Linear Vibration System Research Articles

A new compound control method for sine-on-random mixed vibration test

Vibration environmental test (VET) is one of the important and effective methods to provide supports for the strength design, reliability and durability test of mechanical products. A new separation control strategy was proposed to apply in multiple-input multiple-output (MIMO) sine on random (SOR) mixed mode vibration test, which is the advanced and intensive test type of VET. As the key problem of the strategy, correlation integral method was applied to separate the mixed signals which included random and sinusoidal components. The feedback control formula of MIMO linear random vibration system was systematically deduced in frequency domain, and Jacobi control algorithm was proposed in view of the elements, such as self-spectrum, coherence, and phase of power spectral density (PSD) matrix. Based on the excessive correction of excitation in sine vibration test, compression factor was introduced to reduce the excitation correction, avoiding the destruction to vibration table or other devices. The two methods were synthesized to be applied in MIMO SOR vibration test system. In the final, verification test system with the vibration of a cantilever beam as the control object was established to verify the reliability and effectiveness of the methods proposed in the paper. The test results show that the exceeding values can be controlled in the tolerance range of references accurately, and the method can supply theory and application supports for mechanical engineering.

A Monte Carlo simulation method for non-random vibration analysis

In recent years, the authors developed a non-random vibration analysis method for structural dynamic analysis under uncertain excitations. In non-random vibration analysis, the interval process model is employed to describe the uncertain dynamic load rather than the traditional stochastic process model, and the structural dynamic response is obtained in the form of upper and lower bounds, rather than its precise probability distribution. Since the probability distribution information is not required, the non-random vibration analysis generally could decrease the dependence on large experimental sample number; meanwhile, the bounds of dynamic response are easy to understand conceptually and convenient to use in practical structural reliability or safety design. On the basis of our previous work, this paper further proposes a Monte Carlo simulation method, aiming to provide a general way for non-random vibration analysis and also offer a reference solution for other non-random vibration analysis methods proposed in the future. Firstly, a sampling approach is presented to realize the precise sampling of the single interval process and the multi-dimensional interval process vector. Then, based on the sampling approach, a calculation procedure of non-random vibration analysis is constructed to obtain the structural dynamic response bounds under uncertain dynamic load. Finally, the proposed method is not only applied to single-degree-of-freedom and multi-degree-of-freedom linear vibration systems, but also to more complex vibration systems such as nonlinear systems and continuum structures.

Analysis of interaction between bubbles and particles in a dense gas-vibro fluidized bed

Gas-solid fluidized beds are widely used for their excellent characteristics of heat and mass transfer. An active pulsating air flow is introduced into a dense gas-solid fluidized bed, forming a dense gas-vibro fluidized bed (DGVFB), to modify the fluidization quality. Interaction between the bubbles and particles in the DGVFB was investigated based on the results of numerical simulations and experiments. Micro-bubbles in the DGVFB were regarded as springs, and therefore, the interaction between the bubbles and particles was considered to be equivalent to a linear vibration system with n degrees of freedom. A dynamic model for the vibration system was developed, and modal analysis was conducted. Results of this theoretical analysis showed that the dominant frequency of pressure fluctuations in the DGVFB was equal to the frequency of active pulsating air flow. The dynamic model described the interaction between the bubbles and particles effectively in the DGVFB at low gas pulsating frequency, and shallow fluidized beds.

Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters

The field of random vibrations of large-scale systems with millions of degrees-of-freedom (DOF) is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by nonstationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem, and recent advances in time-dependent reliability using an integral equation involving the upcrossing and joint upcrossing rates. A space-filling design, such as optimal symmetric Latin hypercube (OSLH) sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional time-dependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the upcrossing and joint upcrossing rates. A time-dependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure. The proposed method is demonstrated using a vibratory beam example.

