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In this study, the critical load and natural vibration frequency of Euler–Bernoulli single nanobeams based on Eringen's nonlocal elasticity theory are investigated. Cantilever nanobeams with attached sprung masses were subjected to compressed concentrated and distributed follower forces. The parameter that determines the direction of nonconservative follower forces was given the positive and negative values, therefore, sub-tangential and super-tangential load were analyzed. The stability analysis is based on dynamical stability criterion and was carried out using a numerical algorithm for solving segmental nanobeams with many boundary conditions. The presented algorithm is based on the exact solutions of motion equations which are derived from equilibrium conditions for each separated segment of the nanobeam. Two comparison studies are conducted to ensure the validity and accuracy of the presented algorithm. The excellent agreement of critical load for Beck's nano-column on Winkler foundation observed was confirmed as reported by other researchers. The effect of different values of the nonlocality parameter, tangency coefficient, spring stiffness coefficient, location of sprung mass and the greater number of attached sprung masses on a critical load of nanobeams compressed by nonconservative load are discussed. One of the presented results shows that significant differences between local and nonlocal theory appear when the beam subjected to follower forces loses its stability by flutter. [ABSTRACT FROM AUTHOR]

A good suspension system is mandatory for ensuring stability, comfort and safety in land vehicles; therefore, advanced semi and fully active suspension systems have been developed along with their associated management strategies to overcome the limitations of passive suspensions. This paper presents a suspension algorithm for land vehicles traveling through a deterministic topography. The kinematics of a half-vehicle model and the algorithm are implemented in Simulink. The algorithm's inputs are the measurements provided by a position scanner located on the front wheel of the vehicle. Based on this input, the algorithm reconstructs the topography in real-time and sends the corresponding command to an actuator located on the rear wheel to compensate for the irregularities of the terrain. The actuation is governed by the parameter "D", which represents the distance over which the algorithm averages the height of the terrain. Two ground profiles were tested and sensitivity analysis of the parameter "D" was performed. Results show that larger values of "D" usually yield less vibration on the actuated mass, but this value also depends on the irregularities of the terrain. [ABSTRACT FROM AUTHOR]

In cases where the natural frequencies of vibrations of a vehicle system are closed to the excitation frequencies from the road surface, dynamic vibration absorber provides the vibration isolation by shifting the resonant frequencies of the system. In the present work, the performance of a dynamic vibration absorber is evaluated with two degrees of freedom quarter car model of a road vehicle system when excited with deterministic inputs. The transmissibility of vibrations from the track to the sprung mass, the transfer function of sprung mass acceleration, the transfer function of suspension deflection and the transfer function of tire deflection is determined. [ABSTRACT FROM AUTHOR]

The vertical tyre force is crucial to the study of the dynamics of a tractor semi-trailer. The paper presents an experimental method for determining the vertical tyre force by determining the vertical acceleration of the un-sprung mass and the vertical acceleration of the sprung mass when the tractor semi-trailer moves. The results of this study form the basis for determining the dynamic tyre force without the installing of sensors on road. [ABSTRACT FROM AUTHOR]

In this paper, first, the vibrational governing equations for the suspension system of a selected sports car were derived using Lagrange's Equations. Then, numerical solutions of the equations were obtained to find the characteristic roots of the oscillating system, and the natural frequencies, mode shapes, and mass and stiffness matrices were obtained and verified. Next, the responses to unit step and unit impulse inputs were obtained. The paper compares the effects of various values of the damping coefficient and spring stiffness in order to identify which combination causes better suspension system performance. In this regard, we obtained and compared the time histories and the overshoot values of vehicle unsprung and sprung mass velocities, unsprung mass displacement, and suspension travel for various values of suspension stiffness (KS) and damping (CS) in a quarter-car model. Results indicate that the impulse imparted to the wheel is not affected by the values of CS and KS. Increasing KS will increase the maximum values of unsprung and sprung mass velocities and displacements, and increasing the value of CS slightly reduces the maximum values. By increasing both KS and CS we will have a smaller maximum suspension travel value. Although lower values of CS provide better ride quality, very low values are not effective. On the other hand, high values of CS and KS result in a stiffer suspension and the suspension will provide better handling and agility; the suspension should be designed with the best combination of design variables and operation parameters to provide optimum vibration performance. Finally, multiobjective optimization has been performed with the approach of choosing the best value for CS and KS and decreasing the maximum accelerations and displacements of unsprung and sprung masses, according to the TOPSIS method. Based on optimization results, the optimum range of KS is between 130 000-170 000, and the most favorable is 150, and 500 is the optimal mode for CS. [ABSTRACT FROM AUTHOR]

