Nonlinear Stiffness Properties Research Articles

Active control of a non-linear landing gear system having oleo pneumatic shock absorber using robust linear quadratic regulator approach

This paper deals with the active control of a non-linear active landing gear system equipped with oleo pneumatic shock absorber. Runway induced vibration can cause reduction of pilot’s capability of control the aircraft and results the safety problem before take-off and after landing. Moreover, passenger–crew comfort is adversely affected by vertical vibrations of the fuselage. The active landing gears equipped with oleo pneumatic shock absorber are highly non-linear systems. In this study, uncertain polytopic state space representation is developed by modelling the pneumatic shock absorber dynamics as a mechanical system with non-linear stiffness and damping properties. Then, linear matrix inequalities-based robust linear quadratic regulator controller having pole location constraints is designed, since the classical linear quadratic regulator control design is dealing with linearized state space models without considering the non-linearities and uncertainties. Thereafter, numerical simulation studies are carried out to analyse aircraft response during taxiing. Bump- and random-type runway irregularities are used with various runway class and wide range of longitudinal speed. Simulation results revealed that neglecting the non-linear dynamics associated with oleo pneumatic shock absorber results significant performance degradation. Consequently, it is demonstrated that proposed robust linear quadratic regulator controller has a superior performance in terms of passenger–crew comfort and operational safety when compared to classical linear quadratic regulator.

Optimization under uncertainty of parallel nonlinear energy sinks

Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy over a wider range of frequencies. Nevertheless, they are still only efficient over a limited range of excitations. In order to mitigate this limitation and maximize the efficiency range, this work investigates the optimization of multiple NESs configured in parallel. It is well known that the efficiency of a NES is extremely sensitive to small perturbations in loading conditions or design parameters. In fact, the efficiency of a NES has been shown to be nearly discontinuous in the neighborhood of its activation threshold. For this reason, uncertainties must be taken into account in the design optimization of NESs. In addition, the discontinuities require a specific treatment during the optimization process. In this work, the objective of the optimization is to maximize the expected value of the efficiency of NESs in parallel. The optimization algorithm is able to tackle design variables with uncertainty (e.g., nonlinear stiffness coefficients) as well as aleatory variables such as the initial velocity of the main system. The optimal design of several parallel NES configurations for maximum mean efficiency is investigated. Specifically, NES nonlinear stiffness properties, considered random design variables, are optimized for cases with 1, 2, 3, 4, 5, and 10 NESs in parallel. The distributions of efficiency for the optimal parallel configurations are compared to distributions of efficiencies of non-optimized NESs. It is observed that the optimization enables a sharp increase in the mean value of efficiency while reducing the corresponding variance, thus leading to more robust NES designs.

Stochastic optimization of nonlinear energy sinks

Nonlinear energy sinks (NES) are a promising technique to achieve vibration mitigation. Through nonlinear stiffness properties, NES are able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NES absorb energy from a wide range of frequencies. Many studies have focused on NES behavior and dynamics, but few have addressed the optimal design of NES. Design considerations of NES are of prime importance as it has been shown that NES dynamics exhibit an acute sensitivity to uncertainties. In fact, the sensitivity is so marked that NES efficiency is near-discontinuous and can switch from a high to a low value for a small perturbation in design parameters or loading conditions. This article presents an approach for the probabilistic design of NES which accounts for random design and aleatory variables as well as response discontinuities. In order to maximize the mean efficiency, the algorithm is based on the identification of regions of the design and aleatory space corresponding to markedly different NES efficiencies. This is done through a sequence of approximated sub-problems constructed from clustering, Kriging approximations, a support vector machine, and Monte-Carlo simulations. The refinement of the surrogates is performed locally using a generalized max-min sampling scheme which accounts for the distributions of random variables. The sampling scheme also makes use of the predicted variance of the Kriging surrogates for the selection of aleatory variables values. The proposed algorithm is applied to three example problems of varying dimensionality, all including an aleatory excitation applied to the main system. The stochastic optima are compared to NES optimized deterministically.

