Nonlinear Shock Absorber Research Articles

Research on energy transfer and vibration suppression of nonlinear energy sink with nonlinear damping

The nonlinear energy sink is a nonlinear shock absorber that provides targeted energy transfer and plays a crucial role in structural vibration suppression. In this paper, the energy transfer and dynamic characteristics of nonlinear damping nonlinear energy sink systems are analyzed. Firstly, the theoretical model of the nonlinear damping NES system is described, and secondly, the equations of the system in the free state are derived by using the complex variable average method and the multi-scale method to obtain the energy transfer efficiency equation of the system. Through the study of the slow invariant manifold and energy transfer efficiency of the system, the influence of each system parameter on the energy transfer efficiency is analyzed. Then the equations of the system under harmonic excitation are processed in the same method to obtain the boundary equations of the system, through which the saddle-node bifurcation diagram of the system is plotted to study the influence of each system parameter on the saddle-node bifurcation characteristics of the system. Finally, the slow-varying equation of the system under harmonic excitation is derived, and the influence of each system parameter on the frequency detuning parameter interval of the strongly modulated response is obtained using the phase trajectory and a one-dimensional mapping diagram of the system, and the time-mileage diagram and Poincare section are used to prove the damping effect of the strongly modulated response.

Analysis of Catapult-Assisted Takeoff of Carrier-Based Aircraft Based on Finite Element Method and Multibody Dynamics Coupling Method

Catapult-assisted takeoff is the initiation of flight missions for carrier-based aircrafts. Ensuring the safety of aircrafts during catapult-assisted takeoff requires a thorough analysis of their motion characteristics. In this paper, a rigid–flexible coupling model using the Finite Element Method and Multibody Dynamics (FEM-MBD) approach is developed to simulate the aircraft catapult process. This model encompasses the aircraft frame, landing gear, carrier deck, and catapult launch system. Firstly, reasonable assumptions were made for the dynamic modeling of catapult-assisted takeoff. An enhanced plasticity algorithm that includes transverse shear effects was employed to simulate the tensioning and release processes of the holdback system. Additionally, the forces applied by the launch bar and holdback bar, nonlinear aerodynamics loads, shock absorbers, and tires were introduced. Finally, a comparative analysis was conducted to assess the influence of different launch bar angles and holdback bar fracture stain on the aircraft’s attitude and landing gear dynamics during the catapult process. The proposed rigid–flexible coupling dynamics model enables an effective analysis of the dynamic behavior throughout the entire catapult process, including both the holdback bar tensioning and release, takeoff taxing, and extension of the nose landing gear phases. The results show that higher launch bar angle increase the load and extension of the nose landing gear and cause pronounced fluctuations in the aircraft’s pitch attitude. Additionally, the holdback bar fracture strain has a significant impact on the pitch angle during the first second of the aircraft catapult process, with greater holdback bar fracture strain resulting in larger pitch angle variations.

Influence of a nonlinear asymmetric shock absorber on vibration of a bus subjected to harmonic excitation

The main focus of paper is to get full understanding of four different types of shock absorbers characteristics and their effects on the vertical evaluation indexes of a bus subjected to harmonic excitation. The quarter car with two degree of freedom (2DOF) model was employed to calculate the vertical evaluation indexes. The bus is assumed to travel at a constant velocity on a road surface with a profile following a sinusoidal function. The four types of the shock absorber are Linear Symmetric (LS), Nonlinear Symmetric (NS), Linear Asymmetric (LA), and Nonlinear Asymmetric (NA). As for the LS type, the damping force is a linear function of the relative velocity, and the damping force is symmetric for the conditions of the positive and negative relative velocities. Same as for the LA type, it means that the damping force is linear, however it is asymmetric and differentiated according to the suspension state of stroke (compression or extension). As for the NS type, the damping force function is symmetric, nonlinear, differentiated according to the magnitude of the relative velocity. As for the last NA type, the damping force function is also nonlinear and differentiated according to the magnitude of the relative velocity, but it is also asymmetric. The obtained evaluation indexes of the relative displacement of the bus suspension, acceleration of the bus body, and the dynamic tire load within the frequency range of 0 and 25 (Hz), the common frequency range of the bus in operations. The results suggest that the NA shock absorber type is more effective in reducing the suspension dynamic deflection stroke, improving the road holding and maintaining the ride comfort. The systematic assessments of the shock absorber characteristics should guide interested readers in selecting the most appropriate damping coefficient.

