Target Natural Frequency Research Articles

Verification of the Mode Decomposition Technique for Closely Distributed Modal Systems in the State Space Domain.

This study aims to propose and validate the state space mode decomposition technique for precise mode separation of non-classical damping systems and closely distributed modal systems. To assess the reliability and applicability of this technique, a 40-story building with a tuned mass damper is investigated, and acceleration responses measured by the building's health monitoring system are used for the verification of the technique. The mode separation results reveal that the separated modal power spectrum becomes distorted at neighboring natural frequency ranges when the performance index only considers the concentration of power spectral energy at the target natural frequency. However, by introducing an augmented performance index that includes a constraint condition to account for distortion, more accurate mode decomposition can be achieved.

Natural frequency assignment of a pipeline through structural modification in layout optimization of elastic supports

Layout optimization of elastic supports is an effective approach to address the resonance problem of an industrial post-manufactured pipeline. However, previous investigations of support layout optimization of a post-manufactured pipeline usually require establishing or updating the numerical model of the whole pipeline system, which may lead to time-consuming calculations and poor optimization results. In order to overcome these drawbacks, a new measurement-based layout optimization method is proposed in this method. Only a small number of experimental modal parameters (natural frequencies, damping ratios, and mode shapes) are needed in this method. Resonance avoidance, in this method, is recast as an assignment of natural frequencies, and the target natural frequencies are realized by performing structural modification in two stages. In addition, each of the elastic supports is viewed as a mass-spring-damper sub-system in this paper, which is represented by its measured dynamic stiffness and does not need a pre-determined simplified form. A numerical example demonstrates that the proposed method can accurately realize the target natural frequencies. The application of the proposed method to optimize the support layout of a real L-shaped pipeline system provides experimental evidence of its effectiveness. This experiment is the first attempt to achieve the layout optimization of pipeline supports for solving the resonance problem of a post-manufacture pipeline, entirely relying on the measured modal data.

Experimental study on adaptive-passive tuned mass damper with variable stiffness for vertical human-induced vibration control

Serviceability problem and human-induced vibration control of slender footbridges are of increasing interest to structural engineers. Passive tuned mass dampers (TMDs) have a wide range of applications in human-induced vibration control. However, a passive TMD is sensitive to the frequency deviation and, as a result a mistuned TMD will lose its control effect. An adaptive TMD can solve the mistuning problem of a passive TMD. However, there is few adaptive TMDs with variable stiffness in this issue. To fill this gap, an adaptive-passive variable stiffness TMD (APVS-TMD) is proposed in this study. The stiffness and frequency of APVS-TMD can be retuned through changing the length of free end of cantilever beam, while the damping can be retuned by adjusting the air gap between the conductor plate and magnets. As for the target natural frequency to be adjusted, the first two modal frequencies of the TMD-structure coupled system are identified under ambient excitation first, and then, the decoupled structural natural frequency is obtained according to the developed method based on the undamped 2-degree of freedom (DOF) modal analysis. By means of numerical simulation, the identification strategy is verified using a SDOF lumped mass main structure and an ideal simply supported beam model. Then, the identification and stiffness retuning operations of the APVS-TMD are further verified through a footbridge model experiment. Here, control effects of the APVS-TMD to walking- and running-induced vibrations are highlighted and compared with those of a mistuned TMD. Experimental results show that the APVS-TMD can identify the decoupled structural natural frequency from the coupled system accurately, and control human-induced vibrations effectively.

Sensitivity Analysis and Robust Assignment of Natural Frequencies for Vibrating Systems Using the Receptance Method

