Uniqueness theorem,theorem of reciprocity,and eigenvalue problems in linear theory of porous piezoelectricity

The uniqueness theorem and the theorem of reciprocity in the linearized porous piezoelectricity are established under the assumption of positive definiteness of elastic and electric fields. General theorems in the linear theory of porous piezoelectric materials are proved for the quasi-static electric field approximation. The uniqueness theorem is also proved without using the positive definiteness of the elastic field. An eigenvalue problem associated with free vibrations of a porous piezoelectric body is studied using the abstract formulation. Some properties of operators are also proved. The problem of frequency shift due to small disturbances, based on an abstract formulation, is studied using a variational and operator approach. A perturbation analysis of a special case is also given.     

Exploiting internal resonance for vibration suppression and energy harvesting from structures using an inner mounted oscillator

The flexural vibration of a symmetrically laminated composite cantilever beam carrying a sliding mass under harmonic base excitations is investigated. An internally mounted oscillator constrained to move along the beam is employed in order to fulfill a multi-task that consists of both attenuating the beam vibrations in a resonance status and harvesting this residual energy as a complementary subtask. The set of nonlinear partial differential equations of motion derived by Hamilton’s principle are reduced and semi-analytically solved by the successive application of Galerkin’s and the multiple-scales perturbation methods. It is shown that by properly tuning the natural frequencies of the system, internal resonance condition can be achieved. Stability of fixed points and bifurcation of steady-state solutions are studied for internal and external resonances status. It results that transfer of energy or modal saturation phenomenon occurs between vibrational modes of the beam and the sliding mass motion through fulfilling an internal resonance condition. This study also reveals that absorbers can be successfully implemented inside structures without affecting their functionality and encumbering additional space but can also be designed to convert transverse vibrations into internal longitudinal oscillations exploitable in a straightforward manner to produce electrical energy.     

Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction

In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: friction-induced torsional vibrations and torsional vibrations due to the coupling between torsional and lateral dynamics in the system. Moreover, both the numerical and experimental results show that a higher level of mass-unbalance, which generally increases the lateral vibrations, can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Both types of analysis provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility, mass-unbalance and discontinuous friction which support the design of such flexible rotor systems.     

Justification of equivalent substitution circuits used to optimize the dissipative properties of electroelastic bodies with external electric circuits

We consider elastoplastic systems which are piecewise homogeneous bodies composed of piezoelectric elements some of which have piezoelectrical properties. Electric series circuits consisting of resistors, capacitors, and inductance coils are applied to piezoelectric elements through the electrode coating on the body surface. The goal of the study is to develop efficient methods of mathematical modelling for determining the parameters of elements of the external electric circuit, which ensure, at prescribed resonance frequencies, the maximum damping properties of electroelastic bodies with external electric circuits. To choose effective circuits for solving the problem posed above, we suggest to pose the problem of natural vibrations of elastic bodies whose elements exhibit piezoeffect and have external electric circuits.As the most efficient approaches for calculating the electric circuit parameters necessary for the maximal damping, we propose some versions of equivalent circuits, which can be used to substitute elastic systems with piezoelectric elements. The most reliable equivalent substitution circuits are justified on the basis of the proposed problem of natural vibrations. Numerical results are obtained for a cantilever plate with a piezoelement connected through the electrode coated surface with a series electric circuit consisting of resistors, capacitors and inductance coils.     

Thermo-mechanical instability in vibration absorbers

We analyze a problem of the thermo-mechanical instability caused by small changes of a viscous damping in vibration absorbers. The nonlinear coupling between the oscillations and temperature takes place due to a linear thermal dependence of the coefficient of energy dissipation. This provides typical phase–amplitude frequency patterns inherent in unstable regimes. While the damping coefficient decreases with the increase in the temperature, the effect of bifurcated oscillations can be exhibited brightly as some abnormal operating regimes. The vibration absorber appears as a complex dynamical system, behaving strongly upon the ambient temperature. Typical thermo-mechanical instability patterns are traced in detail within a parametric analysis along an approach closed to the Lie method. This study would explain some unwanted dynamical effects accompanying the utilizing of vibration absorbers.     

