Large Amplitude Nonlinear Vibration Research Articles

Nonlinear Coupled Vibration Behavior of BFRP Cables on Long-Span Cable-Stayed Bridges under Parametric Excitation

Based on the cable-stayed beam model, this paper studies the nonlinear coupled vibration behavior of basalt fiber-reinforced polymer (BFRP) cables on long-span cable-stayed bridges under parametric excitation. Considering the sag, damping of BFRP cables, and the coupled interactions between stayed cables and the main girder, the nonlinear coupling vibration model of the BFRP cable–beam composite structure has been established. Taking the longest cable of Sutong Bridge as a case study, the nonlinear coupled vibration behavior of BFRP cables under parametric excitation has been numerically analyzed using the finite difference method. The analysis results indicate that (1) under parametric excitation, the large amplitude nonlinear vibration of the BFRP cable will be induced with an evident “beat” phenomenon. (2) Under the same parametric excitation, the nonlinear coupling vibration response and the beta frequency of the BFRP cable were both smaller than that of the traditional steel cable. (3) The nonlinear coupling vibration response of the BFRP cable increased with an increment in excitation amplitude and a decrement in cable force. With the increase in the excitation frequency, weight per unit length, and axial stiffness, the nonlinear vibration response of the BFRP cable increased first and then decreased. Meanwhile, the damping ratio of the BFRP cable had no significant influence on the nonlinear coupling vibration.

Large amplitude free vibration analysis of circular arches with variable thickness

This study aims to investigate the large amplitude nonlinear vibration of variable thickness arches with different cross-sectional shapes under different boundary conditions. The governing equations of the arches are derived using Hamilton's principle by considering their geometric nonlinearities. Then, the differential quadrature method (DQM) is employed for the discretization to obtain the ordinary differential equations of motion for the circular arches with variable thickness. The theoretical model is validated by comparing the linear and nonlinear natural frequencies of arches. The nonlinear vibration characteristics of arches are solved using the direct iteration scheme. The effects of the slenderness ratio, modified slenderness ratio of the arch, and variable thickness parameters under different cross-sectional shapes on the nonlinear to linear frequency ratios of the arches with clamped and pin-ended boundary conditions are investigated. The results indicate that appropriate variable thickness parameters can improve the linear frequency and the nonlinear to linear frequency ratio of arches, which offers some suggestions for the design of variable thickness arches.

Dynamic modeling and control of a solar sail considering large-amplitude nonlinear vibration

The solar sail spacecraft utilizes Solar Radiation Pressure (SRP) to achieve propulsion, which can realize long-term acceleration without fuel consumption, making it an appealing option for deep space exploration and polar-sitter observation. However, because of the large-scale and high-flexibility of the membrane structure, the solar sail poses challenging dynamic and control issues. Precise dynamic modeling and effective control design can provide theoretical guidance for the efficient functioning of solar sail, which are of great significance and urgently need to be studied. In this paper, a dynamic model that can describe the large-amplitude vibrations of the solar sail is established. Additionally, an attitude tracking controller and a cable-based nonlinear vibration controller are designed to control the attitude motion and flexible vibration of the solar sail. The results show that the established nonlinear rigid-flexible coupling dynamic model is more accurate compared to the linear dynamic model. The polynomial fitting method can characterize the nonlinear dynamics of the solar sail extremely effectively while cutting the program runtime to 5% of the original. Two controllers designed in this paper can make the solar sail maneuver follow the desired trajectory accurately while reducing the sail surface vibration by more than 40%. The research outcomes of this paper can provide references for the dynamic study and active control of large-scale membrane spacecraft.

Vibration Suppression of HTS Maglev System Based on Negative Resistance Electromagnetic Shunt Damper

The high-temperature superconducting (HTS) maglev system has tremendous possibilities for future high-speed transportation application owing to its salient advantages of self-stable levitation and zero pollution operation. However, previous study indicated that the relatively low damping of HTS system may lead the undesired large-amplitude nonlinear vibration in system. Thus, electromagnetic shunt damper (EMSD), which usually consists of electromagnets, permanent magnets and shunt impedance connected to the terminals of the coils, is introduced in the system to improve the damping of the system. The effect of EMSD is to transfer the mechanical energy to electrical energy and consume it in the form of Joule heat. For better vibration suppression performance, this paper proposes a negative resistance electromagnetic shunt damper (NR-EMSD) in HTS maglev vehicle model. The negative resistance can offset the inherent resistance of the electromagnet coils and as a consequence, the induced current of the circuit will increase as well as the induced electromagnetic force. Also, the change of total resistance of the circuit will influence the vibration reduction performance. In this paper, the effect of NR-EMSD is tested by experiment under different working conditions compared with the model without EMSD. The results are analyzed and basic conclusions are summarized. This work may provide references for further practical application in HTS system.

