Modal Kinetic Energy Research Articles

Optimal Design of Vehicle Power-Train Mounting System Based on Improved Particle Swarm Optimization

Applying the multi-dynamic theory, a dynamic model of the power-train mounting system of motor vehicles is established. An optimization model for the power-train mounting system is constructed, in which decoupling efficiency of six freedom vibrations is selected as objective function, and the natural frequency distribution of system as constraint condition, the stiffness and installing angles as design variables of optimization. Based on improved particle swarm optimization, as an example, isolation characteristics of a truck power-train mounting system are analyzed. The comparison between the optimal and original design shows that distribution of both the modal kinetic energy and the system natural frequency are more reasonable, that means NVH of the power-train mount system can be improved using the optimal design.

Modal analyses of herringbone planetary gear train with journal bearings

A generalized dynamic model for herringbone planetary gear train (HPGT) is developed to investigate its modal properties. The model includes the axial vibration of two helical ring gears in addition to three planar degrees of freedom for the carrier and all gears. Four stiffness coefficients are applied to describe the asymmetry and the interaction of the oil film stiffness of journal bearings for supporting the planets. Vibration modes are classified into rotational and axial mode, translational mode, planet mode, rotational and axial ring mode and translational ring mode. For each type of mode, the reduced-order eigenvalue problems are derived according to the modal properties. The formulas for calculating the modal strain and kinetic energy distributions are also given for each mode. The proposed dynamic model and analysis methods can be applied to HPGT with any number of planets. Only when the asymmetric interaction exists in journal bearings, will the dramatic change of mode shape for translational mode occur. The new relations between deflections of planets in translational mode are also derived in this research.

Optimal Placement of Triaxial Accelerometers Using Modal Kinetic Energy Method

Modal kinetic energy (MKE) method gives a measure of the dynamic contribution of each finite element model physical degree of freedom to each of the target mode shapes, and provides a rough idea where the maximum responses could be measured. It could help to select those sensor positions with possible large amplitudes, and to increase the signal to noise ratio, which is critical in harsh and noisy circumstances. Kammar proposed a new optimal placement method of triaxial accelerometers based up on the effective independence algorithm (EfI3), which places triaxial accelerometers as single units in an optimal fashion. On the basis of EfI3, this paper fully considers the mutual influence of three directions and makes some improvements for the traditional MKE method. A novel optimal placement method of triaxial accelerometers called MKE3 is proposed which is proved rational and effective by analysis the relationship between the EfI algorithm and MKE method.

Placement of sensors in operational modal analysis for truss bridges

A modal approach is considered for sensor placement evaluation in operational modal analysis (OMA) where modal participation at individual degree of freedom (DOF) is evaluated separately for the target modes and subsequently locations are identified using these participation profiles. Modal contribution in output energy (MCOE) is proposed as modal measure to evaluate modal participation and has been applied in this modal approach framework for sensor placement evaluation. MCOE is evaluated using observability grammian for any types of response measurement (displacement, velocity or acceleration), while a system is released from any initial condition. Further, existing modal measures e.g. modal Hankel singular value (MHSV) and system norms (H2, H∞ and Hankel) are explained in perspective of OMA. To understand the efficiency of this proposed technique, MCOE is compared in terms of modal participation with existing modal measures as well as with other techniques like effective independence (EI) and modal kinetic energy (MKE). Analytical similarity is found for participation of a mode with EI method. Further, an existing large truss bridge structure is considered for comparative study based on modal participation of individual target modes along each DOF with acceleration measurement. In this comparison, MCOE technique is found to be in very good agreement with EI method as expected, while good agreement is observed with MHSV as well as norms and reasonable agreement with MKE method. Further, the adopted modal approach uses a flexible and insightful methodology for sensor location evaluation for multiple target modes.

509 制振材を積層した曲面板を有する自動車用吸音二重壁構造のFEMとMSKE法による減衰応答解析

A numerical method is proposed to calculate response analysis for automotive sound proof structure including elastic body, viscoelastic body and porous body using three dimensional FEM and MSKE method. Displacement vectors as common unknown variable under coupled condition. The explicit expressions of modal loss factors for the sound proof structures are derived using Modal Strain and Kinetic Energy Method (MSKE method) proposed by authors in our previous paper. Using this technique, eigenvalue analysis and frequency response analysis are performed for the automotive sound proof structure. In this report, we deal with a porous material sandwiched between a steel cover plate and a base plate (steel plate with a viscoelastic damping layer). We investigate vibration transmission characteristics from the base plate to the cover plate. Especially, we focus on the influences of curvature of the base plate on the vibration transmission. We set the curved plate as a convex upward structure, while the cover plate is leveled. Thus, the distance between the base plate and the cover plate become short locally because of the curvature. This caused sound bridge phenomena.