Application of simulation methods on vibration analysis of a bus driver seat using the quarter car 3DOF model subjected under harmonic excitation

Vibration of bus driver's seat subjected under harmonic excitation, 3DOF (3 degrees of freedom) dynamic model is employed to carry out the calculation by 3 simulation methods. Mathematical model - numerical using Matlab programming language (Numerical model), Multi Body Dynamics (MBD) using Matlab Simmechanics tool (MBD model) and finite element model using Ansys APDL (FEM model) are employed. The strengths and limitations of each method are analyzed through the process of building models and retrieving the resulting data. The evaluation indexes include the response of driver's seat acceleration, response of the seat suspension's relative displacement and the seat suspension's vibration isolation ability according to two investigated cases of natural frequency and damping ratio. The obtained results from all 3 methods have no difference and the evaluation indexes are suitable according to the studies on vehicle vibration response. The Numerical model method requires the user to perform complex mathematical modeling. The MBD model method using Matlab Simmechanics is simpler, using built-in function blocks, requiring declarations to establish the exact initial equilibrium position of the mass elements. The FEM model method using Ansys APDL with keypoints and lines describing the model elements requires precise setting of the displacement of each keypoint. However, both the MBD and FEM model methods are only effective when investigating the response in the time domain for a particular instance of the excitation frequency. When analyzing the response in the frequency domain, which requires accessing and synthesizing data of many cases in the investigated frequency range, these two methods have many limitations in the calculation process, specifically, in performing complex computations with many loops and variables. Solving problems also takes longer than numerical method using mathematical model. The obtained results are analyzed in the time domain, frequency domain, and the value domain of the driver's seat suspension parameters. This result serves as a basis for developing the design of the driver's seat suspension system with nonlinear spring and shock absorber, and the selection of a calculation method suitable for each problem in the field of vehicle vibration.

Calculations of vibration isolation systems by means of SCAS KiDyM in a nonlinear setting

The problem of vibration isolation of a device installed on four three-degree elastic shock absorbers with nonlinear characteristics, as an example of vibration isolation of a discrete system of arbitrary structure with several nonlinear elastic shock absorbers is considered in given paper. An analytical description of mechanical models is applied According to this description a special computer algebra system KiDyM (SCAS KiDyM) constructs differential equations of motion, linearizes inertial and elastic terms by means of elimination of the first small terms, carrying out harmonic linearization of the second one. After getting linear multi-mass mathematical model, the KiDyM software package performs calculations of free vibrations and presents the results in the form of skeletal curves. It allows to determine their sensitivity to the values of elastic and inertial parameters, It makes possible to carry out a cycle of calculations with varying model parameters to achieve optimal characteristics of the vibration protection system by shear and deformation of skeletal curves. An example of the problem analysis solution to the above-mentioned vibration protection system of a device performing spatial vibrations is given. Thus, the system contains 12 nonlinearities. The method for determining the experimental elastic characteristics for specimens of two types of shock absorbers is described. The possibilities of narrowing the spectrum of free vibrations by taking into account the nonlinearity of shock absorbers and the problem of skeletal curves construction of systems with several nonlinearities with generalized coordinates as the main coordinates of the oscillatory system.

