Degree Of Freedom System Research Articles

Dynamic Vibration Characteristics Analysis of Truck Transmission Gearbox Casing with Fixed Constraint of Vehicle Frame Based on FEA

Truck transmission gearbox casing is subjected to vibration induced by the harmonic excitation, meshing excitation, load fluctuations, gear defects, varying speed and torque conditions. Noise and vibrations are the reasons for the transmission failure. The transmission gearbox casing vibrations are the resultant of internal excitation caused by the gear meshing process and transmission error. This internal excitation produces a dynamic mesh force, which is transmitted to the casing through the shafts and bearings. The objective of this research work is to simulate the relation between dynamic vibrations of transmission and fixed constraint of vehicle frame. Transmission casing is tightly fixed on vehicle frame using connecting bolts. 37 connecting bolts were used to fix the casing on vehicle frame. If connecting bolts were loosened, it causes heavy vibration and deformation. For transmissions type multi degree freedom system the natural frequency and vibration mode are important modal parameters. First 10 inherent natural frequencies and corresponding mode shapes were evaluated. Grey cast iron HT200 was used as casing material. FEA based numerical simulation method was used to find the dynamic response of the casing. The numerical simulation method used reciprocity principle to apply the mesh forces transmitted to the casing and to determine the main responsible forces for the vibration of the casing. The FEA simulation results show that the natural frequency of one bolt unconstraint condition varies from (1637.2 – 2674) Hz. The analysis results were verified with experimental result available in literature.

Optimization Design of the Ultra-High-Speed Vertical Rotor’s Supporting Mechanism

How to increase the rotational speed and decrease vibration of the rotor in the acceleration has become an attractive subject, especially for the vertical rotors. This paper introduces a novel supporting mechanism to make the vertical rotor work at 80000 r/min smoothly. How to design and optimize the sensitive parameters of the supporting mechanism is the core problem to reduce the vibration in passing through critical speeds. Therefore, the FEM (finite element method) considering the gyroscopic couple is introduced to get the dynamic characteristic of the rotor system. The matching principle of the upper and lower supporting mechanism in the two-degree freedom system is extended to the multiple degree-freedom system, which is applied to optimize the parameters of the supporting mechanism combining with dynamic characteristic of the rotors system. At last, the rotor system can work at 80000 r/min smoothly in experiment.

A variational integrators approach to second order modeling and identification of linear mechanical systems

The theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system, preserving key properties of the continuous time flow. The discrete-time model obtained by variational integration theory inherits structural conditions which in general are not guaranteed under general discretization procedures. We discuss a simple class of variational integrators for linear second order mechanical systems and propose a constrained identification technique which employs simple linear transformation formulas to recover the continuous time parameters of the system from the discrete-time identified model. We test this approach on a simulated eight degrees of freedom system and show that the new procedure leads to an accurate identification of the continuous-time parameters of second-order mechanical systems starting from discrete measured data.

Robust optimization of a hybrid control system for wind-exposed tall buildings with uncertain mass distribution

In this paper is studied the influence of the uncertain mass distribution over the floors on the choice of the optimal parameters of a hybrid control system for tall buildings subjected to wind load. In particular, an optimization procedure is developed for the robust design of a hybrid control system that is based on an enhanced Monte Carlo simulation technique and the genetic algorithm. The large computational effort inherent in the use of a MC-based procedure is reduced by the employment of the Latin Hypercube Sampling. With reference to a tall building modeled as a multi degrees of freedom system, several numerical analyses are carried out varying the parameters influencing the floors' masses, like the coefficient of variation of the distribution and the correlation between the floors' masses. The procedure allows to obtain optimal designs of the control system that are robust with respect to the uncertainties on the distribution of the dead and live loads.

Smooth Hamiltonian Systems with Soft Impacts

In a Hamiltonian system with impacts (or "billiard with potential"), a point particle moves about the interior of a bounded domain according to a background potential, and undergoes elastic collisions at the boundaries. When the background potential is identically zero, this is the hard-wall billiard model. Previous results on smooth billiard models (where the hard-wall boundary is replaced by a steep smooth billiard-like potential) have clarified how the approximation of a smooth billiard with a hard-wall billiard may be utilized rigorously. These results are extended here to models with smooth background potential satisfying some natural conditions. This generalization is then applied to geometric models of collinear triatomic chemical reactions (the models are far from integrable $n$-degree of freedom systems with $n\geq2$). The application demonstrates that the simpler analytical calculations for the hard-wall system may be used to obtain qualitative information with regard to the solution structure of the smooth system and to quantitatively assist in finding solutions of the soft impact system by continuation methods. In particular, stable periodic triatomic configurations are easily located for the smooth highly-nonlinear two and three degree of freedom geometric models.