This paper presents a new receptance-based method for the robust assignment of natural frequencies. This method aims to address the deviation of the actually achieved natural frequencies for target natural frequencies when assigning natural frequencies, which usually arises due to uncertainties in passive structural modifications (i.e. mass and stiffness modifications). The mathematical expression is derived for the sensitivity of the target natural frequency to the uncertainties in modification parameters, which are subsequently employed to characterize the potential deviations of the target natural frequencies in the total differential form. The obtained deviation expression is integrated into the optimization calculation of the natural frequency assignment as an extra penalty term to boost the acquisition of highly robust modification parameters. The proposed robust assignment method, as a non-probabilistic technique, can be employed without any knowledge of the probabilistic distribution of uncertainty in modification parameters. Moreover, it uses only the measured frequency response functions (FRFs), preserving the advantage of the receptance method not needing a numerical model. Two numerical examples and a comparison with a typical eigenstructure assignment method (reported in the literature) demonstrate that the proposed method can provide highly robust modification parameter solutions. The application of the proposed method to the natural frequency assignment of a laboratory water-filled pipeline system gives experimental evidence of its effectiveness.

Generative Design of Structured Materials for Controlled Frequency Responses.

Spatially varying material properties allow the dynamic response of structural systems to be almost arbitrarily tailored, far beyond the first or fundamental natural frequency. Continuing advances in manufacturing technology are making it possible to achieve the necessary range of stiffness and density variations, but the design of these property distributions is a challenging task because of the complex multidimensional nature of the problem. Generative design methods based on evolutionary optimization algorithms have been successfully used to obtain solutions based on multi-material distributions. However, the applicability of these solutions is limited by their reliance on multi-material additive manufacturing (AM), which currently only offers digitally mixed acrylic polymer options that are generally unsuitable to produce functional parts. A novel structured material solution is proposed here, in which the problem domain is divided into several volume elements (voxels), each of which contains a structure whose geometrical form is altered to adjust its effective properties to desired values. The single material structural solution will be amenable for ready fabrication by the powder-based selective laser sintering and melting processes with real engineering polymer and metal systems, thereby allowing for the realization of the benefits in real-world applications. The resulting continuous design spaces are searched using a modern evolutionary algorithm, the covariance matrix adaptation evolution strategy (CMA-ES). A MATLAB implementation of this evolutionary design method, in conjunction with finite element simulations for fitness evaluation, showed good convergence for several different cantilever beam test cases when tested against several different sets of target natural frequencies. Correlations with the multi-material solutions show that the single structured material approach is on par or even better in some cases, even though the test domain was discretized into 80% fewer voxels than for the multi-material case. Furthermore, the voxel structures can be realized using current AM technologies.

Analysis Methods for High Energy Line Break Jet Flows in Nuclear Power Plants

Abstract The effects of postulated accidents, including dynamic effects of pipe ruptures, must be analyzed for licensing of nuclear power plants (NPPs). Applicants and licensees of NPPs have struggled to address U.S. Nuclear Regulatory Commission (NRC) expectations to assess if high energy line break (HELB) jet impingement on structures and components can lead to dynamic amplification, and to accurately simulate blast wave-induced loadings. In this paper, evaluation of the potential for load amplification and occurrence of resonance conclusively demonstrates that the phenomenon does not occur. In a HELB, several physical parameters of jets issuing from a ruptured pipe—such as nonequilibrium condensation of steam, unsteady separation between the jet exit and target, nonorthogonal alignment of jet axis to impingement surface, uneven impingement surfaces, or mismatch of jet excitation frequency and target natural frequency—prevent occurrence of the phase lock conditions needed to initiate and maintain a resonance. The analytical approach to evaluate the blast wave-induced loading applied a pressure vessel burst (PVB) correlation instead of performing computational fluid dynamics (CFD) analysis for all break locations. Three-dimensional (3D) CFD analysis of blast wave transient propagation provided the basis to develop benchmarking factors for use with the PVB correlation. The simplified methodology utilizes shockwave reflection, shape, and environment factors for application to impacted targets, which significantly reduces the amount of time to evaluate all break locations. The modified PVB method is also more appropriate than an explosion-type correlation to model the blast wave pressures from steam pipe breaks.