Compactly modelling and analysing the roll dynamics of a partly filled tank truck

In this study, a compact roll dynamics model for a partly filled tank truck is formulated based on Lagrange's approach. A trammel pendulum equivalent mechanical model is used to simulate the fluid lateral sloshing, and the nonlinear stiffness property of the suspension is also taken into account. The model is indirectly validated by comparing the state response with Salem's trammel pendulum model (Salem et al., 2009). The analysis results reveal that the lateral fluid sloshing in a partly filled tank generally couples with the body roll dynamics of the vehicle, and the rollover stability threshold can be enhanced by increasing the vehicle suspension stiffness. It is concluded that there is a potential of optimising the parameters of tank-sectional shape, suspension stiffness and damping, and some other configurable parameters to elevate the rollover stability of a partly filled tank truck in a wide fill level range.

Vibration isolation by exploring bio-inspired structural nonlinearity

Inspired by the limb structures of animals/insects in motion vibration control, a bio-inspired limb-like structure (LLS) is systematically studied for understanding and exploring its advantageous nonlinear function in passive vibration isolation. The bio-inspired system consists of asymmetric articulations (of different rod lengths) with inside vertical and horizontal springs (as animal muscle) of different linear stiffness. Mathematical modeling and analysis of the proposed LLS reveal that, (a) the system has very beneficial nonlinear stiffness which can provide flexible quasi-zero, zero and/or negative stiffness, and these nonlinear stiffness properties are adjustable or designable with structure parameters; (b) the asymmetric rod-length ratio and spring-stiffness ratio present very beneficial factors for tuning system equivalent stiffness; (c) the system loading capacity is also adjustable with the structure parameters which presents another flexible benefit in application. Experiments and comparisons with existing quasi-zero-stiffness isolators validate the advantageous features above, and some discussions are also given about how to select structural parameters for practical applications. The results would provide an innovative bio-inspired solution to passive vibration control in various engineering practice.

Band stop vibration suppression using a passive X-shape structured lever-type isolation system

In the paper, band-stop vibration suppression property using a novel X-shape structured lever-type isolation system is studied. The geometrical nonlinear property of an X-shape supporting structure is used to improve the band-stop characteristics in the low frequency range of the lever-type vibration isolator. With the dynamics modeling of this hybrid structural system, it is shown that the proposed hybrid vibration system has very beneficial nonlinear stiffness and damping properties which are helpful to achieve much wider stop bandwidth. Theoretical results demonstrate that the anti-resonant frequencies, width and magnitude of the stop band can all be flexibly designed with structural parameters, and the parameters of the X-shape supporting structure are very critical for designing the band-stop frequency to achieve excellent low-frequency isolation performance. The results in the study provide a new approach to the design of the passive vibration suppression system in the low frequency region.

Vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure

This study presents some novel results about analysis and design of low-frequency or broadband-frequency vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure in passive or semi-active control manners. It is shown that the system has inherent nonlinear stiffness and damping properties due to structure geometrical nonlinearity. Theoretical analysis reveals that the hybrid isolation system can achieve very good ultra-low-frequency isolation through a significantly-improved anti-resonance frequency band (by designing structure parameters). Noticeably, the system can realize a uniformly-low broadband vibration transmissibility, which has never been reported before. Cases studies show that the system can work very well with good isolation performance subject to multi-tone and random excitations. The results provide a new innovative approach to passive or semi-active vibration control (e.g., via a simple linear stiffness control) for many engineering problems with better ultra-low/broadband-frequency vibration suppression.

Seismic assessment of out-of-plane loaded unreinforced masonry walls in multi-storey buildings

A procedure is proposed to evaluate the dynamic out-of-plane stability of cracked unreinforced masonry (URM) walls located in multi-storey URM buildings. The equations of dynamic motion are derived from first principles and representative single-degree-of-freedom (SDOF) models are proposed. The models have nonlinear stiffness properties that correspond to the restoring gravitational forces. A method is suggested to transform the nonlinear problem to a corresponding linear equivalent so that conventional spectral methods can be used to calculate wall response.
 The dynamic interaction between the URM building as the main structural system and the out-of-plane loaded walls as secondary elements is addressed by developing floor response spectra. Several buildings were assumed in a parametric study and subjected to code-compatible ground motion records. The absolute acceleration response at floor levels was calculated and the response spectra for that modified acceleration were subsequently obtained.
 The results from the study suggest that modifications should be made to the equations proposed for the Parts response spectra in the New Zealand seismic loading standard, NZS 1170.5:2004, in order to calculate the spectral response of out-of-plane loaded URM walls. Several worked examples are presented to demonstrate application of the procedure.

