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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of the paper is to analyze the active suppression of the aeroelastic vibrations of ailerons with strongly nonlinear characteristics by neural network/reinforcement learning (NN/RL) control method and comparing it with the classic robust methods of suppression.

The flexible wing and aileron with hysteresis nonlinearity is treated as a plant-controller system and NN/RL and robust controller are used to suppress the nonlinear aeroelastic vibrations of aileron. The simulation approach is used for analyzing the efficiency of both types of methods in suppressing of such vibrations.

The analysis shows that the NN/RL controller is able to suppress the nonlinear vibrations of aileron much better than linear robust method, although its efficiency depends essentially on the NN topology as well as on the RL strategy.

Only numerical analysis was carried out; thus, the proposed solution is of theoretical value, and its application to the real suppression of aeroelastic vibrations requires further research.

The work shows the NN/RL method has a great potential in improving suppression of highly nonlinear aeroelastic vibrations, opposed to the classical robust methods that probably reach their limits in this area.

The work raises the questions of controllability of the highly nonlinear aeroelastic systems by means of classical robust and NN/RL methods of control.

The existing Nonlinear Dynamic Vibration Absorbers (NLDVAs) have the disadvantages of complex structure, high cost, high installation space requirements and difficulty in miniaturization. And most of the NLDVAs have not been applied to reality. To address the above issues, a novel Triple-magnet Magnetic Dynamic Vibration Absorber (TMDVA) with tunable stiffness, only composed of triple cylindrical permanent magnets and an acrylic tube, is designed, modeled and tested in this paper.

(1) A novel TMDVA is designed. (2) Theoretical and experimental methods. (3) Equivalent dynamics model.

It is found that adjusting the magnet distance can effectively optimize the vibration reduction effect of the TMDVA under different resonance conditions. When the resonance frequency of the cantilever changes, the magnet distance of the TMDVA with a high vibration reduction effect shows an approximately linear relationship with the resonance frequency of the cantilever which is convenient for the design optimization of the TMDVA.

Both the simulation and experimental results prove that the TMDVA can effectively reduce the vibration of the cantilever even if the resonance frequency of the cantilever changes, which shows the strong robustness of the TMDVA. Given all that, the TMDVA has potential application value in the passive vibration reduction of engineering structures.

The purpose of this paper is to analyze the active suppression of the nonlinear aeroelastic vibrations of ailerons caused by freeplay by robust H_∞ and linear quadratic Gauss (LQG) methods of control in case of incomplete measurements of the state of the system.

The flexible wing with nonlinear aileron with freeplay is treated as a plant-controller system with H_∞ and LQG controllers used to suppress the aeroelastic vibrations. The simulation approach was used for analyzing the impact of completeness of measurements on the efficiency and robustness of the controllers.

The analysis shows that the H_∞ method can be effectively used for suppression of nonlinear aeroelastic vibrations of aileron, although its efficiency depends essentially on completeness and types of measurements. The LQG method is less effective, but it is also able to prevent aileron vibrations by reducing their amplitudes to acceptable, safe level.

Only numerical analysis was carried out for the problem described; thus, the proposed solution is of theoretical value at this stage of analysis, and its application to the real suppression of aeroelastic vibrations requires further research.

The work presents a potentially useful solution to the problem of interest and results are a theoretical basis for further research.

This work may lead to a hot debate on the advantages and drawbacks of the active suppression of vibrations in the aeroelasticians community.

The work raises the important questions of practical stabilizability of the nonlinear aeroelastic systems, their dependence on completeness and types of measurements and robustness of the controllers.

This paper studies the nonlinear dynamics of membrane structure considering wrinkling effect. The coupling between wrinkles and vibration is investigated elaborately, and new insight on the dynamics of wrinkled membrane is unveiled.

Based on the stability theory of plates and shells, the wrinkling model of the membrane structure is established. Considering the effects of wrinkling and nonlinearity, the dynamic response is calculated with NewMark method.

Wrinkling will impact the dynamics of the membrane structure significantly for asymmetrical tension loading cases, dynamic response of the wrinkled membrane structure can be classified into three categories: when the vibration is small, the dynamics of the wrinkled membrane structure will behave linearly, and the wrinkles will only affect the dynamic properties as initial conditions; when the vibration is relatively large, the wrinkles will interact with the vibration during the dynamic process, and the dynamics of the structure shows very complex features; when the vibration is large enough, the dynamics will be dominated by the geometric nonlinearity of large-amplitude vibration.

In the previous works on dynamics of wrinkled membrane structure, only the vibration modes have been studied, which means all those investigations are confined with linear vibration; little research has been conducted on the nonlinear dynamics of wrinkled membrane structure. In view of this, this paper presents an investigation of dynamic properties of membrane structure considering the wrinkling and geometric nonlinear effects. This research work presents some novel discoveries on the nonlinear dynamics of wrinkled membrane.

The purpose of this paper is to investigate nonlinear vibrations of triple-walled carbon nanotubes buried within Pasternak foundation carrying viscous fluids.