On the Nonlinear Seismic Responses of Shock Absorber-Equipped Porcelain Electrical Components

Porcelain electrical equipment is prone to brittle failure due to resonance under seismic effects. To improve its seismic resistance, some researchers have conducted research on shock absorption technology for porcelain electrical equipment. However, extant research fails to provide a detailed and systematic study of the effect of the nonlinear characteristics of these shock absorbers on the performance of equipment under seismic effects. This paper provides a theoretical analysis, verified by shaking table testing, of the performance of a 1000 kV pillar-type porcelain lightning arrester. The Bouc–Wen model is fitted to the force-displacement curve of hysteretic nonlinear metal shock absorbers, and a dynamic model of, and equations for, pillar-type porcelain electrical components are derived, taking into account their nonlinear characteristics. This reveals the influence of the nonlinear characteristics of shock absorbers on the nonlinear seismic response characteristics of these components. Our results indicate that the seismic responses of pillar-type porcelain components can be effectively suppressed by hysteretic nonlinear shock absorbers and that the greater the intensity of the seismic waves, the more obvious the efficiency of shock absorption. However, as the installation radius and yield force of the installed shock absorbers increase, their shock absorption efficiency gradually decreases.

Construction principle of NES shock absorber and its application in frame structure

PurposeThe 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.Design/methodology/approachThe 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.FindingsThrough 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.Originality/valueNew shock absorbers reduce earthquake-induced damage to buildings.

Analysis of a quarter car suspension system based on nonlinear shock absorber damping models

Shock absorber is a critical element of vehicle suspension system with nonlinear characteristics. In the present work, performance of vehicle characteristics was analysed by quarter car model to study the effect of shock absorber, on the basis of linear and nonlinear damping characteristics. In addition to linear and piecewise linear, polynomial damping characteristics were considered to address the nonlinear aspect of damping characteristics. The linear and nonlinear properties of the shock absorber were incorporated in a two degree of freedom quarter car suspension system. The modelling and simulation is carried out in Adams view environment and Matlab/Simulink. A bump road profile was used to excite the quarter car suspension models. The polynomial shock absorber model was validated using experimental data taken from established literature. Simulation was undertaken to study the dynamic performance in terms of sprung mass acceleration, body displacement, suspension deflection and unsprung mass acceleration. Experimental hysteresis characteristics data, taken from established literature, were also modelled in Adams view environment and the simulated results were used for validation purpose. The suspension system response incorporating shock absorber represented by nonlinear model, hysteresis model and piece wise linear model were provided in the result section for comparison. It was observed from quantitative comparisons that the RMS values for body acceleration and body displacement of the polynomial model matched fairly well with the results of experimental hysteresis response. It was concluded that in order to study the dynamic characteristics of the vehicle accurately, nonlinear behaviour of the damper is required to be captured properly. Therefore, the proposed polynomial shock absorber model can be a better option for vehicle dynamic analysis as compared to the complex hysteresis model.

Use of nonlinear asymmetrical shock absorbers in multi-objective optimization of the suspension system in a variety of road excitations

In this study, a new method to improve ride comfort, vehicle handling, and workspace was presented in multi-objective optimization using nonlinear asymmetrical dampers. The main aim of this research was to provide suitable passive suspension based on more efficiency and the low cost of the mentioned dampers. Using the model with five degrees of freedom, suspension system parameters were optimized under sinusoidal road excitation. The main functions of the suspension system were chosen as objective functions. In order to better illustrate the impact of each objective functions on the suspension parameters, at first two-objective and finally five-objective were considered in the optimization problem. The obtained results indicated that the optimized viscous coefficients for five-objective optimization lead to 3.58% increase in ride comfort, 0.74% in vehicle handling ability, and 2.20% in workspace changes for the average of forward and rear suspension.