In order to estimate accurately the vehicle suspension state， an interactive multiple model adaptive Kalman filter(IMMKF)state observer was proposed. Firstly， a standard road excitation model and a quarter vehicle linear model were established. Secondly， by combining recursive least square algorithm with IMMKF theory， an IMMKF state observer was designed based on the augmented suspension model in various working conditions. Finally， the influence on the state estimation of the suspension system with the change of sprung mass under the ISO level C road input excitation was analyzed. The results of simulation and experiment on a quarter of vehicle test rig showed that compared with the tradition Kalman filter(KF)state observer， the estimation accuracy of the proposed IMMKF state observer could be improved beyond 20% with the change of sprung mass. [ABSTRACT FROM AUTHOR]

The dynamic response of a moving vehicle has been utilized to extract the frequencies of the supporting bridge. In most previous studies, the vehicle was modeled as a single-degree-of-freedom sprung mass moving over a simple beam, which suffers from the drawback that the sprung mass may be affected by the vehicle motion. To overcome this drawback, this paper presents a two-mass vehicle model for extracting the bridge frequencies, which contains a sprung mass (vehicle body) and an unsprung mass (axle mass). By using the response of the unsprung mass, the bridge response can be more realistically extracted. The main findings of the present study are as follows: (1) the use of unsprung mass in the vehicle model can faithfully reveal the dynamic responses of both the vehicle and bridge, (2) the increase in the unsprung mass can effectively help the extraction of bridge frequencies, including the second frequency, (3) under high levels of road roughness, the proposed model can identify the bridge frequencies, while the single-mass model cannot, and (4) in the presence of vehicle damping, the proposed model can identify the bridge frequencies under high levels of road roughness without additional techniques of processing. [ABSTRACT FROM AUTHOR]

A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation. The solution provided in the paper is general and includes several special cases, such as the plate with classical boundary conditions, the plate attached with discrete rigid masses, the plate supported by discrete springs and the plate restricted by rigid vertical point-supports. [ABSTRACT FROM AUTHOR]

The study presents the development and analysis of a dynamic model, which simulates the loads induced on a tire of a vehicle as well as its suspension elements including their deformations when passing over a step-shaped obstacle. The possibilities of application of the quarter- and half-car models are considered. The models are used to analyze the influence of vehicle mass and suspension parameters on dynamic loads with the aim to provide recommendations and requirements for the development of active suspensions enabling to reduce dynamic loads generated when crossing over the considered obstacles. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, free vibration of three-layered symmetric sandwich beam carrying sprung masses is investigated using the dynamic stiffness method and the finite element formulation. First the governing partial differential equations of motion for one element are derived using Hamilton’s principle. Closed form analytical solution of these equations is determined. Applying the effect of sprung masses by replacing each sprung mass with an effective spring on the boundary condition of the element, the element dynamic stiffness matrix is developed. These matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the well known Wittrick–Williams algorithm. Free vibration analysis using the finite element method is carried out by increasing one degree of freedom for each sprung mass. Finally, some numerical examples are discussed using the dynamic stiffness method and the finite element formulation. After verification of the present model, the effect of various parameters such as mass and stiffness of the sprung mass is studied on the natural frequencies. [ABSTRACT FROM AUTHOR]

Abstract: Previous studies on the extraction of the bridge frequencies indirectly from the dynamic response of a passing vehicle were focused primarily on the feasibility of the technique. Few investigations have been conducted to study the effects of key dynamic parameters of the system on the vertical response of the passing vehicle. To fill such a gap, the key parameters will be studied not only for evaluating their relative influence, but for increasing the probability of successfully identifying the bridge frequencies of concern. Various amplitude ratios will be defined and expressed in terms of the key parameters, serving as useful indicators for evaluating the probability of successful identification of the bridge frequencies from the passing vehicle. For the two cases studied, in which either one or two bridge frequencies are to be identified, it was shown that the initial amplitude ratio plays a role that is more important than the others in successful identification of the bridge frequencies. Suggestions are made for application of the technique in the field. [Copyright &y& Elsevier]