Role of spectrally varying mount properties in influencing coupling between powertrain motions under torque excitation

The influence of spectrally varying mount properties (including stiffness and damping) on the dynamics of powertrain motions is analytically examined. To overcome the deficiency of the direct inversion method (limited to only the frequency domain analysis), two methods are developed that describe the mount elements via a transfer function (in Laplace domain) or analogous mechanical model. New analytical formulations are verified by comparing the frequency responses with numerical results obtained by the direct inversion method (based on Voigt type mount model). Eigensolutions and transient responses of a spectrally varying mounting system are also predicted from new models. Based on complex eigenstructure, new coupling indices, including modal kinetic energy fractions, are defined for each method. Complex eigenvalue problem formulation with spectrally varying properties provides a closer match with measured natural frequencies than the real eigensolution with frequency-independent mounts. Given spectral variance in the mount properties, a simple roll mode decoupling scheme is suggested for the powertrain isolation system. Finally, an axiom for torque roll axis decoupling is provided by employing direct and adjoint eigenvalue problems.

Optimal sensor placement for modal identification of structures using genetic algorithms—a case study: the olympic stadium in Cali, Colombia

Adequate sensor placement plays a key role in such fields as system identification, structural control, damage detection and structural health monitoring of flexible structures. In recent years, interest has increased in the development of methods for determining an arrangement of sensors suitable for characterizing the dynamic behavior of a given structure. This paper describes the implementation of genetic algorithms as a strategy for optimal placement of a predefined number of sensors. The method is based on the maximization of a fitness function that evaluates sensor positions in terms of natural frequency identification effectiveness and mode shape independence under various occupation and excitation scenarios using a custom genetic algorithm. A finite element model of the stadium was used to evaluate modal parameters used in the fitness function, and to simulate different occupation and excitation scenarios. The results obtained with the genetic algorithm strategy are compared with those obtained from applying the Effective Independence and Modal Kinetic Energy sensor placement techniques. The sensor distribution obtained from the proposed strategy will be used in a structural health monitoring system to be installed in the stadium.

Determination of Structural Damping and Optimal Vibration Control of an Adhesively-Bonded Double Containment Cantilever Joint

In this study, the loss factors of an adhesively-bonded double containment cantilever joint were determined for different plate and support lengths. The response of the adhesive joint subjected to a transverse excitation force was measured with a contactless eddy-current sensor and the first bending natural frequency was determined using the Fast Fourier Transform method. The loss factor was calculated using the half-power bandwidth method based on the power spectrum of the joint vibration. After an excitation force was applied to the joint, the damped free vibration analysis was carried out using the finite element method and its measured loss factor. The transverse vibration attenuation was actively controlled with different numbers of actuators located on the top surface of the plate. The optimal control of the vibration attenuation was achieved based on a performance index by considering the strain energy, the kinetic energy, the work done on the adhesive joint by the actuators as well as the vibration attenuation time. Genetic Algorithm was implemented to this optimization problem in which the optimal control force histories, the optimal locations and the optimal numbers of the actuators were searched. Eight actuators exhibited the best control force history minimizing the performance index to 3.34 × 10–2. Thus, the attenuation time was reduced from 16 s to 0.15 s and the absolute displacement was decreased from 13.1 mm to 17.15 × 10–3 mm for 0.15 s. In addition, the modal strain energy and kinetic energy were found to be at lowest levels. As the actuator number was increased only a minor decrease in the performance index was observed after four actuators.

A note on fast computation of effective independence through QR downdating for sensor placement

A simple and fast computational algorithm of the Effective Independence for sensor placement is presented in the paper. It is based on the relationship between the Effective Independence and Modal Kinetic Energy method, and on a downdating algorithm of the QR decomposition for a reduced modal matrix. Traditional computations of the Effective Independence, which tries to render the target modes as linearly independent at possible and is significant and influential in the field of sensor placement, require the eigenvalue decomposition or inversion of the Fisher Information matrix, and both are costly. By virtue of the connection between the Modal Kinetic Energy and Effective Independence derived by the authors, the norms of the orthonormal rows after the QR decomposition of the modal matrix can be employed to compute the Effective Independence. Moreover, new downdating steps of the QR decomposition based on the combination of the modified Gram–Schmidt and Householder transformations are implemented, which further improved its efficiency by eliminating unnecessary expensive QR decompositions in the iterations. The computational burden for traditional methods and the proposed ones are investigated in terms of the floating point operations required. Finally, a numerical example shows that the new algorithms run much more quickly with fewer computation steps, has the advantages of simplicity and clarity in physical significance, and is stable.

