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Investigation of boundary flexibility on the performance of piezoelectric vibration energy harvesting beam systems by DTFM

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JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES 2023年第1期34卷 47-64页

作者： Amoozegar, Shahram Tan, Chin An Wayne State Univ Dept Mech Engn 5050 Anthony Wayne Dr Detroit MI 48202 USA

The purpose of this paper is to investigate the effect of boundary flexibility on the performance of piezoelectric vibration energy harvester (PVEH) beam systems, which has not been studied comprehensively in the literature despite its importance. The coupled electromechanical equations of motion of a piezoelectric cantilever beam with a tip mass are established, with the base boundary constrained by translational and rotational springs. An exact closed-form solution of the frequency response function (FRF) of the PVEH is obtained by the distributed transfer function method (DTFM). The DTFM is a systematic powerful tool for the dynamic analysis of distributed parameter continua with non-classical boundary conditions, intermediate constraints, coupled fields, and non-proportional damping without adding much complexity to the solution formulation. Moreover, the DTFM computes the derivatives of the response, that is, the strains, which are required in the electromechanical coupling formulation, simultaneously without any differentiation. Numerical results showing the effects of boundary flexibility on energy harvesting efficiency are presented. A first-order rational function relating the boundary stiffness parameters and the harvesting efficiency is determined by nonlinear curve fitting of the calculated data. Physical insights and applicability of this analytical function for end-of-line quality check of the boundary of PVEH are discussed.

关键词： Piezoelectric vibration energy harvesting non-ideal boundary condition support flexibility distributed transfer function method coupled electromechanical modeling power harvesting efficiency

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Apparent Mass function Model for Nonstructural Element Influence in Aerospace Structure Vibrations

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JOURNAL OF SPACECRAFT AND ROCKETS 2024年第6期61卷 1729-1736页

作者： Raimond, Clement Cadiot, Xavier Tanays, Remy Sanches, Leonardo Foucaud, Simon Michon, Guilhem Univ Toulouse Clement Ader Inst ISAE SUPAERO CNRSDept Mech Engn F-31400 Toulouse France Natl Ctr Space Studies Struct & Mech Dept 18 Ave Edouard Belin F-31400 Toulouse France

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Structural dynamic responses of a stripped solar sail subjected to solar radiation pressure

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Chinese Journal of Aeronautics 2020年第8期33卷 2204-2211页

作者： Junhui ZHANG Na WU An TONG Yinghua LIU School of Civil Engineering North China University of TechnologyBeijing 100144China School of Aerospace Engineering Tsinghua UniversityBeijing 100144China

The stripped solar sail whose membrane is divided into separate narrow membrane strips is believed to have the best structural *** this paper,the stripped solar sail structure is regarded as an assembly made by connecting a number of boom-strip components in *** the coupling effects between booms and membrane strips,an exact and semianalytical method to calculate structural dynamic responses of the stripped solar sail subjected to solar radiation pressure is *** case study of a 100 m stripped solar sail shows that the stripped architecture helps to reduce the static deflections and amplitudes of the steady-state dynamic *** prestress of the membrane strips will decrease stiffness of the sail and increase amplitudes of the steady-state dynamic *** thickness of the boom will benefit to stability of the sail and reduce the resonant *** proposed semi-analytical method provides an efficient analysis tool for structure design and attitude control of the stripped solar sail.

关键词： distributed transfer function method Frequency response Solar radiation pressure Solar sail Structural dynamic response

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Medium-Frequency Vibration Analysis of Timoshenko Beam Structures

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2020年第13期20卷

作者： Zhang, Yichi Yang, Bingen Univ Southern Calif Dept Aerosp & Mech Engn Los Angeles CA 90089 USA

Medium-frequency (mid-frequency) vibration analysis of complex structures plays an important role in automotive, aerospace, mechanical, and civil engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in various engineering problems. A kinematic hypothesis made in the Euler-Bernoulli beam theory is that the plane sections of a beam normal to its neutral axis remain planes after the beam experiences bending deformation, which neglects shear deformation. However, previous investigations found out that the shear deformation of a beam (even with a large slenderness ratio) becomes noticeable in high-frequency vibrations. The Timoshenko beam theory, which describes both bending deformation and shear deformation, would naturally be more suitable for medium-frequency vibration analysis. Nevertheless, vibrations of Timoshenko beam structures in a medium frequency region have not been well studied in the literature. This paper presents a new method for mid-frequency vibration analysis of two-dimensional Timoshenko beam structures. The proposed method, which is called the augmented distributed transfer function method (DTFM), models a Timoshenko beam structure by a spatial state-space formulation in the s-domain. The augmented DTFM determines the frequency response of a beam structure in an exact and analytical form, in any frequency region covering low, middle, or high frequencies. Meanwhile, the proposed method provides the local information of a beam structure, such as displacement, shear deformation, bending moment and shear force at any location, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated in numerical examples, where the efficiency and accuracy of the proposed method is demonstrated. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are examined through comparison of the T

关键词： Structural dynamics beam structures medium-frequency vibrations mid-frequency analysis Timoshenko beam theory shear deformation distributed transfer function method analytical solution method

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Dynamic effects of harnessing cables on distributed parameter systems for space applications: Analytical modeling and experimental validation

Dynamic effects of harnessing cables on distributed paramete...