Passive piezoelectric subordinate oscillator arrays

Subordinate oscillator arrays (SOAs) attached to a host structure have been shown to achieve flat attenuation of the frequency response over a band around a target natural frequency of the host. Due to their sensitivity to disorders that can arise from sources such as fabrication errors, as well as uncertainties in their structural properties or that of the host, SOAs can be challenging to implement in some applications. To overcome this shortcoming, piezoelectric subordinate oscillator arrays (PSOAs) are studied in this paper. This paper models PSOAs using variational principles to facilitate the analysis and development of design strategies. A closed-form expression for the frequency response function of the host structure is then used to design the PSOAs with and without uncertainties. This paper shows that the flat attenuation over a frequency band around a harmonic of the host can be achieved by assigning a distribution to the mechanical, electrical, or electromechanical properties of the PSOAs. For instance, it is shown that choosing a distribution of capacitive shunt circuits can achieve essentially the same qualitatively flat attenuation as that of classical SOAs. In this sense, the approach in this paper generalizes the results attained for conventional SOAs. Finally, the paper investigates the robustness of PSOAs, that is, their relative insensitivity to types of uncertainties. It is shown that PSOAs afford the chance to ameliorate some types of sensitivities that prove problematic for SOAs that are purely mechanical in nature. The notion of performance recovery is introduced; this measure quantifies how much attenuation loss due to uncertainty in an initial SOA or PSOA design can be recovered by modification of the electrical properties alone.

Closed-form stiffnesses of multi-bucket foundations for OWT including group effect correction factors

Offshore Wind Turbine (OWT) support structures need to satisfy different Limit States (LS) such as Ultimate LS (ULS), Serviceability LS, Fatigue LS and Accidental LS. Furthermore, depending on the turbine rated power and the chosen design (all current designs are soft-stiff), target natural frequency requirements must also be met. Most of these calculations require the knowledge of the stiffnesses of the foundation which, especially in the case of large turbines in intermediate waters (30–60 m), might need to be configured using multiple foundation elements. For this reason, this paper studies, for a homogeneous elastic halfspace, the static stiffnesses of groups of polygonally arranged non-slender suction bucket foundations in soft soils modeled as rigid solid embedded foundations. A set of formulas for correcting the stiffnesses obtained from isolated foundation formulation are proposed. It is shown through the study of several multi-megawatt OWTs that, as expected, group effects becomes more relevant as spacing decreases. Also, group effects are sensitive mainly to shear modulus of soil, foundation shape ratio and diameter, and the number of foundations. The results obtained from the soil-structure system show that ignoring group effects may add significant errors to the estimation of OWT fundamental frequencies and leads to either overestimating or underestimating it by 5%. This highlights the importance of adequately modeling the interaction between elements of closely-separated multi-bucket foundations in soft soils, when current guidelines specify the target fundamental frequency to be at least 10% away from operational 1P and blade passing frequencies (2P/3P frequencies).

Structural Synthesis for Prescribed Target Natural Frequencies and Mode Shapes

A new method for the synthesis of structures with prescribed target natural frequencies and mode shapes is presented. The introduction of a modal Rayleigh quotient approximation based on the target mode shapes is the means to propose a structural synthesis problem whose solution is free from eigenvector sensitivity analysis. The frequencies and mode shapes can be adjusted as close as possible to the desired target values, while minimizing the total mass. Several examples corroborate the efficacy of the proposed method.

On the linear elastic, isotropic modeling of poroelastic distributed vibration absorbers at low frequencies

Several past works have considered a passive vibration absorber device utilizing distributed mass and spring layers. The thickness of the poroelastic foam spring and the area density of the mass layer are modified to achieve a target natural frequency of the device while the foam itself provides adequate dissipation of energy as the mass dynamically compresses it at resonance. A model of the device earlier developed is briefly reviewed and validated by new experiments. The dependence of the absorber natural frequency and damping on the poroelastic spring thickness is observed in detail and is found to be consistent with past work on poroelastic material elastic characteristics outside of the linear dynamic regime. The results set a practical limit on the applicability of linearity assumptions in the present modeling of the distributed poroelastic vibration absorbers and thus determine a design parameter range for which the computationally efficient model is accurate.

