Amplitude Of Forced Vibration Research Articles

Damping of roll vibrations of vehicle suspension

Small forced vibrations of an axle model of independent suspensions having four degrees of freedom are studied. The exact analytical solution of the generalised Lagrange equation enables one to produce 3D plots of the normalised amplitudes of forced vibrations versus frequency and excitation ratio or phase difference of the road inputs. The analysis of these plots exhibits some deficiency in damping of roll vibrations of conventional vehicle suspensions. The possibilities of improvement are discussed.

Issues of dynamics of conductive plate in a longitudinal magnetic field

On the basis of Kirchhoff hypothesis the problem of vibrations of conductive plate in a longitudinal magnetic field is brought to the solution of the singular integral–differential equation with ordinary boundary conditions. The formulated boundary-value problem solved and the influence of magnetic field on the characteristics of vibration process of the examined magnetoelastic system is investigated. Via the analysis of obtained solutions it is shown that the presence of magnetic field can: (a) increase essentially the frequency of free magnetoelastic vibrations of the plate; (b) decrease essentially the amplitude of forced vibrations if r⩽1 , where r=θ/ω,θ – is the frequency of acting force, ω – is the frequency of own vibrations of the plate magnetic field is being absent; (c) increase essentially the amplitude of forced vibrations if r>1; (d) decrease essentially the width of main areas of dynamic instability. It is shown that: (1) in the case of perfectly conductive plates magnetic field constricts essentially the width of main area of dynamic instability; (2) if plate’s material has the finite electroconductivity, then the certain value of the intensity of external magnetic field exists, exceeding of which excludes the possibility of appearance of parametric type resonance. It is shown also that in dependence on the character of initial excitements the plate can vibrate either across the initial non-deformable state, or across the initial bent state.

Flight Vibrations and Bleeding in Helicoptered Patients With Pelvic Fracture

Depending on their amplitude and frequency, vibrations may facilitate bleeding and worsen the prognosis of patients with pelvic fractures transported by helicopter emergency medical services (HEMS). We measured the range of frequencies and amplitudes of forced vibrations produced by the helicopter used by the HEMS of the Italian Friuli Venezia Giulia region on the pelvis of transported persons. We performed 3 flight tests with 3 different volunteers (mass 70, 80, and 90 kg, respectively) loaded on the helicopter's stretcher and recorded the amplitudes and frequencies of vibrations through a triaxis sensor placed on the HEMS stretcher in the pelvis area. The flight profile planned was identical for each of the 3 iterations. Over the whole flight, the frequencies of vibration were between 26.4 and 53.5 Hz, and the greastest amplitude was 0.035 mm. The vibrations recorded in the helicopter may facilitate bleeding in unstable fractures. In the management of patients with pelvic fractures, HEMS crews should provide prehospital care that includes the use of specific splinting devices in addition to the spinal board, which allows an early immobilization of fractures and the limitation of pelvic motion.

Optimization on Mistuning Blades Arrangement of Vibration Absorption Based on Genetic Particle Swarm Algorithm in Aero-Engine

In practical aero-engine bladed disk structure of blade mistuning is inevitable, and seriously affects the vibration characteristics of bladed disk system also on the whole aero-engine performance and life. Through the analysis, the blades arrangement order of a set of mistuned blade can greatly influence the vibration of bladed disk system, on this foundation; put forward a kind of new localization level of vibration parameters method for the characterization of mistuned system vibration localization degree. Furthermore, genetic particle swarm algorithm is used to optimize the blade arrangement sequence. The research shows that the selection of appropriate blade arrangement sequence can effectively reduce the bladed disk system forced vibration amplitude and the localization level of forced vibration.

A Dynamic Optimization Design Method for the Turbine Engine Frame Foundation

An effective optimization method using Kriging model and parametric sampling evaluation strategy is proposed to solve dynamic optimization design. The optimization problem is to find the design variables such that the structural weight is minimum and dynamic displacement of the points concerned plus certain side constraints are satisfied. The types of design variables are considered as the sizing variables of the beams and columns. Kriging model is used to build the approximate mapping relationship between the forced vibration amplitude and design variables, reducing expensive dynamic reanalysis. A dynamic analysis program is used as black-box to obtain dynamic response. Numerical examples show that the method has good accuracy and efficiency. Versatility of this method can be expected to play an important role in future engineering optimization problems.