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作者： Agrawal, Pranav University of Waterloo

学位级别：博士

Power and data signal cables constitute a major component of lightweight spacecraft and satellite structures. These cables can account for up to as high as 30% of the structural mass and hence significantly impact the structural dynamics. Until the last decade, these cables were primarily modeled using ad hoc techniques that considered cables as non-structural mass elements and neglected their stiffness and damping effects. However, in the last decade, accurate modeling of cable-harnessed structures has come into the spotlight by incorporating cable dynamics that are governed by cable's stiffness and damping in addition to its mass. Accuracy of these lightweight space structure models are important because the control systems heavily rely on them for their robust performance. Hence, the primary goal of this research is to create simple analytical models that can predict the accurate dynamic behavior of cable-harnessed structures. The beauty of analytical models lie in the fact that they result in low-order high-fidelity governing partial differential equations (PDE) and hence are advantageous over the numerical methods, such as finite element method. A reliable low-order PDE of a dynamical system ensures the robustness of the control algorithms. Additionally, analytical models provide deeper insights into the system due to the possibility of obtaining closed-form solutions and ease of conducting parametric analysis. The current research can be classified into solving the following two broad problems: 1. modeling the damping mechanisms in cable-harnessed beam structures, 2. modeling the accurate stiffness and inertia effects in cable-harnessed two-dimensional structures. The first problem addresses accurate modeling of material damping in the cable-harnessed beam system which was identified as a major gap in the present literature. The system consists of the cables wrapped around the beam in specific periodic geometry. In the presented research, the energy loss mecha

关键词： cable-harnessed structures homogenization method damping viscoelastic damping hysteretic damping distributed transfer function method frequency response function structural dynamics modal analysis stability plate theory shell theory

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Parametric study of rocking cores-moment frames with supplemental viscous damping and self-centering devices using a distributed parameter model

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SOIL DYNAMICS AND EARTHQUAKE ENGINEERING 2019年第Aug.期123卷 304-319页

作者： Wu, Dayang Lu, Xilin Zhao, Bin Tongji Univ State Key Lab Disaster Reduct Civil Engn Shanghai 200092 Peoples R China

A distributed parameter model is proposed for the rocking cores-moment frames (RCMFs) with supplemental viscous damping and self-centering devices. In this model, the moment frame and rocking cores are simplified as a shear beam and a flexural beam, respectively, while viscous damping and self-centering devices are substituted by rotational constraint with linear viscous damping and elastic stiffness. Three nondimensional parameters, frame-core stiffness parameter, base-rotation fixity parameter and damping parameter, are introduced to describe the dynamic behavior of the full physical structural system. Closed-form solutions for complex modal shapes are derived, and then parametric study is conducted to explore the effects of these three parameters on modal damping ratios, eigenvalues, complex modal shapes, and drift concentration factor. Explicit expressions of modal damping ratios with these three parameters are established through curve-fitting technique that can be conveniently used for engineering practice. Frequency responses of base shear forces and moments are obtained using the distributed transfer function method. It is concluded that the modal damping ratios are significantly affected by these three parameters, and their peak values will be remarkably reduced as the increasing of the frame-core stiffness and base-rotation fixity. For design purpose, appropriate ranges of these three parameters are recommended to achieve better drift uniformity control, response reduction, and higher modes effect mitigation. The proposed model and conclusions of the parametric study can be used as a tool for rapidly evaluating seismic performance in a preliminary design phase of the RCMFs.

关键词： Rocking cores-moment frames distributed parameter model Modal damping ratio distributed transfer function method Drift concentration factor Higher modes effect

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A closed-form analytical solution method for vibration analysis of elastically connected double-beam systems

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COMPOSITE STRUCTURES 2019年 212卷 598-608页

作者： Liu, Shibing Yang, Bingen Hyperloop One 2159 Bay St Los Angeles CA 90021 USA Univ Southern Calif Dept Aerosp & Mech Engn Los Angeles CA 90089 USA

A double-beam system, which is a structure composed of two parallel beams that are interconnected by a viscoelastic layer, is seen in many engineering applications. Vibration analysis is essentially important for the safe and reliable operation, and optimal design of such dynamic systems. This paper presents an analytical method, the distributed transfer function method (DTFM), for modeling and vibration analysis of double-beam systems with arbitrary beam linear densities and flexural rigidities, and general boundary conditions. Exact closed-form analytical solutions for natural frequencies, mode shapes, and steady-state responses to periodic excitations are determined. The proposed method is applicable to a double-beam system with lower beam being fully, partially, or not supported by an elastic foundation. Through numerical study, the accuracy and efficiency of the proposed method are validated, and the effects of the stiffness, length, and location of an elastic foundation are investigated. It is shown that the DTFM is a useful tool for optimal design of elastically connected double-beam systems.