Considering the geometry of nanotubes, the governing equations were initially derived using Timoshenko and modified couple stress theories and by taking into account Von-Karman expressions. Then, by determining boundary conditions, type of fluid motion, Knudsen number and, ultimately, fluid viscosity, the principal equation was solved using differential quadrature method, and linear and nonlinear nanotube frequencies were calculated.

The results indicated that natural frequency is decreased as the fluid velocity and aspect ratio increase. Moreover, as the aspect ratio is increased, the results converge for simple and fixed support boundary conditions, and the ratio of nonlinear to linear frequencies approaches. Natural frequency of vibrations and critical velocity increase as Pasternak coefficient and characteristic length increase. As indicated by the results, by assuming a non-uniform velocity for the fluid and a slip boundary condition at Kn = 0.05, reductions of 10.714 and 28.714% were observed in the critical velocity, respectively. Moreover, the ratio of nonlinear to linear base frequencies decreases as the Winkler and Pasternak coefficients, maximum deflection of the first wall and characteristic length are increased in couple stress theory.

This paper is a numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid.

The purpose of this paper is to describe the structure of nonlinear dampers and the dynamic equations, and nonlinear realization principles and optimize the parameters of nonlinear dampers. Using the finite element method to analyze the seismic performance of the frame structure with shock absorber.

The nonlinear shock absorber was installed in a six-storey reinforced concrete frame structure to study its seismic performance. The main structure was designed according to the eight degree seismic fortification intensity, and the time history dynamic analysis was carried out by Abaqus finite element software. EL-Centro, Taft and Wenchuan seismic record were selected to analyze the seismic response of the structure under different magnitudes and different acceleration peaks.

Through the principle study and parameter analysis of the nonlinear shock absorber, combined with the finite element simulation results, the shock absorption performance and shock absorption effect of the nonlinear energy sink (NES) nonlinear shock absorber are given as follows: first, the damping of the NES shock absorber is satisfied, and the linear spring stiffness and nonlinear stiffness of the shock absorber are based on the relationship k1=kn×kl2, so that the spring design length is fixed, and the linear stiffness of the shock absorber can be obtained. The nonlinear shock absorber has the characteristics of high rigidity and frequency bandwidth, so that the frequency is infinitely close to the frequency of the main structure, and when the mass of the shock absorber satisfies between 0.056 and 1, a good shock absorption effect can be obtained, and the reinforced concrete with the shock absorber is obtained. The frame structure can effectively reduce the seismic response, increase the natural vibration period of the structure and reduce the damage loss of the structure. Second, the spacer and each additional shock absorber have a small difference in shock absorption effect. After the shock absorber parameters are accurately calculated, the number of installations does not affect the shock absorption effect of the structure. Therefore, the shock absorber is properly constructed and accurately calculated. Parameters can reduce costs.

New shock absorbers reduce earthquake-induced damage to buildings.

In this paper, the important aspects of vibration analysis of carbon nanotubes (CNTs) as nano-resonators are studied. This study has covered the important nonlinear phenomena such as jump super-harmonic and chaotic behavior. CNT is modeled by using the modified nonlocal theory (MNT).

In previous research studies, the effects of CNT’s rotary inertia, stiffness and shear modulus of the medium were neglected. So by considering these terms in MNT, a comprehensive model of vibrational behavior of carbon nanotube as a nanosensor is presented. The nanotube is modeled as a nonlocal nonlinear beam. The first eigenmode of an undamped simply supported beam is used to extract the nonlinear equation of CNT. Harmonic balance method is used to solve the equation, while to study its super-harmonic behavior, higher-order harmonic terms were used.

In light of frequency response equation, jump phenomenon and chaotic behavior of the nanotube with respect to the amplitude of excitation are investigated. Also in each section of the study, the effects of elastic medium and nonlocal parameters on the vibration behavior of nanotube are investigated. Furthermore, parts of the results in linear and nonlinear cases were compared with results of other references.

The present modification of the nonlocal theory is so important and useful for accurate investigation of the vibrational behavior of nano structures such as a nano-resonator.

This study aims to establish the friction vibration model.

The friction vibration experiment was carried out on a pin disk friction tester. The causes of friction vibration are discussed, and the friction vibration model is established based on the energy method.

The experimental and simulation results show that the main cause of friction vibration is the nonlinear change of friction coefficient; degree of the friction vibration has a positive relationship with the friction relative velocity and normal contact positive pressure; the proposed friction vibration model is highly consistent in chaotic attractor and time-frequency distribution map and can well predict friction vibration.

The proposed friction vibration model is highly consistent in chaotic attractor and time-frequency distribution map and can well predict friction vibration.

This paper solves the modified-Duffing ordinary differential equation for large-amplitude vibration of imperfect angle-ply rectangular composite plate. Viscous damping is then introduced in the derivation and analyzed under four different boundary conditions (combining two out-of-plane boundary conditions with two in-plane boundary conditions). It has been shown that even a small viscous damping factor, for example 0.1 from an ordinary damped system can largely decrease the vibration amplitude within several periods. Yet at the same time, the vibration frequency only changes slightly. Furthermore, viscous damping is proved to significantly affect the vibration frequency and the vibration mode from nonlinear to much more linear. This effect is irrelevant to boundary conditions and geometric imperfections.