Modelling of segmentation-driven vibration in machining

Excessive vibration, such as chatter, is a common problem in machining processes. Meanwhile, numerous hard, brittle metals have been shown to form segmented chips, also known as sawtooth chips, during machining. In the literature, a cyclic cutting force has been demonstrated where segmented chips are formed, with the force cycle corresponding to the formation of segments. Segmented chip formation has been shown to be linked to high vibration levels in turning and milling processes. Additionally, it has been proposed that the amplitude of chatter vibrations can be limited by interference between the tool flank and wavy workpiece surface, a phenomenon known as tool-flank process damping. In this contribution, a model is proposed to predict the amplitude of forced vibration arising due to the formation of segmented chips during turning. The amplitude of vibration was calculated as a function of cutting parameters. It was demonstrated that the model can be extended to account for the effect of tool-flank process damping. For validation, titanium Ti6Al4V alloy was turned using a flexible toolholder, with surface speed ranging from 10 to 160 m/min, feed rate from 0.1 to 0.7 mm/rev and width of cut from 0.35 to 4 mm. In the experimental validation, 25 of 68 test cuts exhibited high-amplitude vibration. In 16 of these cases, the main cause was concluded to be chip segmentation, which can be predicted by the model. The model is thus considered of practical value to machinists.

Inspection and Evaluation of Load-Bearing Capacity of Single Tower Composite Girder Cable-Stayed Bridge

In order to evaluate single tower composite girder Cable Bridge actual bearing capacity and working property on design using load, a single-tower composite girder cable-stayed bridge is taken as an example, by means of static load test, dynamic load test, reasonably measures evaluates the single tower composite girder cable-stayed bridge's bearing capacity. The static load test measure static properties of bridge structure (static strain, static deflection, etc.), dynamic load test, measure the dynamic properties of bridge structure (vibration frequency, damping, forced vibration amplitude, impact coefficient, etc.). Results show that the rigidity strength integrity and dynamic characteristics of bridge structure are favorable; the structure’s bearing capacity is favorable.

Active vibration control in milling flexible workpieces

During milling of flexible workpieces a regenerative chatter vibration may become a critical factor that limits productivity. It is shown in this paper that a selection of cutting parameters based on a stability lobes diagram may not always be a remedy for low productivity due to increased forced vibration level. Additionally, other factors such as tool wear may limit the selection of stable spindle speeds. This paper presents an active control system that counteracts the development of chatter vibration. The proposed active control system employs Linear Quadratic Gaussian (LQG) algorithm and piezoelectric actuator to suppress vibration during cutting. The Kalman filter is used to estimate the state of the system required by LQG algorithm. The active control introduces damping into the system, thereby raising the critical depth of cut and reducing forced vibration amplitude. It enables stable cutting under a much wider range of cutting parameters than for the uncontrolled system. Cutting tests are performed to demonstrate an effectiveness of the control system. Practical issues limiting applications of the proposed technique are discussed.

Numerical aerodynamic simulations of a NACA airfoil using CFD with block-iterative coupling and turbulence modelling

Numerical aerodynamic simulations are presented for a National Advisory Committee for Aeronautics (NACA) airfoil that is stationary and pitching at high Reynolds numbers. A new improved CFD method based on block-iterative coupling is used with a computational scheme for fluid-structure interaction, in which a form of two-equation RANS turbulence model is adopted. Firstly, basic simulations were performed using the proposed CFD method and turbulence model, which provides good prediction of the airfoil force coefficients and flutter derivatives compared with the well-known experimental measurement and analytical formulation. Then, extended airfoil flow simulations were carried out to examine the potentially significant effects on aeroelasticity from several influencing factors, including non-zero equilibrium angles of attack, increased forced vibration amplitudes and large Reynolds number. Both the basic and extended simulations reveal that using the proposed CFD method can provide effective assessment of aerodynamic and aeroelastic performance of airfoils even for operating conditions beyond those a laboratory test can approach, indicating the possibility of extending the methodology proposed for realistic aerodynamic and aeroelastic prediction of 3D full-scale aircraft structures.

Experimental investigation on using the piezoelectric and electromagnetic vibration absorbers in milling

The paper presents an active control system that counteracts the development of chatter vibration. The vibration amplitude depends on the dynamic properties of the machine tool, cutting tool and work-piece. In the paper we analyze the case when the loss of machining stability is caused by the work-piece. The proposed active control system employs electromagnet or piezoelectric actuator to suppress vibration during milling. The active control introduces damping into the system, thereby raising the critical depth of cut and reducing forced vibration amplitude. It enables stable cutting under a much wider range of cutting parameters that for the uncontrolled system. Cutting tests are performed on JAFO FYN-50 machine with mill DIN 845 B-25 K-N HSS to demonstrate an effectiveness of the proposed systems.