关键词： Vibration Double-beam system Elastic foundation distributed transfer function method Analytical solution Arbitrary boundary conditions

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A New Approach to Dynamic Analysis of a Multi-Span Beam Structure with Multiple Moving Oscillators 36th

A New Approach to Dynamic Analysis of a Multi-Span Beam Stru...

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36th International Modal Analysis Conference and Exposition (IMAC) on Structural Dynamics

作者： Yang, Bingen Gao, Hao Liu, Shibing Univ Southern Calif Los Angeles CA 90007 USA Hyperloop One Los Angeles CA USA

ISBN: (纸本)9783319753904;9783319753898

A multi-span beam structure carrying multiple moving oscillators is seen in a variety of engineering applications, including highway bridges, elevated guideways and railways with moving vehicles, and tubes conveying fast-moving pods. With the oscillators having different speeds and varying inter-distances, the dynamic interactions between the supporting structure and the moving oscillators are usually complicated. Indeed, the number of moving oscillators on the structure is time-varying, and as such, a conventional solution method must frequently check the number of oscillators on the structure and adjust the numerical algorithm accordingly. Because of this, most investigations have been limited to just one or a few moving oscillators. Proposed in this paper is a new semi-analytical method that can systematically handle a beam structure with an arbitrary number of moving oscillators, without tedious number checking and algorithm adjustment. In the development, an extended solution domain (ESD) is firstly defined and a generalized assumed-mode method is then developed based on the ESD, which eventually yields a set of time-varying state equations. Solution of the state equations by a standard numerical integration algorithm gives the dynamic response of the coupled beam-oscillator system. Because the proposed method makes use of the exact eigenfunctions of the multi-span structure that are obtained by a distributed transfer function method, it is highly accurate and efficient in computation, as shown in a numerical study.

关键词： Multi-span beam structures Moving oscillators Fast transit systems distributed transfer function method Semi-analytical solution method

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Optimal Vibration Reduction of Flexible Rotor Systems By the Virtual Bearing method

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JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME 2018年第2期140卷 021008-021008页

作者： Liu, Shibing Yang, Bingen Hyperloop One 2159 Bay St Los Angeles CA 90021 USA Univ Southern Calif Dept Aerosp & Mech Engn Los Angeles CA 90089 USA

This paper presents a new approach to optimal bearing placement that minimizes the vibration amplitude of a flexible rotor system with a minimum number of bearings. The thrust of the effort is the introduction of a virtual bearing method (VBM), by which a minimum number of bearings can be automatically determined in a rotor design without trial and error. This unique method is useful in dealing with the issue of undetermined number of bearings. In the development, the VBM and a distributed transfer function method (DTFM) for closed-form analytical solutions are integrated to formulate an optimization problem of mixed continuous-and-integer type, in which bearing locations and bearing index numbers (BINs) (specially defined integer variables representing the sizes and properties of all available bearings) are selected as design variables. Solution of the optimization problem by a real-coded genetic algorithm yields an optimal design that satisfies all the rotor design requirements with a minimum number of bearings. Filling a technical gap in the literature, the proposed optimal bearing placement approach is applicable to either redesign of an existing rotor system for improvement of system performance or preliminary design of a new rotor system with the number of bearings to be installed being unforeknown.

关键词： flexible rotor systems rotor-bearing systems bearings vibration reduction optimization optimal design optimal bearing placement distributed transfer function method analytical solutions

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Vibrations of a Multi-Span Beam Structure Carrying Many Moving Oscillators

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2018年第10期18卷

作者： Yang, Bingen Gao, Hao Liu, Shibing Univ Southern Calif Dept Aerosp & Mech Engn Los Angeles CA 90089 USA Hyperloop One 2159 Bay St Los Angeles CA 90021 USA

A beam structure carrying multiple moving oscillators is a mathematical model for various engineering applications, including rapid transit systems. With many moving oscillators having different speeds and varying inter-distances, the number of oscillators on the structure is time-varying, which inevitably complicates the beam-oscillator interactions. Consequently, the order of a mathematical model for the coupled beam-oscillator system changes with time, with many possibilities. Because of this, it is extremely difficult, if not impossible, for a conventional method to determine the dynamic response of a beam structure carrying many moving oscillators. In the literature, previous investigations have been limited to a beam structure with only one moving oscillator, which may not totally capture the physical behaviors of a structure with many moving oscillators, as seen in certain engineering applications. Developed in this work is a new semi-analytical method that can systematically handle arbitrarily many moving oscillators in both modeling and solution. In the development, an extended solution domain (ESD) is defined and based on the ESD a generalized assumed-mode method is devised. This modeling method completely resolves the issue of changing order in mathematical modeling. Because the proposed method makes use of the exact eigenfunctions of the beam structure (instead of traditional admissible functions), it renders determination of the dynamic response of a coupled beam-oscillator system highly accurate and efficient. The proposed method is demonstrated in several numerical examples. Furthermore, in a benchmark problem, it is shown that for the same accuracy in computation, the elapsed computation time used by the proposed method is just 3.3% of the time required by the finite element method.

关键词： Multi-span beam structure moving oscillator problem coupled flexible-rigid body systems time-varying systems assumed-mode method distributed transfer function method semi-analytical solutions

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