Mathematical modeling vibration protection system for the motor of the boat

The nonlinear mathematical model of the system to mount the motor in a niche of the outboard motor boat, which protects against external influences by means nonlinear shock absorbers and dampers, has been developed. The mathematical model of the system is represented by three nonlinear differential equations of second order. The nonlinear shock absorbers and dampers, as a function of the generalized coordinates are represented by polynomials up to the fifth degree inclusive. For approximate analytical solution of the nonlinear mathematical model is applied the modified method of polynomial transformations and the numerical method of Runge-Kutta.

Use of nonlinear asymmetrical shock absorber to improve comfort on passenger vehicles

Abstract In this study the behaviour of two different types of shock absorbers, symmetrical (linear) and asymmetrical (nonlinear) is compared for use on passenger vehicles. The analyses use different standard road inputs and include variation of the severity parameter, the asymmetry ratio and the velocity of the vehicle. Performance indices and acceleration values are used to assess the efficacy of the asymmetrical systems. The comparisons show that the asymmetrical system, with nonlinear characteristics, tends to have a smoother and more progressive performance, both for vertical and angular movements. The half-car front asymmetrical system was introduced, and the simulation results show that the use of the asymmetrical system only at the front of the vehicle can further diminish the angular oscillations. As lower levels of acceleration are essential for improved ride comfort, the use of asymmetrical systems for vibrations and impact absorption can be a more advantageous choice for passenger vehicles.

Vibration Investigation of a Quarter Car with Nonlinear Shock Absorber Model

The paper discusses the response and the accuracy of a quarter car model with a non-linear damping force. The non-linear shock absorber model was a result of an experiment that was conducted earlier and the mathematical model was verified. Based on this model simulation responses of the sprung and unsprung masses between a linear and the non-linear damper were compared. The wheel of the quarter car model was excited by a road profile and according to the results the non-linear quarter model showed responses which were not depicted and captured by the linear model.

A NARX damper model for virtual tuning of automotive suspension systems with high-frequency loading

A computationally efficient NARX-type neural network model is developed to characterise highly nonlinear frequency-dependent thermally sensitive hydraulic dampers for use in the virtual tuning of passive suspension systems with high-frequency loading. Three input variables are chosen to account for high-frequency kinematics and temperature variations arising from continuous vehicle operation over non-smooth surfaces such as stone-covered streets, rough or off-road conditions. Two additional input variables are chosen to represent tuneable valve parameters. To assist in the development of the NARX model, a highly accurate but computationally excessive physical damper model [originally proposed by S. Duym and K. Reybrouck, Physical characterization of non-linear shock absorber dynamics, Eur. J. Mech. Eng. M 43(4) (1998), pp. 181–188] is extended to allow for high-frequency input kinematics. Experimental verification of this extended version uses measured damper data obtained from an industrial damper test machine under near-isothermal conditions for fixed valve settings, with input kinematics corresponding to harmonic and random road profiles. The extended model is then used only for simulating data for training and testing the NARX model with specified temperature profiles and different valve parameters, both in isolation and within quarter-car vehicle simulations. A heat generation and dissipation model is also developed and experimentally verified for use within the simulations. Virtual tuning using the quarter-car simulation model then exploits the NARX damper to achieve a compromise between ride and handling under transient thermal conditions with harmonic and random road profiles. For quarter-car simulations, the paper shows that a single tuneable NARX damper makes virtual tuning computationally very attractive.

A Methodology to Integrate a Nonlinear Shock Absorber Dynamics into a Vehicle Model for System Identification

A Methodology to Integrate a Nonlinear Shock Absorber Dynamics into a Vehicle Model for System Identification

Efficient empirical modelling of a high-performance shock absorber for vehicle dynamics studies

This paper develops an intuitive empirical nonlinear dynamic shock absorber model for simulation studies. Unlike other existing dynamic shock absorber models, it does not suffer from the complexity of modelling complex physical behaviour, or the inefficiencies of unstructured black-box modelling. The model consists of an algebraic backbone, which is a function of velocity alone, and a nonlinear low-pass filter, which has been designed based on the observation that the damper can respond more quickly at higher velocities. Due to the simplicity of the model, it can be fitted with data and evaluated quickly. The model was fitted using shock dynamometer test data using a random shock position command. The completed model is then validated using random, sine wave, and bump test data. This analysis shows the strengths and weaknesses of the model and suggests areas for future development.