Detecting and characterizing frequency fluctuations of vibrational modes

We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of the complex amplitude of forced vibrations. The moments of the complex amplitude sensitively depend on the frequency noise statistics and its power spectrum. The analysis applies to classical and to quantum vibrations.

Forced vibrations of orthotropic shells: nonclassical boundary-value problems

The forced vibrations of a cylindrical orthotropic shell are studied. Two types of boundary conditions on the outer surface are examined considering that the displacement vector prescribed on the inner surface varies harmonically with time. Asymptotic solutions of associated dynamic equations of three-dimensional elasticity are found. Amplitudes of forced vibrations are determined and conditions under which resonance occurs are established. Boundary-layer functions are defined. The rate of their decrease with distance from the ends inside the shell is determined. A procedure of joining solutions for the internal boundary-layer problem is outlined in the case for the, if clamping boundary conditions are prescribed at the ends

任意変位周期励振を受けるばね-質量系の定常衝突振動 : 第1報,調和共振,高調波共振および分数調波共振における応答振動解析(機械力学,計測,自動制御)

This paper deals with response vibration in single-degree-of-freedom excited by periodic displacement with arbitrary functions. The analytical model is steady collision vibration in spring-mass system with viscous damping. When the system is subjected to an exciting vibration by displacement and amplitude of the mass increases farther than collision clearance, the mass collides elastically to clamped spring. Then, the restitution force of the mass is assumed an asymmetric piecewise-linear system. In order to clarify harmonic, superharmonic and subharmonic resonances of the collision system, the resulting vibrations are analyzed extending the Fourier series method which is proposed by authors. Following this theoretical analysis, the numerical calculations are performed and the resonance curves are constructed using the resulting vibrations. The numerical results show effects on the damping ratio, the stiffness of clamped spring and the amplitude of forced vibration for resonance curves. Experiments are also carried out to verify the theoretical results. Comparing the theoretical results with the experimental ones, it is shown that they show a fairy good agreement.

Approximate analytical determination of vibrodiagnostic parameters of a cracked elastic body under subharmonic resonance. Part 1. Weak resonance

Using the approach proposed in Part 1, an approximate calculation of vibration parameters is made for an elastic body with a closing crack, in the region of a strong 1/2-order subharmonic resonance with the lower-harmonic amplitude of free vibration spectrum larger than the main amplitude of forced vibrations.

Application of a LIPCA for the structural vibration suppression of an aluminum cantilever beam with a tip mass

Use of bare PZT as an actuator in the field of active vibration suppression may cause some drawbacks such as critical breaks in the installation process, short circuits in the host material and low fatigue performance. To alleviate these problems, we developed a new actuator called a lightweight piezocomposite actuator (LIPCA). The LIPCA has five layers: three glass-epoxy layers, a carbon-epoxy layer and a PZT layer. We implemented a LIPCA as an actuator to suppress the vibration of an aluminum cantilever beam with a tip mass. For the control algorithm in our test, we used positive position feedback. The filter frequency for this type of feedback should be tuned to the frequency of the target mode. The first three experimental natural frequencies of the aluminum cantilever beam agree well with the results of finite element methods. The effectiveness of using a LIPCA as an actuator in active vibration suppression was investigated with respect to the time and frequency domains, and the experimental results show that LIPCAs can significantly reduce the amplitude of forced vibrations as well as the settling time of free vibrations.

