This article presents exact algebraic solutions to optimization problems of a double-mass dynamic vibration absorber (DVA) attached to a viscous damped primary system. The series-type double-mass DVA was optimized using three optimization criteria (the H ∞ optimization, H 2 optimization, and stability maximization criteria), and exact algebraic solutions were successfully obtained for all of them. It is extremely difficult to optimize DVAs when there is damping in the primary system. Even in the optimization of the simpler single-mass DVA, exact solutions have been obtained only for the H 2 optimization and stability maximization criteria. For H ∞ optimization, only numerical solutions and an approximate perturbation solution have been obtained. Regarding double-mass DVAs, an exact algebraic solution could not be obtained in this study in the case where a parallel-type DVA is attached to the damped primary system. For the series-type double-mass DVA, which was the focus of the present study, an exact algebraic solution was obtained for the force excitation system, in which the disturbance force acts directly on the primary mass; however, an algebraic solution was not obtained for the motion excitation system, in which the foundation of the system is subjected to a periodic displacement. Because all actual vibration systems involve damping, the results obtained in this study are expected to be useful in the design of actual DVAs. Furthermore, it is a great surprise that an exact algebraic solution exists even for such complex optimization problems of a linear vibration system.

In this work, exact closed-form solutions are derived for optimizing the resonant shunt circuits of electromagnetic shunt dampers (EMSDs), which use an electromagnetic transducer, and piezoelectric shunt dampers (PZSDs), which use a piezoelectric element, shunted with an electric circuit. Modeling of the EMSD and PZSD is unified by nondimensional parameters. The optimization criteria selected for the EMSD and PZSD are H ∞ -norm minimization, H 2 -norm minimization, and exponential time-decay rate maximization. The aim of this study is to derive for the first time the exact solutions that have not previously been investigated, including cases that consider the inherent damping of the primary system. This paper comprehensively summarizes the exact solutions based on the optimization criteria together with approximated solutions obtained by the fixed-point method, which is commonly used to optimize the dynamic vibration absorber (DVA).

In this paper, transfer function of rotating shaft system for detecting transverse open crack is developed. Rotating shaft system is modeled using one-dimensional finite element method (1D-FEM), and quantitative analysis is performed. Open crack is modeled as weak asymmetry rotating with shaft's rotation. It is known that, when both open crack and support stiffness anisotropy coexist, various frequency components of shaft's vibration are generated through their successive interaction. This paper evaluates the order of these components, and concludes that first five main components are enough to investigate interaction of open crack and support stiffness anisotropy. Then, five sets of transfer functions for these components are derived. The validity of this set of transfer functions is confirmed by numerical simulation. Moreover, excitation experiment utilizing active magnetic bearing (AMB) is performed, and the validity of derived transfer function was verified experimentally.

Although the vibration suppression effects of precisely adjusted dynamic vibration absorbers (DVAs) are well known, multimass DVAs have recently been studied with the aim of further improving their performance and avoiding performance deterioration due to changes in their system parameters. One of the present authors has previously reported a solution that provides the optimal tuning and damping conditions of the double-mass DVA and has demonstrated that it achieves better performance than the conventional single-mass DVA. The evaluation index of the performance used in that study was the minimization of the compliance transfer function. This evaluation function has the objective of minimizing the absolute displacement response of the primary system. However, it is important to suppress the absolute velocity response of the primary system to reduce the noise generated by the machine or structure. Therefore, in the present study, the optimal solutions for DVAs were obtained by minimizing the mobility transfer function rather than the compliance transfer function. As in previous investigations, three optimization criteria were tested: the H ∞ optimization, H 2 optimization, and stability maximization criteria. In this study, an exact algebraic solution to the H ∞ optimization of the series-type double-mass DVA was successfully derived. In addition, it was demonstrated that the optimal solution obtained by minimizing the mobility transfer function differs significantly at some points from that minimizing the compliance transfer function published in the previous report.

Precisions of localization are a function of the size of an array. A kind of parasitoid fly, Ormia ochracea, performs an extraordinary directional hearing ability despite its tiny-scaled auditory organ. In this paper, vibration modes and transfer functions of the Ormia ochracea's ear model were calculated, and the phase difference amplification in responses are analyzed to investigate the directional hearing mechanism. A novel three-element bionic model is proposed for spatial sound source localization for small distance-wavelength ratios. The amplification of the phase difference of this model is verified. In order to realize the bionic localization model, based on electric-mechanic analogy method, a system that consists of a triangular acoustic array and a bionic coupling circuit is designed and tested. Frequency responses of the circuit output, as a means of transfer function of the system, are taken into estimation of the source directions. The result has shown that this circuit design has better performance in estimating the direction of sound sources compared to the uncoupled array with same size.