Steady-State Response to Periodic Excitation in Fractional Vibration System

AbstractThe steady-state response to periodic excitation in the linear fractional vibration system was considered by using the fractional derivative operator . First we investigated the response to the harmonic excitation in the form of complex exponential function. The amplitude-frequency relation and phase-frequency relation were derived. The effect of the fractional derivative term on the stiffness and damping was discussed. For the case of periodic excitation, we decompose the periodic excitation into a superposition of harmonic excitations by using the Fourier series, and then utilize the results for harmonic excitations and the principle of superposition, where our adopted tactics avoid appearing a fractional power of negative numbers to overcome the difficulty in fractional case. Finally we demonstrate the proposed method by three numerical examples.

An Efficient Method to Calculate the Failure Rate of Dynamic Systems with Random Parameters Using the Total Probability Theorem

Abstract : Using the total probability theorem, we propose a method to calculate the failure rate of a linear vibratory system with random parameters excited by stationary Gaussian processes. The response of such a system is non-stationary because of the randomness of the input parameters. A space-filling design, such as optimal symmetric Latin hypercube sampling or maximin, is first used to sample the input parameter space. For each design point, the output process is stationary and Gaussian. We present two approaches to calculate the corresponding conditional probability of failure. A Kriging metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure and the failure rate of the dynamic system. The proposed method is demonstrated using a vibratory system. Our approach can be easily extended to non-stationary Gaussian input processes.

605 特異スペクトル解析を用いた振動解析 : 減衰特性の分離(OS6 オーガナイズドセッション≪振動・音響・制御≫)

In this study, specific spectral analysis as a signal processing method; it is those described for Fundamental Research on vibration data using the (Singular Spectrum Analysis SSA). Viscous damping, and extracted by a specific spectral analysis the decay waveform from the response data obtained in the free vibration of the one-degree-of-freedom linear vibration system having damping, such as Coulomb friction.

A proof on eigenfrequencies of a special linear vibration system

In this contribution the eigenfrequencies of a special linear vibration system are investigated. Based on the properties of the corresponding mass and stiffness matrices of the chain structured mass‐spring vibration system with arbitrary n degrees of freedom an algebraic proof for the determination of the eigenfrequencies is given.

Generalized stochastic resonance of power function type single-well system

To generalize the harmonic potential of the linear random vibration system, a more general power type potential is presented, and the corresponding power function type nonlinear single-well random vibration system is obtained. The first moment of the system steady-state response and the stationary variance of the system response, which are influenced by noise strength, parameters of the potential and the periodic excitation, are studied by using the second order stochastic Runge-Kutta algorithm. The parameter b, which determines the shape of the potential, goes through b b > 2 and b=2 (harmonic potential), and it is shown that varying the noise strength, if b b=2 (harmonic potential) or b > 2, this phenomenon does not occur; varying the parameters of the potential, the first moment of the system steady-state response and the stationary variance of the system response can also be non-monotonic.

CALCULATING THE RIGHT-EIGENVECTORS OF A SPECIAL VIBRATION CHAIN BY MEANS OF MODIFIED LAGUERRE POLYNOMIALS

Abstract This contribution deals with the identification of the right-eigenvectors of a linear vibration system with arbitrary n degrees of freedom as given in [1]. Applying the special distribution of stiffnesses and masses given in [1] yields a remarkable sequence of matrices for arbi- trary n. For computing the (right-)eigenvectors a generalised approach allowing the use of Laguerre polynomials is performed.

감마형 자유피스톤 스털링 엔진의 작동주파수 분석

The dynamic characteristics of a free-piston stirling engine(FPSE) with regard to the working frequency is investigated from theoretical and experimental studies. The FPSE is modeled as a two degree-of-freedom linear vibration system. A theoretical expression on the working frequency is derived from the instability condition for self-excitation based on the linear vibration model. A <TEX>${\gamma}$</TEX>-type free-piston stirling engine is fabricated for experimental studies, and its working frequency is measured on various heater temperatures. Comparisons between the theoretical and experimental results reveal that the working frequency of the test FPSE depends on both the temperature of the compression space and the temperature difference between the expansion and compression spaces.