Designing maximum power output into piezoelectric energy harvesters

Energy harvesting from vibrational sources has been the focus of extensive research in the last decade, but fundamental questions remain concerning the design of these harvesters. We consider a piezoelectric bimorph energy harvester and seek to translate design requirements, such as mass and target natural frequency, into beam dimensions that maximize power output. Our method centers around optimizing the thickness of the piezoelectric layers of a beam relative to the total beam thickness, otherwise known as the thickness ratio. This method uses approximations for the fundamental frequency and mode shape. This allows for the development of algebraic expressions for the modal parameters required for the prediction of power output. The resulting expression for power is fully defined by the fixed system level requirements and the only unknown parameters, the piezoelectric thickness ratio and the damping ratio. We show in an example case that, for typical damping ratio values, the ideal thickness ratio is not significantly affected by changes in the damping ratio. As such, the method requires a simple sweep of the thickness ratio in order to determine the beam design which maximizes the power. We develop the design method for both systems where the piezoelectric material is continuous and where the thickness is selected from a discrete set of values. Because our method produces a single algebraic expression for the power, the resulting beam design can be developed extremely quickly from a set of design requirements, and thus does not require optimization algorithms. We also show that our design method achieves more power output and requires less piezoelectric material than an approach which maximizes the coupling coefficient.

104 可変マルチパラメータを考慮した連続体の固有振動数のマルチパラメータ依存性解析

This paper deals with the parameter dependency analysis of natural frequency of continuum with variable multi-parameter. In the design phase of a component of mechanism, it is important to know how several design parameters such as its dimensions and loading force affect its natural frequencies. The modal hypersurface which is a set of a target natural frequency of variable multi-parameter system is firstly defined. The modal polytope which includes the corresponding modal hypersurface and have two boundary hypersurfaces is secondly defined. A new concept of the modal polytope analysis is further proposed. Proposed method reveals the continuous parameter dependency of natural frequencies with simple calculation. Example of a thin plate which has three variable parameters shows validity of this method.

선내 탑재 장비용 마운팅 시스템의 진동특성 평가에 관한 연구

일반적으로, 선박에 탑재되는 장비의 진동문제는 장비자체의 기진력에 의한 진동문제뿐만 아니라 외부기진력인 주기관과 추진기의 기진력이 장비하부 데크를 통하여 장비에 과도 진동을 유발하는 경우가 많다. 따라서 본 연구에서는, 선박에 탑재되는 장비 마운팅 시스템의 진동 성능을 평가할 수 있도록 고유진동해석, 전달율계산, 강제진동해석 등을 수행할 수 있는 프로그램을 개발하였고, 선내 주요기진원과 장비의 공진시 공진회피를 위한 마운트 설계 변경 프로그램과, 그리고 장비 마운트 하부데크의 진동에 의한 장비의 무게중심에서 속도응답이 최소가 되도록, 마운트 강성을 결정하는 최적화 프로그램을 개발하였다. This study is performed to evaluate and design the vibration characteristics of the onboard machinery with resilient mountings. To reduce the vibration revel of onboard machinery with resilient mountings, it is important to evaluate and, if necessary modify vibration characteristics of the resilient mountings. In this study we have developed a program to calculate natural frequencies of the machinery with resilient mountings, forced vibration levels due to internal excitation force of the machinery itself and external excitation forces of the main engine and the propeller, and the force and motion transmissibility of the resilient mountings. The developed program can be also applied to optimal design of the resilient mountings for obtaining a target natural frequency and for achieving a minimum forced vibration level at the center of gravity of the machinery.

Radar target discrimination by convolution of radar return with extinction-pulses and single-mode extraction signals

A new method of radar target discrimination and identification is presented. This new method is based on the natural frequencies of the target. It consists of synthesizing aspect-independent discriminant signals, called extinction-pulses (E-pulses) and single-mode extraction signals which, when convolved numerically with the late-time transient response of an expected target, lead to zero or single-mode responses. When the synthesized, discriminant signals for an expected target are convolved with the radar return from a different target, the resulting signal will be significantly different from the expected zero or single-mode responses, thus, the differing targets can be discriminated. Theoretical synthesis of discriminant signals from known target natural frequencies and experimental synthesis of them for a complex target from its measured pulse response are presented. The scheme has been tested with measured responses of various targets in the laboratory.