Modelling and dynamic stability of a hingeless active fibre composite blade

The main focus of this investigation was to investigate dynamic stability of what is now commonly referred to as an active twist rotor blade. With the ultimate intention of controlling helicopter blade vibrations, active or smart materials embedded in the rotor blade in various arrangements as opposed to the conventional passive isolation devices and absorbers are used. Structurally integrated interdigitated piezoelectric fibre composite material is considered in this work. This active composite may be used in constructing the blade in place of or concurrent with, composite blades. This fibrous composite is able to twist the blade, when subjected to an electric field, due to its unique arrangement of active fibres. The paper begins with outlining the design for lay-up sequence of the active blade. This is followed by developing a complete structural and dynamic modelling of the equations of motion of the smart blades for hover flight. These equations are used to investigate dynamic stability of the steady state motion of the smart blades under parametric excitation. In closing, as a preliminary step to determine the actuation authority of the active fibres, the open-loop response of the blade to an impulsive type of actuation is also investigated.     

Nonlinear Parametric Vibrations of an Elastic Structure with a Rectangular Liquid Tank

The nonlinear coupled vibrations of an elastic structure and liquidsloshing in a rectangular tank partially filled with liquid, are investigated.The structure on which the liquid tank is attached is vertically subjected to a sinusoidal excitation when the natural frequency of the structure is equal to twicethe natural frequency of one of the sloshing modes. In the theoretical analysis, the modal equations are derivedby taking nonlinear fluid force into account. Responses of the structure and the liquid surface are presented asresonance curves using the harmonic balance method. From this theoreticalanalysis the following predictions are obtained: (a) due to the nonlinearity of the fluid force, harmonic oscillations appear in the structure, while subharmonic oscillations occur on the liquid surface; (b) the shapes of the resonance curves markedly change depending on the liquid level; and (c) when the tuning condition is slightly deviated, amplitudemodulated motions and chaotic oscillations appear during a certain range of the excitation frequency. These were qualitatively in agreement with the experimental results.     

Liquid crystal model of vesicle deformation in alternating electric fields

Considering the effects of osmotic pressure, elastic bending, Maxwell pressure, surface tension, as well as flexo-electric and dielectric properties of phospholipid membrane, the shape equation for sphere vesicle in alternation (AC) electric field is derived based on the liquid crystal model by minimizing the free energy due to coupled mechanical and AC electrical fields. Besides the effect of elastic bending, the influence of osmotic pressure and surface tension on the frequency dependent behavior of vesicle membrane in AC electric field is also discussed. Our theoretical results for membrane deformation are consistent with corresponding experiments. The present model provides the possibility to further disclose the frequency-depended behavior of biological cells in the coupled AC electric and different mechanical fields.     

Whirling frequencies and amplitudes due to deviations of generator shape

Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse the whirling frequencies and amplitude of the response for large synchronous generators with a high number of poles, due to deviations of shape in the rotor and stator. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained by using the law of energy conservation. The UMP is analysed due to different deviations of shape. The result gives the average angular frequency and the magnitude of the UMP for certain deviations of shape. From this result, the whirling frequency and the amplitude of the corresponding response can be approximated. Simulations of the response of a Jeffcott rotor model show good agreement with the theoretical results of the UMP for some generator geometries. The conclusion is that different whirling frequencies, both backward and forward whirling, can occur in these machines due to deviations in shape of the generator. Therefore, the shape of the generator can excite resonance vibrations on several other frequencies than the rotation frequency. During maintenance of hydropower generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complicated whirling motion.     

Takagi–Sugeno fuzzy generalized predictive control for a class of nonlinear systems

The new generations of compact high output power-to-weight ratio internal combustion engines generate broadband torsional oscillations, transmitted to lightly damped drivetrain systems. A novel approach to mitigate these untoward vibrations can be the use of nonlinear absorbers. These act as Nonlinear Energy Sinks (NESs). The NES is coupled to the primary (drivetrain) structure, inducing passive irreversible targeted energy transfer (TET) from the drivetrain system to the NES. During this process, the vibration energy is directed from the lower-frequency modes of the structure to the higher ones. Thereafter, vibrations can be either dissipated through structural damping or consumed by the NES. This paper uses a lumped parameter model of an automotive driveline to simulate the effect of TET and the assumed modal energy redistribution. Significant redistribution of vibratory energy is observed through TET. Furthermore, the integrated optimization process highlights the most effective configuration and parametric evaluation for use of NES.     