This paper presents a novel formulation and exact solution of the frequency response function (FRF) of vibration energy harvesting beam systems by the distributed transfer function method (TFM). The method is applicable for coupled electromechanical systems with nonproportional damping, intermediate constraints, and nonclassical boundary conditions, for which the system transfer functions are either very difficult or cumbersome to obtain using available methods. Such systems may offer new opportunities for optimized designs of energy harvesters via parameter tuning. The proposed formulation is also systematic and amenable to algorithmic numerical coding, allowing the system response and its derivatives to be computed by only simple modifications of the parameters in the system operators for different boundary conditions and the incorporation of feedback control principles. Examples of piezoelectric energy harvesters with nonclassical boundary conditions and intermediate constraints are presented to demonstrate the efficacy of the proposed method and its use as a design tool for vibration energy harvesters via tuning of system parameters. The results can also be used to provide benchmarks for assessing the accuracies of approximate techniques.

Inverse patch transfer functions (iPTF) method has been developed to reconstruct the sound field of irregularly shaped sources in a noisy environment. The iPTF method, which uses classic regularization methods to solve the ill-posed problems generally, would incur some sidelobes ghosting in the process of identifying sparse sources. In view of the fact that the algorithm in wideband holography (WBH) can promote sparsity of results, a technique combining iPTF method with WBH algorithm is proposed to identify sparsely distributed sources in the present work. In the proposed technique, double layer pressure measurements are used to replace the measurements of the pressure and normal velocity which uses costly p-u probes. A gradient descent algorithm and a filtering process are applied to solve the minimization problem of identifying the normal velocities of target sources, which can suppress ghosting sources rapidly by an iterative process. In simulations, the field reconstruction results of two antiphase square piston sources show good sparsity and accuracy by employing the technique, nearly without ghosting sources. At different distances and frequencies of the two sources, the technique still performs well. Experimental validations at 200 Hz and 400 Hz are carried out in the end. The results of experiments are also coinciding with those of simulations.

The root-mean-square (RMS) response of various points in a system comprised of two parallel plates coupled at a point undergoing high frequency, broadband transverse point excitation of one component is considered. Through this prototypical example, asymptotic modal analysis (AMA) is extended to two coupled continuous dynamical systems. It is shown that different points on the plates respond with different RMS magnitudes depending on their spatial relationship to the excitation or coupling points in the system. The ability of AMA to accurately compute the RMS response of these points (namely, the excitation point, the coupling points, and the hot lines through the excitation or coupling points) in the system is shown. The behavior of three representative prototypical configurations of the parallel plate system considered is: two similar plates (in both geometry and modal density), two plates with similar modal density but different geometry, and two plates with similar geometry but different modal density. After examining the error between reduced modal methods (such as AMA) to classical modal analysis (CMA), it is determined that these several methods are valid for each of these scenarios. The data from the various methods will also be useful in evaluating the accuracy of other methods including statistical energy analysis (SEA).

Obtaining head-related transfer functions (HRTFs) is a challenging task, in spite of its importance in localizing sound in a three-dimensional (3D) environment or improving the performance of hearing aids, among their various applications. In this paper, an optimized finite element method through adaptive dimension size based on wavelength (frequency) for acoustic scattering analyses using ansys is presented. Initial investigation of the validity of our method is conducted by simulating scattered sound field for a solid sphere exposed to a far-field plane sound wave at 100 (equally spaced in logarithmic scale) frequencies between 20 and 20 kHz. Comparison of the equivalent HRTF results between the two methods shows a maximum deviation of less than 0.6 dB between our method and the analytical solution depending on the angle of rotation of the sphere with respect to sound source.

Flexible multistage rotor systems that are supported by water-lubricated rubber bearings (WLRBs) are seen in various engineering applications. Vibration analysis is important to design and performance of such dynamic systems. In the past, due to the lack of reliable models of WLRBs, vibration analysis of this type of rotor systems has not been well addressed. In this paper, a method for modeling and analysis of WLRB-supported multistage rotor systems is proposed. In the development, a new model of WLRBs is integrated with a distributed transfer function formulation, which eventually yields accurate results on the eigensolutions, critical speeds, and steady-state responses of WLRB-supported rotor systems. The proposed method is illustrated in a numerical study on a three-stage rotor system. It is shown that the proposed method provides a useful tool for optimal design of flexible multistage rotor systems with WLRBs.