On the nonlinear dynamics of porous composite nanobeams connected with fullerenes

In this study, an attempt is made to investigate the large-amplitude nonlinear vibration response of symmetric porous functionally graded (FG) nanobeams carrying several fullerenes. The influence of various porosity distributions as well as position and mass of fullerenes on the nonlinear vibrational behaviour is particularly studied. To model size effects on the vibration response, a nonlocal elasticity and strain gradient theory in conjunction with the Euler-Bernoulli beam theory is used. Using Hamilton’s variational principles, the strain energy, external work and kinetic energy of the ultrasmall system are formulated. The governing nonlinear equations and the associated boundary conditions that incorporate geometrical nonlinearity are derived. Inhomogeneity in the material parameters of the FG porous nanobeam is modelled according to the power-law mixture of constituent materials with cosine function. A discretization technique based on Galerkin’s approach and a perturbation solution method are employed to estimate the shift in the nonlinear frequencies of the nanobeams due to the attached fullerene. The nonlinear frequency shift of the complex coupled nanosystem is calculated for various boundary conditions. The validity of the estimated results is evaluated by performing several comparison studies with available data in the literature. Several system parameters such as porosity distribution, material index, the number, position and mass of attached fullerenes, as well as size parameters including the length scale and nonlocal coefficients are taken into consideration in the nonlinear vibration analysis.

Nonlinear vibration of temperature-dependent FG-CNTRC laminated plates with negative Poisson's ratio

Abstract This paper reports a study on the large amplitude nonlinear vibration of carbon nanotube-reinforced composite (CNTRC) laminated plates with negative Poisson's ratios in thermal environments. The constituent materials of CNTRCs are temperature-dependent and the plate is functionally graded (FG) in a piece-wise pattern in the thickness direction of plate. An extended Voigt (rule of mixture) model is adopted to quantify the CNTRC material properties of the laminated plate. The governing motion equations for the large amplitude vibration of FG-CNTRC laminated plates are based on the Reddy's third order shear deformation theory and the von Karman-type kinematic nonlinearity framework, and the thermal effects and the reaction from elastic foundation are taken into account. The nonlinear solution of the motion equation can be obtained by applying a two-step perturbation approach. The effects of material property gradient, the temperature variation, stacking sequence as well as the foundation stiffness on the vibration characteristics of CNTRC laminated plates are examined and discussed in depth through a parametric study. The results show that negative Poisson's ratio has a significant effect on the linear and nonlinear vibration characteristics of CNTRC laminated plates.

Vibration Suppression of High-Temperature Superconducting Maglev System via Electromagnetic Shunt Damper

The high-temperature superconducting (HTS) maglev system is characterized with self-stable levitation, low energy consumption, and pollution-free operation, and it has been considered as a promising technology for implementing high-speed transport systems. But the previous studies have shown that the damping of such system is relatively low, which indicates the large-amplitude nonlinear vibration may occur easily under external disturbances and affect the long-term motion stability, operation safety, and comfort of HTS maglev in rail transit application. In order to suppress the harmful vibration, an electromagnetic shunt damper (EMSD) was designed and incorporated into the HTS maglev system. Compared with other systems which employ the EMSD to diminish the vibration, the HTS maglev system does not need to set up external devices to supply magnetic field for the damper, because the permanent magnet guideway (PMG) in this system is directly taken advantages of. The natural frequency of the damper is adjusted to a value close to that of the maglev system. In this way, the damper becomes most effective because the moving vehicle body and the circuit resonate simultaneously. The feasibility of the damper was demonstrated through systematic experiments, and the effects of different field cooling heights (FCHs) of the HTS maglev system on EMSD’s performance were experimentally studied as well. Also, how the change of resistors in the EMSD circuit affects its working efficiency was preliminarily explored in this work. The results show that under the definite external disturbance, the damper can effectively attenuate the acceleration of vibration, furthermore, and it is found that the damper works better in condition of lower FCH. Within the scope of our experiments, the EMSD with a resistor in lower resistance performs better as results have shown. This investigation indicates that the vehicle will run in a more smooth and comfortable way along the track with this damper. The work is important for the further practical application of the technology.