Controller design for delay-independent stability of linear time-invariant vibration systems with multiple delays

One of the critical parameters that can deteriorate the effectiveness of active vibration control (AVC) is the delay in sensors. Especially, in remote sensing where delays are large, and in high-speed applications with even small delays, instability can be inevitable. This paper presents algebraic approaches to design controllers in order to achieve stability regardless of the amount of delays for AVC applications modeled by linear time-invariant systems with “multiple” constant delays. The approaches are based on a nonconservative framework, and can identify the regions in the controller gain space where delay-independent stability (DIS) is achievable. With these controllers, we demonstrate via simulations that vibration suppression, within certain excitation frequency bands, can be improved or be as effective as those in AVC applications without delays.

Vibration Analysis of Nonlinear Isolator’s Characteristics by ADAMS

A nonlinear spring-mass model is established to study the dynamic characteristics of nonlinear vibration isolator. By use of ADAMS software, the influence of stiffness, foundation displacement excitation and frequency of external excitation on the nonlinear vibration isolation systems are analyzed. Results indicate that the linear vibration system needs 4s to achieve stability, but the nonlinear vibration system only needs 0.1s. The response value increases with the increase of excitation frequency, the response pick value increases by 61.58% and 102.35% and each corresponding stable value increases by 159.35% and 309.87%.

すべり摩擦型振動の応答解析手法に関する研究

Vibration systems with sliding friction are analyzed by using the Linear Accelerated Method based upon a new analytical logic which can study in detail the state of sliding motion within the constant time step. The logic was applied to linear single-mass systems with and without external force. The obtained numerical values are compared with the theoretical one and also the one without this logic. Then it was proved that the computing time is shortened greatly. In other words, much shorter time step is demanded, if the same computing accuracy is expected without the new logic.It is also shown that the new logic is applicable to linear two-mass systems and non-linear vibration systems in which the upper part is a non-linear structure and the lower part is a sliding friction.

Modeling and Control of the Vibration of Two Beams Coupled with Fluid and Active Links

Investigated are modeling and control approaches for vibration analysis of two identical beams which are coupled with fluid and active mechanical links. In the modeling of the coupled beam system, orthogonal functions are used to represent vibration of the beams and the fluid-structure interaction is considered. Frequency Response Functions (FRFs) are derived from the coupled governing equations and the superposition principle for linear vibration systems. In the control of vibration of the beams, impulse response functions corresponding to the FRFs and an adaptive control algorithm are employed to attenuate vibration transmission between the two beams. Natural frequencies, mode shapes as well as the pressure distribution in the fluid are computed. The results obtained by the proposed modeling method are in good consistency with those obtained by the finite element analysis. Moreover, it is demonstrated that the active mechanical link is able to reduce vibration transmission and change the deformation of beams as well as the distribution of fluid pressure.

Modeling and Control of the Vibration of Two Beams Coupled with Fluid and Active Links

Investigated are modeling and control approaches for vibration analysis of two identical beams which are coupled with fluid and active mechanical links. In the modeling of the coupled beam system, orthogonal functions are used to represent vibration of the beams and the fluid-structure interaction is considered. Frequency Response Functions (FRFs) are derived from the coupled governing equations and the superposition principle for linear vibration systems. In the control of vibration of the beams, impulse response functions corresponding to the FRFs and an adaptive control algorithm are employed to attenuate vibration transmission between the two beams. Natural frequencies, mode shapes as well as the pressure distribution in the fluid are computed. The results obtained by the proposed modeling method are in good consistency with those obtained by the finite element analysis. Moreover, it is demonstrated that the active mechanical link is able to reduce vibration transmission and change the deformation of beams as well as the distribution of fluid pressure.