Particle relaxation method of Monte Carlo filter for structure system identification

In this paper, we apply Monte Carlo filter (MCF) to identify dynamic parameters of structural systems and improve the efficiency of its algorithm. The algorithms using MCF so far have not been practical for applying to structural identification of large-scale systems because computation time increases exponentially as the degrees of freedom of the system increases. To overcome this problem, we developed a method with the ability to reduce the number of particles which express possible structural response state vector. In MCF, there are two steps which are the prediction and filtering processes. The idea is very simple. The prediction process remains intact but the filtering process is conducted at each node of structural system in the proposed method. We named this algorithm as relaxation Monte Carlo filter (RMCF) and demonstrated its efficiency to identify large degree of freedom systems. Moreover, to increase searching field and speed up convergence time of structural parameters, we proposed an algorithm combining the genetic algorithm with RMCF and named GARMCF.

Analytical Solutions of a Class of Nonlinear Single Degree-of-Freedom Systems to Nonstationary Random Excitations

An analytical method for responses of a class of nonlinear single degree-of-freedom (DOF) systems under nonstationary random excitations (NSREs) is presented. It is based on the transformation of the nonlinear stochastic differential equations that govern the vibrations of nonlinear systems under NSREs into a polynomial of which the exact roots are available, and therefore solutions without approximation of the nonlinear system can be evaluated. For demonstration purposes, the van der Pol-Duffing oscillator under a time-modulated zero mean Gaussian white noise process is considered. Representative solutions are verified by the Monte Carlo simulation (MCS) technique. The main conclusions are as follows. First, a simple and relatively straightforward method has been developed to transform the nonlinear stochastic differential equations of a class of nonlinear single DOF systems into polynomials for which exact solutions are available. The analytical solution developed in this paper is for the deterministic equation of motion for a specific realization of the input excitation function f(t). The statistics of the displacement response are obtained using the expectation operator applied to the exact solutions computed for every realization of f(t). Second, for the first time solutions without approximation are obtained for a nonlinear single DOF system with nonlinearities involving nonlinear velocity as well as displacement and under NSRE. Third, for solutions of the van der Pol-Duffing oscillator the computational time required by the present method is much more efficient than that using the MCS technique.

Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses

In this study, a new analytical approach is developed to analyze the free nonlinear vibration of conservative two-degree-of-freedom (TDOF) systems. The mathematical models of these systems are governed by second-order nonlinear partial differential equations. Nonlinear differential equations were transferred into a single equation by using some intermediate variables. The single nonlinear differential equations are solved by using the first order of the Hamiltonian approach (HA). Different parameters, which have a significant impact on the response of the systems, are considered and discussed. Some comparisons are presented to verify the results between the Hamiltonian approach and the exact solution. The maximum relative error is less than 2.2124 % for large amplitudes of vibration. It has been established that the first iteration of the Hamiltonian approach achieves very accurate results, does not require any small perturbations, and can be used for a wide range of nonlinear problems.

Free vibration analysis of linear particle chain impact damper

Impact dampers have gained much research interest over the past decades that resulted in several analytical and experimental studies being conducted in that area. The main emphasis of such research was on developing and enhancing these popular passive control devices with an objective of decreasing the three parameters of contact forces, accelerations, and noise levels. To that end, the authors of this paper have developed a novel impact damper, called the Linear Particle Chain (LPC) impact damper, which mainly consists of a linear chain of spherical balls of varying sizes. The LPC impact damper was designed utilizing the kinetic energy of the primary system through placing, in the chain arrangement, a small-sized ball between each two large-sized balls. The concept of the LPC impact damper revolves around causing the small-sized ball to collide multiple times with the larger ones upon exciting the primary system. This action is believed to lead to the dissipation of part of the kinetic energy at each collision with the large balls.This paper focuses on the outcome of studying the free vibration of a single degree freedom system that is equipped with the LPC impact damper. The proposed LPC impact damper is validated by means of comparing the responses of a single unit conventional impact damper with those resulting from the LPC impact damper. The results indicated that the latter is considerably more efficient than the former impact damper. In order to further investigate the LPC impact damper effective number of balls and efficient geometry when used in a specific available space in the primary system, a parametric study was conducted and its result is also explained herein.