任意斜裂纹转子的耦合振动研究

对包含不同类型裂纹(横裂纹、横-斜裂纹以及任意斜裂纹)的转子的耦合振动进行研究,以揭示裂纹转子在不同方向上刚度参数的变化规律及其交叉耦合机理,特别是由此引发的振动特征. 对于包含不同类型裂纹的转子轴段,采用六自由度Timoshenko梁单元模型对其进行单元建模,并基于应变能理论推导计算柔度参数和刚度矩阵. 在此基础上, 采用纽马克-$\beta$数值算法求解裂纹转子的运动方程,获得裂纹转子在单故障或多故障激励(不平衡激励、扭转激励或不平衡激励加扭转激励)作用下的耦合振动响应,进而分析耦合振动谱特征. 与横裂纹和横-斜裂纹相比,任意斜裂纹使转子刚度矩阵的交叉耦合效应更显著,导致转子发生更强烈的弯-扭耦合甚至是纵-弯-扭耦合振动.无论是在不平衡激励还是扭转激励作用下, 弯曲振动与扭转振动幅度都更大. 而且,包含不同类型裂纹的转子的耦合振动特征频率,例如旋转基频与二倍频、扭转激励频率及其边带成分的幅值,对裂纹面方向角具有不同的敏感性. 所得的这些研究结果,可以为转子裂纹的特征参数辨识与诊断提供理论依据.      

Large amplitude oscillations of a hollow spherical dielectric

Based on the Truesdell theorem on quasi-equilibrated motions and an electroelastostatics theory of elastic dielectrics due to Toupin and Eringen, the problem of large amplitude radial oscillations of hollow spherical dielectrics is analysed, assuming a semi-general strain energy density function for the hyperelastic, incompressible dielectric material under consideration. Criteria of existence of oscillatory motions are established. The expressions for the periods of free oscillations initiated under large initial deformation as well as forced oscillations due to a sudden Heaviside impact are given in integral form.     

泡沫铝冲击吸能器被动冲击隔离技术研究

对隔振系统中引入泡沫铝冲击吸能器进行探讨.首先,在综合考虑最大加速度和最大相对位移这2个影响舰船设备防护的重要指标情况下,对舰船单层隔振系统中引入泡沫铝冲击吸能器进行了理论分析,在此基础上进行了实验验证.通过实验结果可知,泡沫铝冲击吸能器能有效消除舰船设备的二次冲击.实验结果与理论结果吻合较好,可为泡沫铝冲击吸能器的应...     

DYNAMIC ANTI-PLANE PROBLEMS OF PIEZOCERAMICS AND APPLICATIONS IN ULTRASONICS——A REVIEW

We review theoretical results on anti-plane motions of polarized ceramics based on the linear theory of piezoelectricity.Solutions to dynamic problems of the propagation of bulk acoustic waves (BAW) and surface acoustic waves (SAW),vibrations of finite bodies,and applications to various piezoelectric devices including piezoelectric waveguides,resonators,mass sensors,fluid sensors,actuators,nondestructive evaluation,power harvesters (generators),transformers,and power transmission through an elastic wall by acoustic waves are discussed.Complications due to material inhomogeneity,initial stress,electromagnetic coupling,electric field gradient and semiconduction are also discussed. The paper cites 82 references.     

Parametric vibrations of flexible hoses excited by a pulsating fluid flow,Part II: Experimental research

The paper presents the results of experimental studies of vibrations of an elastic hose which are induced by a pulsating fluid flow. It was found that there is a possibility of parametric resonances: principal and combination associated with certain modes of vibrations. The influence of frequency and the amplitude of pulsation, average flow velocity, pressure inside pipe, the length of the hose, and the temperature on the ranges of parametric vibrations were analysed. The character of vibrations in resonance ranges was determined by showing time histories and the results of spectral analyses. A flexible hose applied in high-pressure hydraulic systems was used as an object of research. The values of basic parameters which describe the hose׳s mechanical properties were identified experimentally. The results of the experiments were compared with the results of numerical simulations conducted on the basis of the methodology proposed in Part I of this paper.     

DYNAMIC ANTI-PLANE PROBLEMS OF PIEZOCERAMICS AND APPLICATIONS IN ULTRASONICS—A REVIEW

We review theoretical results on anti-plane motions of polarized ceramics based on the linear theory of piezoelectricity. Solutions to dynamic problems of the propagation of bulk acoustic waves (BAW) and surface acoustic waves (SAW), vibrations of finite bodies, and applications to various piezoelectric devices including piezoelectric waveguides, resonators, mass sensors, ?uid sensors, actuators, nondestructive evaluation, power harvesters (generators), transformers, and power transmission through an elastic wall by acoustic waves are discussed. Complications due to material inhomogeneity, initial stress, electromagnetic coupling, electric field gradient and semiconduction are also discussed. The paper cites 82 references.     