Nonmodal model order reduction (MOR) techniques present accurate and efficient ways to approximate input–output behavior of large-scale mechanical structures. In this regard, Krylov-based model reduction techniques for second-order mechanical structures are typically known to require a priori knowledge of the original system parameters, such as expansion points (or eigenfrequencies). The calculation of the eigenfrequencies of the original finite-element (FE) model can be significantly time-consuming for large-scale structures. Existing iterative rational Krylov algorithm (IRKA) addresses this issue by iteratively updating the expansion points for first-order formulations until convergence criteria are achieved. Motivated by preserving the model properties of second-order systems, this paper extends the IRKA method to second-order formulations, typically encountered in mechanical structures. The proposed second-order IRKA method is implemented on a large-scale system as an example and compared with the standard Krylov and Craig-Bampton reduction techniques. The results show that the second-order IRKA method provides tangibly reduced error for a multi-input-multi-output (MIMO) mechanical structure compared to the Craig-Bampton. In addition, unlike the standard Krylov methods, the second-order IRKA does not require the information on expansion points, which eliminates the need to perform a modal analysis on the original structure. This can be especially advantageous for large-scale systems where calculations of the eigenfrequencies of the original structure can be computationally expensive. For such large-scale systems, the proposed MOR technique can lead to significant reductions of the computational time.

In Paper I, some test cases of centrifugal pump impellers which showed unconventional impedances curves were reviewed and possible sources of the bump and dip in the impedance curves were investigated by simulating a wear-ring seal pump impeller. In this paper, the unconventional impedances determined in Paper I are converted into a form for inclusion in rotordynamic stability and forced response analyses. First of all, a finite element (FE) rotor model is considered to investigate the influence of the bump and dip in the impedance curves on the rotordynamic stability. With the same FE model, speed-dependent impedances are calculated to obtain unbalance frequency response. Finally, a new linear curve-fit approach is developed to model the fluctuating impedances since the unconventional impedance cannot be expressed by the second-order polynomials with the rotordynamic coefficients (stiffness, damping, and mass). In order to validate the newly developed method, a Jeffcott rotor model with the impeller forces is considered and rotordynamic stability analysis is implemented. The results of the analysis show that the existence of the bump and dip in the impedance curves may further destabilize the rotor system.

Fluidic flexible matrix composite (F2MC) tubes with resonant fluidic circuits can absorb vibration at a specific frequency when bonded to flexible structures. The transverse structural vibration applies cyclic axial strain to the F2MC tubes. The anisotropic elastic properties of the composite tube amplify the axial strain to produce large internal volume change. The volume change forces fluid through a flow port and into an external accumulator. The fluid inertance in the flow port (inertia track) and the stiffness of the accumulator are analogous to the vibration absorbing mass and stiffness in a conventional tuned vibration absorber. An analytical model of an F2MC-integrated cantilever beam is developed based on Euler–Bernoulli beam theory and Lekhnitskii's solution for anisotropic layered tubes. The collocated tip force to tip displacement analytical transfer function of the coupled system is derived. Experimental testing is conducted on a laboratory-scale F2MC beam structure that uses miniature tubes and fluidic components. The resonant peak becomes an absorber notch in the frequency response function (FRF) if the inertia track length is properly tuned. Tuning the fluid bulk modulus and total flow resistance in the theoretical model produces results that match the experiment well, predicting a magnitude reduction of 35 dB at the first resonance using an F2MC absorber. Based on the experimentally validated model, analysis results show that the cantilever beam vibration can be reduced by more than 99% with optimally designed tube attachment points and flow port geometry.

Many methods to detect, quantify, or reconstruct acoustic sources exist in the literature and are widely used in industry (near-field acoustic holography, inverse boundary element method, etc.). However, the source identification in a reverberant or nonanechoic environment on an irregularly shaped structure is still an open issue. In this context, the inverse patch transfer functions (iPTF) method first introduced by Aucejo et al. (2010, “Identification of Source Velocities on 3D Structures in Non-Anechoic Environments: Theoretical Background and Experimental Validation of the Inverse Patch Transfer Functions Method,” J. Sound Vib., 329(18), pp. 3691–3708) can be a suitable method. Indeed, the iPTF method has been developed to identify source velocity on complex geometries and in a nonanechoic environment. However, to obtain good results, the application of the method must follow rigorous criteria that were not fully investigated yet. In addition, as it was first defined, the iPTF method only provides source velocity while wall pressure or intensity should also give useful information to engineers. In the present article, a procedure to identify wall pressure and intensity of the source without any additional measurement is proposed. This procedure only needs simple numerical postprocessing. Using this new intensity identification, the influence of background noise, evanescent waves, and mesh discretization are illustrated on numerical examples. Finally, an experiment on a vibrating plate is shown to illustrate the iPTF procedure.

