained from the amplitude-frequency response curve, and the optimal parameter used for improving the vibration reduction effect of semi-active particle damper can be calculated based on this point. The nonlinear phenomenon caused by nonlinear oscillators is also investigated.

The results show that the nonlinear stiffness parameter p will cause the jump phenomenon while p is close to 87; with the variation of nonlinear damping parameter μ, the pitchfork bifurcation phenomenon will occur with an unstable branch after the transient response; with the change of fractional-order coefficient k_p, a segmented bifurcation phenomenon will happen, where an interval that k_p between 18.5 and 21.5 has no bifurcation phenomenon.

This study establishes a mathematical model of the typical semi-active particle damping vibration isolation system according to fractional-order theory and researches its nonlinear characteristics.

The purpose of this paper is to detail the design of a fractional controller which was developed for the suppression of the flexural vibrations of the first mode of a smart beam.

During the design of the fractional controller, in addition to the classical control parameters such as the controller gain and the bandwidth; the order of the derivative effect was also included as another design parameter. The controller was then designed by considering the closed loop frequency responses of different fractional orders of Continued Fraction Expansion (CFE) method.

The first, second, third and fourth order approximations of CFE method were studied for the performance analysis of the controller. It was determined that the increase in the order resulted in better vibration level suppression at the resonance. The robustness analysis of the developed controllers was also conducted.

The experimentally obtained free and forced vibration results indicated that the increase in the order of the approximations yielded better performance around the first flexural resonance region of the smart beam and proved to yield better performance than the classical integer order controllers.

Evaluation of the performance of a developed fractional controller was realized by using different approach orders of the CFE method for the suppression of the flexural vibrations of a smart beam.

The purpose of this paper is to analyze a new, whole‐spacecraft isolator and its performance of vibration isolation, which has been designed to ensure spacecraft safety at the launching stage.

The design is based on the analysis of fractional derivative stress‐strain constitutive relationship of viscoelastic materials. First, the authors study the constitutive relationships for viscoelastic solid of the damping materials, then the authors introduce the results obtained to the equations of motion for the damped isolator.

By performing a series of transformation, the authors obtain the analytical solution of the equations. It is shown that the results compare favourably to the numerical simulations and experiments. In addition, a saturation phenomenon for the first order damping ratio is also discussed.

It is found that the constitutive relationships written in terms of the fractional calculus can be applied in the system function of the whole‐spacecraft vibration isolator. Such relationships, developed previously from a model analysis base, have been shown to be useful tools for engineering analyses.

Some suggestions are given to improve the design of viscoelastic whole‐spacecraft isolators. The establishment of a theoretical basis for the new fractional differential dynamical system enhances their value, as they may now be used with increased reliability of satellite.

The purpose of this offered research is to articulate a multifaceted kind of highly unstable initial perturbation and further analyze the performance of the plasma particles for time-fractional order evaluation.

For this purpose, the authors designed specific geometry and further interpreted it into the mathematical model using the concepts of the Vlasov Maxwell system. The suggested algorithm is based on the finite-difference and spectral estimation philosophy. The management of time and memory in generic code for computational purposes is also discussed.

The main purpose is to analyze the fractional behavior of plasma particles and also the capability of the suggested numerical algorithm. Due to initial perturbations, there are a lot of sudden variations that occurred in the formulated system. Graphical behavior shows that SR parameter produces devastation as compared to others. The variation of fractional parameter between the defend domain demonstrates the hidden pictures of plasma particles. The design scheme is efficient, convergent and has the capability to cover the better physics of the problem.

Plasma material is commonly used in different areas of science. Therefore, in this paper, the authors increase the capability of the mathematical plasma model with specific geometry, and further suitable numerical algorithm is suggested with detailed physical analysis of the outcomes. The authors gave a new direction to study the performance of plasma particles under the influence of LASER light.

In the recent era, science has produced a lot of advancements to study and analyze the physical natural process, which exist everywhere in the real word. On behalf of this current developments, it is now insufficient to study the first-order time evaluation of the plasma particles. One needs to be more precise and should move toward the bottomless state of it, that is, macroscopic and microscopic time-evaluation scales, and it is not wrong to say that there exits a huge gap, to study the time evaluation in this discussed manner. The presented study is entirely an advanced and efficient way to investigate the problem into the new directions. The capability of the proposed algorithm and model with fractional concepts can fascinate the reader to extend to the other dimensions.