Study on Nonlinear Damping Properties of Hydro-Pneumatic Suspension System for XP302-Pneumatic Tyred Roller

The nonlinear stiffness and damping properties of the hydro-pneumatic suspension system are introduced, and the nonlinear mathematical model of it is established. Using MATLAB 2009b to establish the computer simulation program and draw out the nonlinear stiffness curve and damping properties curve of the hydro-pneumatic suspension system. Then, researching the influences of related parameters' changes on the nonlinear stiffness and damping properties of the hydro-pneumatic suspension system. The simulation of vehicle dynamic performance research's foundation is provided.

Alternative approach to buckling of square hollow section steel columns in fire

Stability of axially loaded steel columns with square hollow sections at elevated temperatures is studied herein. At present the Eurocode model for checking buckling capacity of columns in fire has been developed on the similar basis as for ambient conditions. It is shown that due to the effect of complex non-linear behavior the standard design model is not always adequate and in certain situations prediction of buckling capacity of columns according to the common design formulas may even reach results on the unsafe side. The main focus of this work is the performance of an analytical model against advanced numerical methods. For this purpose extensive numerical study was performed using non-linear FE method. Based on the results obtained with advanced calculation models of column behavior at elevated temperatures an analytical model has been proposed and verified. The proposed model accounts for variable non-linear stiffness properties, which have significant effect on the buckling capacity of axially loaded columns in fire. The advantage of the method is the format, which is convenient for incorporation into common design algorithms.

Design and optimization of a bend-and-sweep compliant mechanism

A novel contact aided compliant mechanism called bend-and-sweep compliant mechanism is presented in this paper. This mechanism has nonlinear stiffness properties in two orthogonal directions. An angled compliant joint (ACJ) is the fundamental element of this mechanism. Geometric parameters of ACJs determine the stiffness of the compliant mechanism. This paper presents the design and optimization of bend-and-sweep compliant mechanism. A multi-objective optimization problem was formulated for design optimization of the bend-and-sweep compliant mechanism. The objectives of the optimization problem were to maximize or minimize the bending and sweep displacements, depending on the situation, while minimizing the von Mises stress and mass of each mechanism. This optimization problem was solved using NSGA-II (a genetic algorithm). The results of this optimization for a single ACJ during upstroke and downstroke are presented in this paper. Results of two different loading conditions used during optimization of a single ACJ for upstroke are presented. Finally, optimization results comparing the performance of compliant mechanisms with one and two ACJs are also presented. It can be inferred from these results that the number of ACJs and the design of each ACJ determines the stiffness of the bend-and-sweep compliant mechanism. These mechanisms can be used in various applications. The goal of this research is to improve the performance of ornithopters by passively morphing their wings. In order to achieve a bio-inspired wing gait called continuous vortex gait, the wings of the ornithopter need to bend, and sweep simultaneously. This can be achieved by inserting the bend-and-sweep compliant mechanism into the leading edge wing spar of the ornithopters.

Realization of a Strongly Nonlinear Vibration-Mitigation Device Using Elastomeric Bumpers

AbstractRecent research has shown the viability of using nonlinear energy-sink (NES) devices for vibration mitigation in mechanical and structural systems. When attached to a primary structure, these lightweight passive devices can effectively reduce the structural vibration response through their nonlinear stiffness properties. In this research, a two-degree-of-freedom NES device is designed using innovative elastomeric bumpers as the critical components providing nonlinear restoring forces. A number of elastomeric bumper configurations are evaluated experimentally, and the effect of geometric bumper parameters is investigated with a focus on their influence on the stiffness properties of the bumper. A NES device employing different bumpers is then implemented on a 6-story model building and tested using impulse-like base motion. Nonlinear system identification of the NES device shows that nonlinear stiffness properties are achieved using the elastomeric bumpers. Shake-table testing of the building equip...