Hidden Nambu mechanics: A variant formulation of Hamiltonian systems

We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extended dynamics whose master equation is the Nambu equation or its generalization. Partition functions associated with the extended dynamics in many degrees of freedom systems are given. Our formulation can also be applied to Hamiltonian systems with first class constraints.

비선형 수치해석을 통한 단자유도 얕은기초 구조물의 지진 응답특성 검증

Seismic response of single degree of freedom system supported by shallow foundation was analyzed by using nonlinear explicit finite difference element code. Numerical analysis results were verified with dynamic centrifuge test results of the same soil profile and structural dimensions with the numerical analysis model at a centrifugal acceleration of 20 g. Differences between the analysis and the test results induced by the boundary conditions of control points can be reduced by adding additional local damping to the natural born cyclic hysteretic damping of the soil strata. The analysis results show good agreement with the test results in terms of both time histories and response spectra. Thus, it can be concluded that the nonlinear explicit finite difference element code will be a useful technique for estimating seismic residual displacement, earthpressure etc. which are difficult to measure during laboratory tests and real earthquake.

Fuzzy Control Embedded in Microcontroller and Applied to an Experimental Apparatus Using Magnetorheological Fluid Damper

This work focuses on applying fuzzy control embedded in microcontrollers in an experimental apparatus using magnetorheological fluid damper. The non-linear behavior of the magnetorheological dampers associated with the parametric variations on vehicle suspension models corroborate the use of the fuzzy controllers. The fundamental formulation of this controller is discussed and its performance is shown through numeric simulations. An experimental apparatus representing a two degree of freedom system containing a magnetorheological damper is used to identify the main parameters and to evaluate the performance of the closed-loop system with the embedded low-cost microcontroller-based fuzzy controller.

Numerical Analysis of Inclined Flexible Beam Carrying One Degree of Freedom Moving Mass Including Centrifugal and Coriolis Accelerations and Rotary Inertia Effects

A numerical procedure is proposed in this paper to study the response of an inclined beam subjected to sprung mass. The first-order shear deformation theory (FSDT) including rotary inertia is assumed for the beam element. The effects of inertial force as well as Coriolis and centrifugal forces induced by the moving sprung mass are considered in governing equations. The Newmark time integration method is adopted in solving equations. In this paper, the horizontal and vertical deformations of the beam, along with the Coriolis force and the inclined angle are investigated. The moving system is considered as a one degree of freedom system including two masses located at the ends of the moving load system, one spring and viscous damping. The effects of spring constant and damper ratio on the dynamic magnification factor (DMF) of the inclined beam are also studied. The results obtained from the present study show that the Coriolis force in lower speed has significant influence on the dynamic response of the beam.

Equivalent mechanical model for tuned liquid damper of complex tank geometry coupled to a 2D structure

Tuned liquid dampers (TLDs) control the wind-induced vibrations of tall buildings using sloshing fluid. TLD tanks of complex geometry may be required in practice due to space limitations; however, their behaviour has not been considered in the literature. This study develops and experimentally validates a model to describe the structure–TLD interaction of a 2D system when the TLD tank geometry is complex. The equations of motion of the structure–TLD system are developed using Lagrange's equation. In general, the 2D structure–TLD interaction must be represented as a coupled four degree of freedom system. The model is validated using new structure–TLD system tests where the structure is subjected to 1D and 2D harmonic and random excitation. Two TLD tanks of complex geometry are considered; the first tank is anti-symmetric about both axes, whereas the second tank is symmetric about both axes. For the anti-symmetric tank, energy transfer between orthogonal structural sway modes and sloshing modes is significant; however, for the symmetric tank, this energy transfer is negligible. Experimental results indicate that the model adequately predicts the structural response; however, the nonlinear behaviour of the fluid response cannot be captured by the linearized model. Copyright © 2013 John Wiley & Sons, Ltd.