Application of He’s homotopy perturbation method to nonlinear shock damper dynamics

In order to obtain the equations of motion of vibratory systems, we will need a mathematical description of the forces and moments involved, as function of displacement or velocity, solution of vibration models to predict system behavior requires solution of differential equations, the differential equations based on linear model of the forces and moments are much easier to solve than the ones based on nonlinear models, but sometimes a nonlinear model is unavoidable, this is the case when a system is designed with nonlinear spring and nonlinear damping. Homotopy perturbation method is an effective method to find a solution of a nonlinear differential equation. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler differential equations. These sets of equations are then solved iteratively. Finally, a linear series of the solutions completes the answer if the convergence is maintained; homotopy perturbation method (HPM) is enhanced by a preliminary assumption. The idea is to keep the inherent stability of nonlinear dynamic; the enhanced HPM is used to solve the nonlinear shock absorber and spring equations.

Numerical analysis for dynamic transmissibility of a mixed nonlinear shock absorber

AbstractThe objective of this paper is to present a systematic numerical analysis for a mixed nonlinear model of shock absorber under vibration excitation. The mixed nonlinear model is presented for attenuating vibration by considering the coupling of quadratic damping, viscosity damping, Coulomb damping and nonlinear spring forces. An approximate computational analytical solution for the dynamic transmissibility of the shock absorber was deduced by combining Fourier transforms and the harmonic balance method with deterministic excitation. The mathematical characteristics of the dynamic transmissibility were analyzed to illustrate the dynamic performance of the shock absorber. The results show multiple solutions, especially the low‐frequency attenuation characteristics below the resonance frequency. The results provide a theoretical basis for the design of nonlinear shock absorbers. Copyright © 2007 John Wiley & Sons, Ltd.

A systematic approach on computational analysis and optimization design: for a nonlinear coupling shock absorber

The aim of this article is to provide a systematic approach to perform computational simulation and optimization design of parameters matching selection for a nonlinear coupling shock absorber. A theoretical mathematical model with nonlinear coupling for shock absorber is induced based on relative literature. The model considers the coupling of quadratic damping, viscosity damping, coulomb damping and nonlinear spring. Approximate computational solution is deduced by introducing harmonic balance method and Fourier transform method. These approximate theoretical solutions include output response of the system, absolute acceleration transmissibility in vibration or impact, and the maximum relative displacement in impact process, etc. The approximate computational results are compared with those obtained by numerical integration to confirm the validity of the mathematical model. In the meantime, an optimization design model for parameters is built. The design example is illustrated to confirm the validity of the modeling method and the theoretical solution.

Determination of the inertial, stiffness, and damping parameters of a solid resting on nonlinear shock absorbers

Determination of the inertial, stiffness, and damping parameters of a solid resting on nonlinear shock absorbers

An approximated approach to the study of motor vehicle suspensions with nonlinear shock absorbers

It is well known that most shock absorbers used in the motor vehicle industry are neither linear nor symmetrical. Usually the complex behaviour of these elements is neglected when the study of the dynamic behaviour of vehicles is performed using simplified models in order to get closed form solutions. Only when resorting to numerical simulations shock absorbers are modeled in more realistic ways. A simple computation procedure which allows to take into account in an approximate way both nonsymmetry and nonlinearity is here proposed. It allows to extend the scope of the usual simplified models to the study of such effects as nonsymmetry, dry friction and other phenomena often encountered. A result here obtained is the confirmation that linearized models can be used to compute the amplitude of the oscillation of the sprung mass (and of the unsprung masses as well) even in the case of very marked nonsymmetry of the behaviour of shock absorbers.