The connection between effective independence and modal kinetic energy methods for sensor placement

The comparison and inherent relationship between two influencing sensor placement methods, i.e. modal kinetic energy (MKE) and effective independence (EI), are addressed in this paper. The problem is of primary concern for dynamic testing, damage identification and structural health monitoring. By analyzing the sensor placement problem with EI method from the perspective of a new reduced system, the connection of MKE with EI method is revealed. The latter is an iterated version of the former, and the reduced mode shapes are ortho-normalized repeatedly during iterations of the latter. Two alternative forms for efficient computation of the iterative EI method are presented. Finally, both methods are applied to the I-40 Bridge located over the Rio Grande in Albuquerque, New Mexico, and the derived relationship is verified.

Particle transport and flow modification in planar temporally evolving laminar mixing layers. I. Particle transport under one-way coupling

Simulations of two-dimensional, particle-laden mixing layers were performed for particles with Stokes numbers of 0.3, 0.6, 1, and 2 under the assumption of one-way coupling using the Eulerian-Lagrangian method; two-way coupling is addressed in Part II. Analysis of interphase momentum transfer was performed in the Eulerian frame of reference by looking at the balance of fluid-phase mean momentum, mean kinetic energy, modal kinetic energy, and particle-phase mean momentum. The differences in the dominant mechanisms of vertical transport of streamwise momentum between the fluid and particle phases is clearly brought out. In the fluid phase, growth of the mixing layer is due to energy transfer from the mean flow to the unstable Kelvin-Helmholtz modes, and transport of mean momentum by these modes. In contrast, in the particle phase, the primary mechanism of vertical transport of streamwise momentum is convection due to the mean vertical velocity induced by the centrifuging of particles by the spanwise Kelvin-Helmholtz vortices. Although the drag force and the particle-phase modal stress play an important role in the early stages of the evolution of the mixing layer, their role is shown to decrease during the pairing process. After pairing, the particle-phase mean streamwise momentum balance is accounted for by the convection and drag force term. The particle-phase modal stress term is shown to be strongly connected to the fluid phase modal stress with a Stokes-number-dependent time lag in its evolution.

Particle transport and flow modification in planar temporally evolving mixing layers. II. Flow modification due to two-way coupling

Simulations of two-dimensional, two-way coupled particle-laden mixing layers were performed for particles with various Stokes numbers, at mass loadings between 0.1 and 0.5. This component complements Part I of the study, where particle and fluid transport was analyzed under one-way coupling. Under two-way coupling, the accumulation of particles in the periphery of the Kelvin-Helmholtz vortices results in the formation of intricate undulating patterns, and rupture and break-up of the vortices. At higher mass loadings the vortex structure is completely destroyed. The overall accumulation at the edges of the mixing layer is significantly reduced due to two-way coupling. The rate of evacuation of the vortex core was found to be much slower compared to one-way coupling. In a global sense, particles delay the development of the mixing layer in terms of saturation of the fundamental and the subharmonic modes. Significant generation of small-scale vorticity and higher energy in the small scales is observed at higher mass loadings. Particles are shown to increase the modal kinetic energy dissipation rate. The mean fluid kinetic energy balance shows that most of the kinetic energy exchange between the particle and fluid phases takes place at the edges of the mixing layer. As the mixing layer evolves, the kinetic energy exchange with the particle phase was shown to decrease in importance compared to the other terms in the mean kinetic energy balance; namely, the energy exchange between the mean and the modal fields and the modal transport term.

Nonlinear Development of Particle-Laden Mixing Layers at Low Mach Number

The two-phase coupling effects on the particle-laden compressible mixing layer are studied for low convective Mach numbers. A full Eulerian approach is used to obtain a set of conservative partial differential equations. The initial condition is provided by the solution of the solution of the linear problem. The numerical solutions show that the presence of particles in the flow does not alter the typical development of the mixing layer observed for one-phase flows: the amplification of linear instability waves, the formation of two-dimensional large-scale vortices, and the pairing of vortices. The shape of the vortical structures is modified compared to single-phase calculations. The particle density distribution is greatly dependant on their inertia that can lead to a particle-free zone in the vortex. The compressibility effects are clearly seen on the modal kinetic energy, which decreases when the convective Mach number increases

Configuration and sizing design optimisation of powertrain mounting systems

A configuration and sizing design optimisation problem for powertrain mounting systems is formulated. The objective function is to decouple and maximise the component modal kinetic energy of the powertrain subsystem. Natural frequencies and collinear roll vector condition are used as the constraints. Cartesian coordinates and spring rates of the mounts are selected as the design parameters. An automated design optimisation procedure is developed using an optimisation code based on the method of feasible direction (MFD) and MSC/NASTRAN as a finite clement solver. The necessary gradient information is obtained using the central finite difference method. For the obtained optimum model, forced response analyses are performed in engine idling and wheel unbalancing conditions to show that overall accelerations are greatly reduced at the response positions.