An investigation on lateral and torsional coupled vibrations of high power density PMSM rotor caused by electromagnetic excitation

Electromagnetic excitation in high power density permanent magnet synchronous motors (PMSMs) due to eccentricity is a significant concern in industry; however, the treatment of lateral and torsional coupled vibrations caused by electromagnetic excitation is rarely addressed, yet it is very important for evaluating the stability of dynamic rotor vibrations. This study focuses on an analytical method for analyzing the stability of coupled lateral/torsional vibrations in rotor systems caused by electromagnetic excitation in a PMSM. An electromechanically coupled lateral/torsional dynamic model of a PMSM Jeffcott rotor is derived using a Lagrange–Maxwell approach. Equilibrium stability was analyzed using a linearized matrix of the equation describing the system. The stability criteria of coupled torsional–lateral motions are provided, and the influences of the electromagnetic and mechanical parameters on mechanical vibration stability and nonlinear behavior were investigated. These results provide better understanding of the nonlinear response of an eccentric PMSM rotor system and are beneficial for controlling and diagnosing eccentricity.     

Non-linear longitudinal vibrations of non-slender piezoceramic rods

Characteristic non-linear effects can be observed, when piezoceramics are excited using weak electric fields. In experiments with longitudinal vibrations of piezoceramic rods, the behavior of a softening Duffing-oscillator including jump phenomena and multiple stable amplitude responses at the same excitation frequency and voltage is observed. Another phenomenon is the decrease of normalized amplitude responses with increasing excitation voltages. For such small stresses and weak electric fields as applied in the experiments, piezoceramics are usually described by linear constitutive equations around an operating point in the butterfly hysteresis curve. The non-linear effects under consideration were, e.g. observed and described by Beige and Schmidt [1,2], who investigated longitudinal plate vibrations using the piezoelectric 31-effect. They modeled these non-linearities using higher order quadratic and cubic elastic and electric terms. Typical non-linear effects, e.g. dependence of the resonance frequency on the amplitude, superharmonics in spectra and a non-linear relation between excitation voltage and vibration amplitude were also observed e.g. by von Wagner et al. [3] in piezo-beam systems. In the present paper, the work is extended to longitudinal vibrations of non-slender piezoceramic rods using the piezoelectric 33-effect. The non-linearities are modeled using an extended electric enthalpy density including non-linear quadratic and cubic elastic terms, coupling terms and electric terms. The equations of motion for the system under consideration are derived via the Ritz method using Hamilton's principle. An extended kinetic energy taking into consideration the transverse velocity is used to model the non-slender rods. The equations of motion are solved using perturbation techniques. In a second step, additional dissipative linear and non-linear terms are used in the model. The non-linear effects described in this paper may have strong influence on the relation between excitation voltage and response amplitude whenever piezoceramic actuators and structures are excited at resonance.     

Dynamic characteristics of a rub-impact rotor-bearing system for hydraulic generating set under unbalanced magnetic pull

Electromagnetic and mechanical forces are main reasons resulting in vibrations in hydraulic generating set. The non-symmetric air-gap between the rotor and stator creates an attraction force called unbalanced magnetic pull (UMP). The UMP can produce large oscillations which will be dangerous to the machines. In this paper, the nonlinear dynamic characteristics of a rotor-bearing system with rub-impact for hydraulic generating set under the UMP are studied. The rubbing model is established based on the classic impact theory. Through the numerical calculation, the excitation current, mass eccentricity, stiffness of shaft and radial stiffness of stator are used as control parameters to investigate their effect on the system, by means of bifurcation diagrams, Poincaré maps, trajectories and frequency spectrums. Various nonlinear phenomena including periodic, quasi-periodic and chaotic motions are observed. The results reveal that the UMP has significant influence in the response of the rotor system that the continuous increase in the excitation current induces the alternation of quasi-periodic and chaotic motions, the co-occurrence of oil whip and rub in a wide excitation range aggravates the vibration and leads to the instability of the system. In addition, the large eccentricity and radial stiffness of stator, as well as the small stiffness of shaft may lead to the occurrence of full annular rubbing while increasing the stiffness of the shaft can play an important role of suppressing the chaotic motion, reducing the vibration and improving stability of the system.     

Electrically forced shear horizontal vibration of a circular cylindrical elastic shell with a finite piezoelectric actuator

We analyze anti-plane vibrations of a circular cylindrical elastic shell electrically driven by a piezoelectric actuator. The equations of linear elasticity and linear piezoelectricity are used. The mathematical problem is solved using trigonometric series. Basic vibration characteristics including resonant frequencies, mode shapes and electric admittance are calculated.