Multiaxial fatigue investigation of titanium alloy annular discs by a vibration-based fatigue test

A novel vibration-based fatigue experimental system has been established to study the fatigue properties of titanium alloy annular discs in near resonance conditions. The excitation frequency-response curves are experimentally obtained in order to clarify the large amplitude nonlinear vibration characteristics of the discs. Then a vibration-based fatigue test of the discs and the corresponding 10° segment specimens are conducted respectively to obtain the S-N curves and the fatigue limit stresses. A multiaxial fatigue criterion is subsequently proposed to predict the fatigue properties of the discs, which is compared with the present experimental results finally. It is demonstrated that the high-cycle fatigue properties of the discs can be obtained by the present vibration-based fatigue test, which is an in-phase biaxial fatigue test. The fatigue limit stress of the discs can be predicted well by the proposed elliptic multiaxial fatigue criterion together with the fatigue testing results of the corresponding segment specimens.

Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities

In this paper, the large-amplitude nonlinear vibration characteristics of functionally graded (FG) Timoshenko beams made of porous material is investigated for the first time. Material properties of FG porous beam are supposed to vary continuously along the thickness according to the rule of mixture which modified to approximate material properties with porosity phases. The governing equations are derived based on Timoshenko beam theory through Hamilton׳s principle and they are solved utilizing both Galerkin׳s method and the method of multiple scales. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG porous beams as compared to the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as material distribution profile, porosity volume fraction, aspect ratio and mode number on the normalized natural frequencies of the FG porous beams in detail. It is explicitly shown that the vibration behavior of a FG beams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG porous beams.

Vibration Suppression in High- <inline-formula> <tex-math notation="TeX">${\rm T}_{\rm c} $</tex-math></inline-formula> Superconducting Levitation System Utilizing Nonlinearly Coupled Electromagnetic Shunt Damper

Superconducting levitation systems have been considered as a promising technology for implementing high-speed transport systems. A superconducting levitation system can levitate a magnet without active feedback control. However, due to the system's low damping and nonlinearity, large-amplitude nonlinear vibration can easily occur. Although an electromagnetic shunt damper can suppress the vibration without contact by transforming the vibrational kinetic energy into electrical energy, the inductance value of the damper often becomes too large to realize practically. Therefore, we propose a new type of electromagnetic shunt damper that is nonlinearly coupled with the levitated body, and its value of inductance can be reduced to one-fourth the conventional one. First, we evaluate the levitation force via the advanced mirror image method. Next, we perform numerical calculation via the Runge-Kutta method and nonlinear analysis via the method of multiple scales. We obtain the system's frequency responses via both these methods. From the results, we observe that internal resonance can occur and the proposed electromagnetic shunt damper can reduce the vibration amplitude.

DYNAMIC ANALYSIS FOR NONLINEAR VIBRATION OF PRESTRESSED ORTHOTROPIC MEMBRANES WITH VISCOUS DAMPING

This paper is concerned with the nonlinear damped vibration of prestressed orthotropic membrane structures. The Krylov–Bogolubov–Mitropolsky (KBM) perturbation method is employed for solving the governing equations of large amplitude nonlinear vibration of rectangular orthotropic membranes with viscous damping. Presented herein are asymptotic analytical solutions for the frequency and displacement function of large amplitude nonlinear damped vibration of rectangular orthotropic membranes with four edges simply supported or fixed. Through the computational example, we compared and analyzed the frequency results. Meanwhile, the vibration mode of the membrane and the displacement and time curve of each feature point on the membrane surface were analyzed. The results obtained herein provide a simple and convenient approach to calculate the frequency and lateral displacement of large amplitude nonlinear vibration of rectangular orthotropic membranes with low viscous damping. In addition, the results provide some computational basis for the vibration control and dynamic design of membrane structures.

Influence of Thermal Loading on the Dynamic Response of Thin-Walled Structure under Thermo-Acoustic Loading