A new cutting tool is always well-defined and sharp at the onset of the metal cutting process and gradually losses these properties as the machining process advances. Similarly, at the beginning of the machining process, amplitude of tool vibrations is considerably low and it increases gradually and peaks at the end of the service period of the cutting tool while machining. It is significant to provide a corresponding real-time varying damping to control this chatter, which directly influences accuracy and quality of productivity. This paper aims to review the literature related to the application of smart fluid to control vibration in metal cutting and also focused on the challenges involved in the implementation of active control system during machining process.

Smart dampers, which are used as semi-active and active dampers in metal cutting, were reviewed and the research studies carried out in the field of the magnetorheological (MR) damper were concentrated. In smart materials, MR fluids possess some disadvantages because of their sedimentation of iron particles, leakage and slow response time. To overcome these drawbacks, new MR materials such as MR foam, MR elastomers, MR gels and MR plastomers have been recommended and suggested. This review intents to throw light into available literature which exclusively deals with controlling chatter in metal cutting with the help of MR damping methods.

Using an MR damper popularly known for its semi-active damping characteristics is very adaptable and flexible in controlling chatter by providing damping to real-time amplitudes of tool vibration. In the past, many researchers have attempted to implement MR damper in metal cutting to control vibration and were successful. Various methods with the help of MR fluid are illustrated.

A new cutting tool is always well-defined and sharp at the onset of metal cutting process and gradually losses these properties as the machining process advances. Similarly, at the beginning of the machining process, amplitude of tool vibrations is considerably low and it increases gradually and peaks at the end of service period of cutting tool while machining. Application of MR damper along with the working methodology in metal cutting is presented, challenges met are analyzed and a scope for development is reviewed.

This study provides corresponding real-time varying damping to control tool vibration which directly influences accuracy and quality of productivity. Using an MR damper popularly known for its semi-active damping characteristics is very adaptable and flexible in controlling chatter by providing damping to real-time amplitudes of tool vibration.

This study attempts to implement smart damper in metal cutting to control vibrations.

It is significant to provide corresponding real-time varying damping to control tool vibration which directly influences accuracy and quality of productivity.

The objective of this research is to investigate various neural network (NN) observer techniques for sensors fault identification and diagnosis of nonlinear system in consideration of numerous faults, failures, uncertainties and disturbances. For the importunity of increasing the faults diagnosis and reconstruction preciseness, a new technique is used for modifying the weight parameters of NNs without enhancement of computational complexities.

Various techniques such as adaptive radial basis functions (ARBF), conventional radial basis functions, adaptive multi-layer perceptron, conventional multi-layer perceptron and extended state observer are presented. For increasing the fault detection preciseness, a new technique is used for updating the weight parameters of radial basis functions and multi-layer perceptron (MLP) without enhancement of computational complexities. Lyapunov stability theory and sliding-mode surface concepts are used for the weight-updating parameters. Based on the combination of these two concepts, the weight parameters of NNs are updated adaptively. The key purpose of utilization of adaptive weight is to enhance the detection of faults with high accuracy. Because of the online adaptation, the ARBF can detect various kinds of faults and failures such as simultaneous, incipient, intermittent and abrupt faults effectively. Results depict that the suggested algorithm (ARBF) demonstrates more confrontation to unknown disturbances, faults and system dynamics compared with other investigated techniques and techniques used in the literature. The proposed algorithms are investigated by the utilization of quadrotor unmanned aerial vehicle dynamics, which authenticate the efficiency of the suggested algorithm.

The proposed Lyapunov function theory and sliding-mode surface-based strategy are studied, which shows more efficiency to unknown faults, failures, uncertainties and disturbances compared with conventional approaches as well as techniques used in the literature.

For improvement of the system safety and for avoiding failure and damage, the rapid fault detection and isolation has a great significance; the proposed approaches in this research work guarantee the detection and reconstruction of unknown faults, which has a great significance for practical life.

In this research, two strategies such Lyapunov function theory and sliding-mode surface concept are used in combination for tuning the weight parameters of NNs adaptively. The main purpose of these strategies is the fault diagnosis and reconstruction with high accuracy in terms of shape as well as the magnitude of unknown faults. Results depict that the proposed strategy is more effective compared with techniques used in the literature.