경량 압전 복합재료 작동기를 이용한 끝단 질량이 부착된 보의 진동 제어

PZT와 같은 압전 재료는 능동 진동 억제 분야에서 널리 사용되고 있지만 단일 PZT의 경우 장착 과정에서의 손상, 전기 누전, 낮은 피로 성능과 같은 문제가 지적되고 있다. 이러한 문제를 해결하기 위하여 개발된 LIPCA 작동기는 여러 층의 복합재료와 PZT 층으로 구성되어 있다. 본 연구에서는 LIPCA 작동기를 끝단 질량이 부착된 알루미늄 외팔보의 진동을 억제하는데 적용하였다. 양변위 되먹임 제어 알고리듬을 사용하였으며, 필터 주파수를 대상 모드의 첫 번째 고유진동수에 맞추었다. 실험적으로 구한 알루미늄 보의 고유 진동수는 유한요소 해석의 결과와 잘 일치하였다. LIPCA 작동기를 능동 진동제어에 적용할 때 효율성을 시간과 주파수 영역에서 확인하고자 하였는데, 실험 결과 PPF제어를 사용한 LIPCA 작동기가 자유 진동의 안정화 시간과 강제 진동의 진폭을 효과적으로 제어할 수 있었다. 사례 연구로 다른 두께를 가지는 보의 강제 진동 제어를 수행하였다. Although piezoelectric materials such as PZT have been widely used as actuators in the field of active vibration suppression, the use of bare PZT as an actuator may cause some drawbacks such as critical breaks in the installation process, short circuits in the host material and low fatigue performance. The LIPCA-C2 (lightweight piezocomposite actuator) was developed to alleviate these problems. We implemented the LIPCA as an actuator to suppress the vibration of an aluminum cantilever beam with a tip mass. In our test, we used positive position feedback control algorithm. The filter frequency for this type of feedback should be tuned to the natural frequency of the target mode. The first three experimental natural frequencies of the aluminum cantilever beam agree well with the results of finite element analysis. The effectiveness of using the LIPCA as an actuator in active vibration suppression was investigated with respect to the time and frequency domains, and the experimental results show that LIPCAs with PPF control can significantly reduce the amplitude of forced vibrations and the settling time of free vibrations. For a case study, the forced vibration control of several beams with different thicknesses were performed.

Transverse Vibrations of Laminated Beams in Three-Dimensional Formulation

A new asymptotic method is proposed to describe the free and forced transverse vibrations of elastic laminated beams of arbitrary cross section using the three-dimensional elastic equations without additional hypotheses and constraints. For beams with layers of equal Poisson's ratio, the zero-order natural frequencies are equal to the natural frequencies predicted by classical beam theory based on the Bernoulli hypothesis. The method makes it possible to calculate the frequencies of free vibrations and amplitudes of forced vibrations with prescribed accuracy for the first natural modes

Low-Engine-Order Excitation Mechanisms in Axial-Flow Turbomachinery

One particular regime of forced response, occurring at much lower frequencies than the blade-passing frequency, is the so-called low-engine-order (LEO) forced response. The source of LEO excitation is a loss of symmetry in the flow, such as that caused by stator blade throat width variations, flow exit angle variations, perturbations in the passage cooling flow,or temperature distortions. Using a 3D integrated time-domain aeroelasticity code, parametric forced response studies were conducted for a high-pressure turbine stage with 36 stator and 90 rotor blades. Both whole-annulus and sector models were used to investigate the effects of individual and combined LEO parameters. For individual parameters, the amplitude of the excitation was, proportional to the imposed variation. For combined cases, the total excitation was found to be determined by the phasing between the individual excitations. A ballpark comparison suggested that LEO and blade-passing forced response vibration amplitudes were similar for typical variations of the controlling LEO parameters.

MORE DETAILS ABOUT THE INTERACTION OF FORCED AND PARAMETRIC RESONANCES ARISING FROM IN-PLANE EXCITATION OF IMPERFECT RECTANGULAR PLATES

The goal of the present paper is to improve our understanding of the response of the in-plane loaded rectangular plates containing initial geometric imperfection. Besides the frequency responses and FFT curves, which were used as diagnostic tools in previous investigations, the temporal response and the phase diagram have been added to better study the transition zones between two kinds of vibration modes. The phase portrait shows that the plate response has a number of “unusual and perhaps chaotic” characteristics in the transition from one mechanism of vibration of another, which distinguished it from the more classical periodic response. Moreover, the effect of one particular spatial mode of imperfection on a different mode of vibration has been investigated for the first time. It was found that the maximum amplitude of forced vibrations is large when vibration and imperfection are in the same mode while the first mode of vibration is always excited whatever the mode of imperfection is.

Modeling Vibratory Drilling Dynamics

The dynamic behavior of deep-hole vibratory drilling is analyzed. The mathematical model presented allows the determination of axial tool and workpiece displacements and cutting forces for significant dynamic system behavior such as the engagement and disengagement of the cutting tool into the workpiece material and tool breakthrough. Model parameters include the actual rigidity of the tool and workpiece holders, time-varying chip thickness, time lag for chip formation due to tool rotation and possible disengagement of drill cutting edges from the workpiece due to tool and/or workpiece axial vibrations. The main features of this model are its nonlinearity and inclusion of time lag differential equations, which require numeric solutions. The specific cutting conditions (feed, tool rotational velocity, amplitude and frequency of forced vibrations) necessary to obtain discontinuous chips and reliable removal are determined. Calculated bifurcation diagrams make it possible to derive the relevant domain of user-specified system parameters along with the determination of optimal cutting conditions.