Optimal damping of selected eigenfrequencies using dimension reduction

SUMMARYWe consider linear vibrational systems described by a system of second‐order differential equations of the form , where M and K are positive definite matrices, representing mass and stiffness, respectively. The damping matrix D is assumed to be positive semidefinite. We are interested in finding an optimal damping matrix that will damp a certain (critical) part of the eigenfrequencies. For this, we use an optimization criterion based on the minimization of the average total energy of the system. This is equivalent to the minimization of the trace of the solution of the corresponding Lyapunov equation AX + XAT = −GGT, where A is the matrix obtained from linearizing the second‐order differential equation, and G depends on the critical part of the eigenfrequencies to be damped. The main result is the efficient approximation and the corresponding error bound for the trace of the solution of the Lyapunov equation obtained through dimension reduction, which includes the influence of the right‐hand side GGT and allows us to control the accuracy of the trace approximation. This trace approximation yields a very accelerated optimization algorithm for determining the optimal damping. Copyright © 2011 John Wiley &amp; Sons, Ltd.

파력을 이용한 하이브리드 발전에 대한 연구

본 논문에서는 파도의 상하운동에 의해 발전되는 선형발전시스템과 진동발전시스템이 결합된 하이브리드 발전방법을 제안한다. 선형발전시스템은 권선과 영구자석으로 구성되어있고, 파도의 상하운동 속도를 직접적으로 사용하므로 파도의 주파수에 관계없이 안정적인 발전을 한다. 그리고 진동발전시스템은 진동시스템인 영구자석, 스프링과 발전시스템인 영구자석, 권선으로 구성되어 있다. 진동발전시스템은 파도의 주파수와 진동시스템의 고유진동수를 일치시킨 공진대역에서 구동함으로써 파도의 상하운동 속도보다 더 큰 속도를 이용하여 더 많은 전기에너지를 얻을 수 있다. 따라서 본 연구에서 제안한 하이브리드 파력발전방법은 공진영역에서 더 많은 전기에너지를 얻을 수 있을 뿐만 아니라 공진영역을 벗어난 대 역에서도 안정적으로 발전할 수 있는 장점을 가짐을 알 수 있다.

Equivalent damping and frequency change for linear and nonlinear hybrid vibrational energy harvesting systems

A unified approximation method is derived to illustrate the effect of electro-mechanical coupling on vibration-based energy harvesting systems caused by variations in damping ratio and excitation frequency of the mechanical subsystem. Vibrational energy harvesters are electro-mechanical systems that generate power from the ambient oscillations. Typically vibration-based energy harvesters employ a mechanical subsystem tuned to resonate with ambient oscillations. The piezoelectric or electromagnetic coupling mechanisms utilized in energy harvesters, transfers some energy from the mechanical subsystem and converts it to an electric energy. Recently the focus of energy harvesting community has shifted toward nonlinear energy harvesters that are less sensitive to the frequency of ambient vibrations. We consider the general class of hybrid energy harvesters that use both piezoelectric and electromagnetic energy harvesting mechanisms. Through using perturbation methods for low amplitude oscillations and numerical integration for large amplitude vibrations we establish a unified approximation method for linear, softly nonlinear, and bi-stable nonlinear energy harvesters. The method quantifies equivalent changes in damping and excitation frequency of the mechanical subsystem that resembles the backward coupling from energy harvesting. We investigate a novel nonlinear hybrid energy harvester as a case study of the proposed method. The approximation method is accurate, provides an intuitive explanation for backward coupling effects and in some cases reduces the computational efforts by an order of magnitude.

The Green's Function and its Oscillatory Properties for a Single Branch Structure of a Pinned Beam-Rod System

This paper concerns the determination of qualitative properties of linear vibrational systems, in particular for a single branch structure consisting of a pinned beam-rod system. First, we establish the characteristic equations satisfied by the Green’s function for this structure. The Green’s functions corresponding to support conditions where the left end of the beam was pinned-end are deduced by adopting the direct integral method. Using the theory of oscillation kernels established by Gantmakher and Krein, oscillatory properties of the Green's function for the beam-rod system are proved. Furthermore, four oscillation properties associated with frequencies and mode functions for the system are given.