SENSITIVITY OF PLANETARY GEAR NATURAL FREQUENCIES AND VIBRATION MODES TO MODEL PARAMETERS

The natural frequency and vibration mode sensitivities to system parameters are rigorously investigated for both tuned (cyclically symmetric) and mistuned planetary gears. Parameters under consideration include support and mesh stiffnesses, component masses, and moments of inertia. Using the well-defined vibration mode properties of tuned planetary gears, the eigensensitivities are calculated and expressed in simple, exact formulae. These formulae connect natural frequency sensitivity with the modal strain or kinetic energy and provide efficient means to determine the sensitivity to all stiffness and inertia parameters by inspection of the modal energy distribution. The natural frequency sensitivity to operating speed is calculated to estimate the impact of gyroscopic effects. While the terminology of planetary gears is used throughout, the results apply for general epicyclic gears.

99/01953 Catalytic partial oxidation of methane to synthesis gas over Ni-based catalysts II. Transient, FTIR and XRD measurements: Tsipouriari, V. A. and Verykios, X. E. J. Catal., 1998, 179, (1), 292–299

The capacity and size of hydro-generator units are increasing with the rapid development of hydroelectric enterprises, and the vibration of the powerhouse structure has increasingly become a major problem. Field testing is an important method for research on dynamic identification and vibration mechanisms. Research on optimal sensor placement has become a very important topic due to the need to obtain effective testing information from limited test resources. To overcome inadequacies of the present methods, this paper puts forward the triaxial effective independence driving-point residue (EfI3-DPR3) method for optimal sensor placement. The EfI3-DPR3 method can incorporate both the maximum triaxial modal kinetic energy and linear independence of the triaxial target modes at the selected nodes. It was applied to the optimal placement of triaxial sensors for vibration testing in a hydropower house, and satisfactory results were obtained. This method can provide some guidance for optimal placement of triaxial sensors of underground powerhouses.

Zonal wave number 2 baroclinic outbreak episodes in winter

Long-lasting episodes, so-called baroclinic outbreaks (BO), with extra-ordinary baroclinic conversions favouring one ultralong wave with zonal wavenumber m were studied in a previous paper (Schilling, 1988). This paper is concentrated on m = 2 winter BO's with durations of more than 7 days. In addition, almost hemispherically-averaged energy parameters (10° N ≪ φ 90° N) and a two-dimensional spectral representation (n is the meridional mode index) are used. From 10 years (1967–1976) of data, we find 15 ultra-persistent winter cases, but only 11 are considered for further investigation, since 4 episodes fail to show sufficient growth of kinetic energy of m = 2 ( K 2 ) despite large input C ( A z A 2 ). During m = 2 BO's in winter, the meridional mode n ≅ 2 (one node between southern boundary at 10° N and pole) exhibits large amplification and K 2 concentrates dramatically in precisely this mode. Mainly, the available potential energy of the super-rotational mode of the zonal mean vertical wind shear supplies that energy inflow. During the first stages of m = 2 BO's, the kinetic energy and baroclinic activity of synoptic waves ( m = 5–8) appear to be significantly suppressed. An unusual distribution of modal eddy kinetic energy in 500 mb results so that approximately 25–30% of it is concentrated in only one wave mode ( m = 2, n = 2). DOI: 10.1111/j.1600-0870.1989.tb00377.x

Volume perturbers as possible sound field randomizers in room‐average spectrum measurement procedures

The use of moving volumes (people) instead of rotating vanes for sound field randomization has been proposed as a plausible and convenient technique. A perturbing volume Vp in a room of volume V0 shifts the frequency of the lmn mode by an amount (Δf/f)lmn = ∫vp(U − K)lmndV/∫v0(U + K)lmndV, where U and K are the modal potential and kinetic energy densities of the sound field. Computer experiments confirm that when Vp is moved throughout a room, the rms frequency shift is given by (Δf/f)rms = 3(Vp/V0)H(ka). For a cube of side a, H≃1 for ka⩽1, falling basically as (1/ka) above this. For Vp a thin square of side a, or bar of length a, the same asymptotic relations hold, but the transition to (1/ka) behavior is much less abrupt. If (Δf/f)rms⩾ the mean intermode frequency spacing (c3/4πV0f3), one expects adequate randomization of the room modes for frequencies above fp = c/(12πVp)1/3 provided Vp is displaced sufficiently between recordings of the spectral samples. Measurements of spectra using fixed source and microphone but moving Vp as outlined show however that the observed mean spectrum has a variance only slightly less than the ± 5.2 dB value associated with a single reading. That is, the expected randomization due to moving Vp hardly takes place. Other types of experiment confirm this. Possible reasons will be discussed. [Assisted by NSF.]