Ultimate stress and age-dependent deformation characteristics of the iliotibial tract

Background and aimsTo understand biomechanics of ligaments and tendons data on their material properties are necessary. The iliotibial tract is a suitable model for virtual pelvic or lower extremity ligaments due to its parallel fibers, which facilitates biomechanical testing. Here, we determined Young's modulus (YM) as secant stiffness between defined limits of the iliotibial tract and correlated the data to ultimate stress (US) of the specimens and to age, gender and body weight of the body donors. Materials and methodsThirty eight specimens from 12 iliotibial tracts of 10 young donors (mean age 31.2±9.1 years) were investigated biomechanically. After preconditioning, YM were determined in the ranges of 0–4 and 4–11N/mm² of applied stress and from 4N/mm² of applied stress to US. ResultsYM of the specimens were 84.7±30.2 (0–4N/mm²), 335.4±101.9 (4–11N/mm²), and 369.1±191.5 (4N/mm² to US) N/mm², respectively. The mean US was 35.8±16.4N/mm². YM and US correlated closely in the ranges of 4–11N/mm² (r=0.95) and 4N/mm² to US (r=0.91). YM did not correlate to age, body weight or gender within these young donors. Concerning tissue behavior a decrease of YM, i.e. weakening, is more common than an increase of YM, i.e. stiffening, before specimen failure. Overall, YM of specimens from young donors were significantly lower compared to those of old donors. Discussion and conclusionsThis is the first study providing age-dependent nonlinear stiffness properties of the iliotibial tract. YM is significantly lower in young than in old donors and is thus a subject of alteration during life time.

The non-ideal problem behavior using a dynamic vibration absorber with nonlinear essential stiffness and time-dependent damping properties

The purpose of this study is to develop a dynamic vibration absorber using viscoelastic material with nonlinear essential stiffness and time-dependent damping properties for a non-ideal vibrating system with Sommerfeld effect, resonance capture, and jump phenomenon. The absorber is a mass-bar subsystem that consists of a viscoelastic bar with memory attached to mass, in which the internal dissipative forces depend on current, deformations, and its operational frequency varies with limited temperature. The non-ideal vibrating system consists of a linear (nonlinear) oscillator (plane frame structure) under excitation, via spring connector, of a DC-motor with limited power supply. A viscoelastic dynamic absorber modeled with elastic stiffness essentially nonlinearities was developed to further reduce the Sommerfeld effect and the response of the structure. The numerical results show the performance of the absorber on the non-ideal system response through the resonance curves, time histories, and Poincaré sections. Furthermore, the structure responses using the viscoelastic damper with and without memory were studied.

The Research on the Dynamic Characteristic of Rubber Isolator

This paper aims at to study the damping ratio and nonlinear stiffness property of rubber isolator effect on vibration response under different excitation level and temperature. By the means of experiment, the curves of amplitude-frequency of rubber isolator were obtained. Based on the experimental results, the damping ratio was ascertained by the method of half power point. A single freedom mechanics model that describes the isolated system was built, and the equation of frequency response deduced and solved by harmonic balance method. Furthermore, the effects of nonlinear factor of stiffness effect on vibration response were analyzed. The precision of the approximation that solved by harmonic balance method was validated using Runge-Kutta method. It is indicated that the equation of frequency-response can be used to describe the property of frequency-response of rubber isolator.

Stiffness properties of particulate composites containing debonded particles

This paper considers the problem of determining the nonlinear bimodular stiffness properties, i.e., the tensile and compressive Young’s moduli and Poisson’s ratios, and the shear modulus, of particulate composite materials with particle–matrix interfacial debonding. It treats the general case in which some of the particles are debonded while the others remain intact. The Mori–Tanaka approach is extended to formulate the method of solution for the present problem. The resulting auxiliary problem of a single debonded particle in an infinite matrix subjected to a remote stress equal to the average matrix stress, for which Eshelby’s solution does not exist, is solved by the finite element method accounting for the particle–matrix separation and contact at the debonded particle–matrix interface. Because of the nonlinear nature of the problem, an iterative process is employed in calculating the stiffness properties. The predicted stiffness properties are compared to the exact solutions of the stiffness properties of particulate composites with body-centered cubic packing arrangement.