The Influence of Tank Orientation Angle on a 2D Structure-Tuned Liquid Damper System

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy, thereby reducing wind induced dynamic motion. By selecting the appropriate tank length, width, and fluid depth, a rectangular TLD can control two structural sway modes simultaneously if the TLD tank is aligned with the principal axes of the structure. This study considers the influence of the TLD tank orientation on the behavior of a 2D structure-TLD system. The sloshing fluid is represented using a linearized equivalent mechanical model. The mechanical model is coupled to a 2D structure at an angle with respect to the principal axes of the structure. Equations of motion for the system are developed using Lagrange’s equation. If the TLD and structure are not aligned, the system responds as a coupled four degree of freedom system. The proposed model is validated by conducting structure-TLD system tests. The predicted and experimental structural displacements and fluid response are in agreement. An approximate method is developed to provide an initial estimate of the structural response based on an effective mass ratio. The results of this study show that for small TLD orientation angles, the performance of the TLD is insensitive to TLD orientation.

Design of 2 Degree of Freedom Continuous-time Generalized Minimum Variance Control with Double Controller

This research designs a Continuous-time Generalized Minimum Variance Control (CGMVC) of two degree of freedom. The conventional CGMVC cannot be optimized the both property of the setpoint response and the disturbance rejection because its structure is one degree of freedom system. Therefore, a double controller structure is applied to the CGMVC. The double controller is the method, which the two degree of freedom system can be achieved by adding a PID controller. As a result, the setpoint response and the disturbance rejection can be independently designed. The effectiveness of the double controller is shown by the numerical example.

Cross Beam STAP for Nonstationary Clutter Suppression in Airborne Radar

A novel space-time adaptive processing (STAP) method for nonstationary clutter suppression is proposed. The developed method forms a multibeam along the cross line to participate in adaptive processing, which sufficiently utilizes the spatial information both in azimuth and elevation and guarantees the least system degrees of freedom (DOFs). The characteristics of this structure help to suppress the short-range clutter which is the primary component of nonstationary clutter. Therefore, this method provides favorable clutter suppression performance when clutter range dependence exists. Approach analysis and simulation results are given to demonstrate the effectiveness of the method.

PROCEDIMIENTO DE EVALUACIÓN DE EDIFICIOS DE CONCRETO REFORZADO BASADO EN DESEMPEÑO: DESARROLLO Y VALIDACIÓN

Se presenta un método para evaluar sísmicamente edificios de concreto reforzado, fundamentado en conceptos de ingeniería basada en desempeño; en la validez de la curva de capacidad como una propiedad del sistema estructural; y en la consideración de energía disipada por histéresis, introducida en el procedimiento mediante tasas de amortiguamiento equivalente en un sistema simplificado de un grado de libertad. El método permite evaluar de manera directa el desempeño de estructuras sometidas a demandas sísmicas crecientes ya que conduce a una curva de capacidad que aproxima satisfactoriamente la correspondiente derivada de análisis dinámicos incrementales.

The Research of Impact Ball End Mills Geometric Parameters on Processing Stable Region

In this paper, modal analysis of ball end mills is modeled by finite element to work out natural frequency and chatter model in tooling system and to calculate the limit curve of stability in single degree freedom system. The effect of cutter flute length and cutter tooth number on maching stability area is also discussed. The results of research show that steady critical cutting depth of milling system declines while the cutter flute length increases, but the trend is not linear, which shows increase partly. An engineering optimization design is made on milling cutter geometrical parameters based on this conclusion.

A Novel Seismic Base Isolation System Consisting of a Lead Rubber Bearing in Series with a Friction Slider. Part I: Nonlinear Modeling of the System

In this paper a new seismic base isolator, called High Damping Hybrid Seismic Isolator (HDHSI), is proposed. It is obtained by the assembly in series of a Lead Rubber Bearing (LRB) and a Friction Slider (FS) with a high friction coefficient. The HDHSI device is in contrast with the Resilient-Friction Base Isolator (R-FBI) with the aim of optimizing the Electricité De France (EDF) system. The mathematical model of a structure base isolated by a HDHSI system is analyzed with a two Degree of Freedom System (2-DOF) in which the superstructure is assimilated to a rigid body. Nonlinear finite elements are adopted for modeling the HDHSI device. A dynamic nonlinear analysis is performed and the hysteretic cycles are derived and evaluated for the single components and for the innovative HDHSI device.