Future flight vehicle structures will encounter severe loading conditions, a combination of aerodynamic, thermal, acoustic and mechanical loads. Although the analysis methods for responses of structures under acoustic loads have been developed to some extent, but with thermal loads considered, the responses show fundamental differences, which complicate the analysis immensely. It was reported that hypersonic flight may give rise to surface temperature as high as and intense noise whose overall sound pressure level (OSPL) may reach 180dB. Thin-walled structures subjected to such loadings will exhibit nonlinear responses. Large temperature increments may cause thermal buckling, large thermal deflections and large thermal stresses superimposed on dynamic stresses, coupled with changes in material properties. Both the geometry change by thermal buckling and stiffness change by thermal stress account for the changes of natural frequencies and mode shapes. When the acoustic loading increases to a high enough level, the post-buckled structures will exhibit snap-through motion, a large amplitude nonlinear vibration between different equilibrium positions, which will introduce extra large mean stress. As a result, thermo-acoustic fatigue may be caused, which will reduce the structure's fatigue life dramatically. Therefore it is an urgent need to estimate the influences of thermal loads on the nonlinear response of structures. A numerical investigation of the influences of thermal loads on the dynamic response of thin-walled structure under thermo-acoustic loadings is implemented. With clamped-clamped thin flat plate selected, the response characteristics related to temperature are investigated by changing thermal loads. The thermal load is considered as constant both on the surface and across the thickness. The acoustic load is simulated using stationary Gaussian white noise. Firstly, a thermal buckling analysis is proceeded to obtain critical buckling temperatures, followed by modal analysis under different thermal loads. The pre-buckled and post-buckled mode frequencies and shapes are obtained. Then three types of snap-though motions are predicted: i) vibration around one post-buckled equilibrium position, ii) intermittent snap-through, and iii) persistent snap-through. The relations between thermal loads and the occurrence of snap-though is obtained together with results about the statistics characteristic of dynamic response and their relations with thermal loads, which include critical thermal buckling loads, natural frequencies and mode shapes, RMS response and snap-through frequency. Good agreements have been achieved with previous analytical solutions, which demonstrate the effectiveness and reliability of the method employed.

A new method-ejection method for nondestructive online monitoring of the pretension of building membrane structure

SUMMARY To determine whether the actual pretension of membrane structure tallies with the design pretension and whether the membrane structure is relaxed after employing, we must monitor the actual pretension of the building membrane structure accurately and then adopt some measures to ensure the engineering quality and reduce the engineering accidents. The pretension monitoring of the building membrane structure belongs to the structural nondestructive health monitoring field. The authors of this paper developed a new method—ejection method for monitoring the pretension of building membrane structure accurately and nondestructively. The basic idea of this method was represented, and the theoretical model of this method was established by studying the large amplitude nonlinear vibration problem of the orthotropic membrane, and then the theoretical measurement formula was derived by the energy conservation principle. Meanwhile, the finite element numerical analysis was carried out for the theoretical model, and the ejection experiment for the three kinds of conventional membrane material (Mehler FR-900 (Mehler Texnologies, Huckelhoven, Germany), Ferrari 502S (Ferrari, Cape Town, South Africa), and Yilong 750 (Yilong, Guangdong, China)) was carried out according to the theoretical idea. The numerical analysis and experimental results proved that the ejection method is feasible and verified that the theoretical derivation is correct. Copyright © 2011 John Wiley & Sons, Ltd.

Higher-order approximate solutions for nonlinear vibration of a constant-tension string

A new harmonic balance approach for solving the large amplitude nonlinear vibration of a constant-tension string is introduced. The coupling of Newton's method with harmonic balancing takes the advantage of reducing the deficiency and complexity of the classical harmonic balance method in dealing with the nonlinear systems. The solutions are directly induced from a set of linear algebraic equations instead of a set of complicated, coupled nonlinear algebraic equations. Illustrative examples are selected and compared to some published data to verify the accuracy of the higher-order solutions.

Nonlinear vector eigen-solver and parallel reassembly processing for structural nonlinear vibration

In the frequency domain solution of large amplitude nonlinear vibration, two operations are computationally costly. They are: (1) the iterative eigen-solution and (2) the iterative nonlinear matrix reassembly. This study introduces a nonlinear eigen-solver which greatly speeds up the solution procedure by using a combination of vector iteration and nonlinear matrix updating. A feature of this new method is that it avoids repeatedly using a costly eigen-solver or equation solver. This solution procedure has also been engaged in parallel processing to further speed up the computation. Parallel nonlinear matrix reassembly is the main interest in this parallel processing. Force Macro is used in the parallel program on a CRAY-2S supercomputer.

A boundary integral equation formulation for large amplitude nonlinear vibration of thin elastic plates

An integral equation formulation for large amplitude free vibration of thin plates is presented. The Von Karman nonlinear plate bending theory is adopted. By using the harmonic balance method and discretizing both on the boundary and in the domain, the amplitude dependent eigenvalue equations are obtained. An appropriate iterative procedure is proposed to solve the nonlinear free vibration problems. A number of numerical examples are given to demonstrate its feasibility and efficiency.