Effect of tooth mesh stiffness asymmetric nonlinearity for drive and coast sides on hypoid gear dynamics

A nonlinear time-varying dynamic model of a hypoid gear pair system with time-dependent nonlinear mesh stiffness, mesh damping and backlash properties is formulated to study the effect of mesh stiffness asymmetry for drive and coast sides on dynamic response. The asymmetric characteristic is the result of the inherent curvilinear tooth form and pinion offset in hypoid set. Using the proposed nonlinear time-varying dynamic model, effects of asymmetric mesh stiffness parameters that include mean mesh stiffness ratio, mesh stiffness variation and mesh stiffness phase angle on the dynamic mesh force response and tooth impact regions are examined systematically. Specifically, the dynamic models with only asymmetric mesh stiffness nonlinearity, with only backlash nonlinearity and with both asymmetric mesh stiffness and backlash nonlinearities are analyzed and compared. Using the parameters of a typical hypoid gear set, the extent of the effect of asymmetry in the mesh coupling on gear pair dynamics is quantified numerically. The results show that the increase in the mean mesh stiffness ratio tends to worsen the dynamic response amplitude, and the mesh stiffness parameters for drive side have more effect on dynamic response than those of the coast side one.

Design and modeling of semi-active squeeze film dampers using magneto-rheologicalfluids

Conventional squeeze film dampers (SFDs) have shown their effectiveness in suppressingunbalanced vibrations in rotor systems, particularly supported by rolling element bearings.Recently, there is an increasing demand for ‘controllable’ SFDs to meet the needof modern rotating machinery, characterized by high operating speed and highload capacity. Thus, this paper presents a controllable semi-active SFD usingmagneto-rheological (MR) fluids, focusing on its design and modeling. It offers acomprehensive design method and an innovative experimental identification and modelingtechnique for MR-SFDs. The primary goal of the MR-SFD design is set to maximizeits dynamic control bandwidth, and the design method includes the materialselection, magnetic circuit analysis and sealing element design. After constructing aprototype MR-SFD based on the final design, this work investigated how someof the critical design parameters affect the performance of the MR-SFD (i.e. itsdynamic control bandwidth change). Furthermore, it characterized the damper’sdynamic behavior experimentally using a novel excitation method that adopts activemagnetic bearing (AMB) units. Unlike conventional methods, the AMB system wasable to precisely control the amplitude and frequency of the input excitation,enabling us to obtain the nonlinear dynamic stiffness properties of the MR-SFDwith varying input current. In modeling the dynamic behavior of the MR-SFD,this study employed the describing function method. The describing functionanalysis effectively captured the nonlinear dynamic behavior of the MR-SFD.

An Experimental Technique for the Evaluation of Strain Dependent Material Properties of Hard Coatings

A novel vibration experiment consisting of a free‐free boundary condition, an electromagnetic excitation source, a vacuum chamber, and a laser vibrometer based surface measurement system has been developed that permits high levels of excitation on highly damped specimens with a minimal amount of unwanted systematic error. While some of the aspects of this experiment are not unique, when combined with a processing technique that accounts for the nonlinearities present in the system, this experiment permits, accurate measurement of strain dependent stiffness and damping properties of hard coatings at high strain levels. This procedure has been demonstrated using a titanium beam that has been coated with a free‐layer damping treatment of Magnesium Aluminate Spinel. The results indicate that Magnesium Aluminate Spinel has both nonlinear stiffness and damping properties. The stiffness asymptotes to a minimum value around 650 microstrain while the damping is a maximum around 100 microstrain. Additionally, the data contained herein cover a larger strain range for this material than previously reported.

The Elastic Analysis of the Construction with Non-linear Stiffness Property and its Application to the Design

The elastic performance brings an appropriate flexibility and a restoring force for installing and maintaining the routing arrangement of the control cable which is widely used as machine elements for transmitting load and displacement. On the other hand, the non-linear elastic performance has also made it difficult to design the control cable theoretically. In this study, we considered the method of the elastic analysis for the construction with non-linear stiffness property, such as a control cable and its application for the actual design. Then, we obtained following conclusions.(1) We developed the precise FEA model for the construction with various non-linear stiffness property.(2) We developed the method to predict the routing arrangement, the performance and the durability performance.(3) This developed simulation technology have been widely used in our company as the optimal and the low-cost design method in the early stage of vehicle's development.