Based on the Donnell assumptions and linear viscoelastic theory, the constitutive relations for the multilayer passive constrained layer damping (PCLD) cylindrical shell are described. In terms of energy, the motion equations and boundary conditions of the cylindrical shell with multilayer PCLD treatment are derived by the Hamilton principle. After trigonometric series expansion and Laplace transform, the state vector is introduced and the dynamic equation in state space is established. The transfer function method is used to solve the state equation. The dynamic performance including the natural frequency, the loss factor, and the frequency response of the multilayer PCLD cylindrical shell is obtained. The results show that with more layers, the more effective in suppressing vibration and noise, if the same amount of visco-elastic and constrained material is applied. It demonstrates a potential application of multilayer PCLD treatment in some critical structures, such as cabins of aircrafts, hulls of submarines, and bodies of rockets and missiles.

A laser Doppler vibrometer measures the translational velocity at a point along the direction of incident light. It has been shown that rotational velocities can also be recovered when the laser scans continuously along a short line or small circular path around that point. This work uses the harmonic transfer function to relate the measured translational and rotational velocities to the input force. With this concept, the continuous-scan approach can be combined with the conventional point-by-point scheme, acquiring three dimensional velocities under various types of excitation conditions in the same amount of time that is required for obtaining only the translational velocity. The proposed approach is validated on a downhill ski under free-free boundary conditions with a circular scan pattern. The influence of the circle size, the scan rate and the surface quality on the noise level is evaluated. It is found that the circular-scan approach provides smoother and more reliable mode shapes than the conventional point-by-point approach given appropriate parameters. Local slopes at the measurement locations are then computed from the identified rotational velocities, providing additional information for model validation and damage detection.

The problem of obtaining a modal (i.e., infinite series) solution of second order flexible structures with viscous damping boundary conditions is considered. In conservative boundary systems, separation of variables is well established and there exist closed form modal solutions. However, no counterpart results exist for the damped boundary case and previous publications fall short of providing a complete solution for the series, in particular, its coefficients. The paper presents the free response of damped boundary structures to general initial conditions in the form of an infinite sum of products of spatial and time functions. The problem is attended via Laplace domain approach, and explicit expressions for the series components and coefficients are derived. The modal approach is useful in finite dimension modeling, since it provides a convenient framework for truncation. It is shown via examples that often few modes suffice for approximation with good accuracy.

In this article, a dynamical model of the vibrations and acoustic radiation of a circular clamped plate excited by a voice coil and two annular piezoelectric patches is derived. This model is used to perform an optimization of the geometries with the objective to minimize the vibration of the plate along its second and third modes, so that the plate's radiation is equilibrated between its first and fourth eigenfrequencies. Experiments are then performed and show a good agreement with the model. Radiation of the designed system presents improvements when compared to a system when only a voice coil is used.

The vibro-acoustic behavior of elastic structures coupled with cavities filled with a heavy fluid can be modeled by using the Finite Element Method. In order to reduce computing time, the Patch Transfer Function (PTF) approach is used to partition the global problem into different sub-problems. Different types of problem partitioning are studied in this paper. Partitioning outside the near field of structures to reduce the number of patches of the coupling surface for frequencies below the critical frequency is of particular interest. This implies introducing a non- standard modal expansion to compute the PTF accurately enough to guarantee the convergence of the PTF method and reduce computation time in comparison to a direct Finite Element resolution. An application on a submarine structure illustrates the interest of this approach.

The paper considers the problem of suppressing the free vibration, induced by nonzero initial conditions, in a flexible system governed by the wave equation. First an exact response of the system, with general linear boundary conditions, is derived in terms of propagating waves that are reflected from the boundaries. The solution is explicit and with clear physical interpretation. The general expressions for the response are then used to investigate the behavior of the system under control with the absolute vibration suppression controller, which was originally designed for tracking control. It is shown that the vibration suppression properties of this controller apply also to nonzero initial conditions. In cases where the load end is free or contains only damping, the vibration stops completely in finite time and if it contains only inertia and damping it decays exponentially without vibration.