主动约束层阻尼梁的数值模型

为对主动约束层阻尼结构建立精确完善的数学模型，采用有限元建模，并考虑到压电材料的机电耦合效应和粘弹性材料的本构关系随温度、频率的变化而变化的特点，将有限元方法与粘弹性材料的GHA模型相结合，从而避免因粘弹性材料导致的非线性微分方程，能直接求解模态频率、模态阻尼及结构响应。为进一步设计控制器，先在物理空间进行动力缩聚，将系统降至适当的维数，然后在状态空间用鲁棒防阶的方法进一步降阶。这样既能大大降低系统维数，又能保证降阶后系统稳定、可控、可观。这对于重量轻、柔度大、低频密集的大型空间柔性结构尤其重要。     

Nonlinear flexural vibration of moderately thick orthotropic circular plates

Summary In this paper a nonlinear vibration theory which includes the effects of transverse shear deformation and rotatory inertia is formulated for rectilinearly orthotropic circular plates using Berger's method. A solution to the governing equations for rigidly clamped plates is obtained on the basis of a single-mode approach by use of Galerkin's method and numerical Runge-Kutta procedure. A good agreement is found between present results and those obtained by a more accurate theory for nonlinear static and dynamic cases. Numerical results indicate significant influence of these effects on the vibration behaviour of moderately thick plates, especially high-modulus composite plates. These effects, however, are not so significant for the radius-to-thickness ratio greater than 10.

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Nichtlineare Schwingungen orthotroper Kreisplatten

Übersicht Eine Theorie nichtlinearer Schwingungen orthotroper Kreisplatten wird mit der Methode von Berger formuliert, wobei Schubverformung und Drehträgheit berücksichtigt werden. Für eingespannte Platten wird mit dem Verfahren von Galerkin eine numerische Lösung bestimmt und mit bekannten Lösungen verglichen. Die numerischen Ergebnisse zeigen, daß der Einfluß von Schubverformung und Drehträgheit bei mäßig dicken Platten beträchtlich sein kann.

     

On the flexural vibration frequencies of statically loaded beams

Summary The problem of vibrations of structures with heavy static loads is a non linear one, and, as such, of difficult solution in its general formulation.A method applicable to undamped structures free from external dynamic actions is proposed: it allows simple linearization on the assumption of elastic behaviour (Hooke's law) and of small oscillations.The problem solution, given in matrix form, is compared with both theoretical and experimental data, showing the high degree of accuracy thus obtainable.Some general conclusions on the influence of different kinds of static load distributions on these dynamic phenomena are also presented.

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Sommario Il problema delle vibrazioni di strutture sollecitate da elevati carichi statici è, nella formulazione generale, non lineare, e, pertanto di complessa soluzione.Si propone qui un metodo che, applicato alle strutture prive di resistenza e di azioni dinamiche esterne, consente una semplice linearizzazione nella sola ipotesi di comportamento elastico (legge di Hooke) e di piccole oscillazioni.La soluzione del problema, ottenuta per via matriciale, è confrontata a livello teorico e sperimentale, dimostrando l'elevata approssimazione ottenibile.Vengono infine presentate alcune conclusioni di carattere generale sull'influenza nel fenomeno dinamico dei diversi tipi di sollecitazioni statiche.

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Research sponsored by C.N.R.     

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping (PCLD) are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders’ thin shell theory. Numerical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.     

Spectral strip-element method for beams treated with active constrained layer damping

For vibration analysis of beams fully treated with active constrained layer damping (ACLD), a new approach called spectral strip-element method (SSEM) based on the spectral finite element method (SFEM) is proposed. It can avoid difficulties in solving the characteristic equation with higher orders and unknown parameters for wave numbers when using the SFEM; simultaneously, advantages of a very few elements and high accuracy of the SFEM are kept. A numerical example shows that the proposed method is very effective and reliable, compared with the exact solutions resulted from the spectral transfer matrix method (STMM).     

A new method for measuring damping in flexural vibration of thin fibers

In this paper we describe a new method for measuring damping in flexural vibration of filamentous matter, such as polymeric or metallic fibers. This method enables us to measure the damping characteristics of very thin fibers (down to lateral dimensions of a few micrometers). The fiber sample is clamped at one extremity and excited in the flexural vibration mode of a cantilever beam configuration, using a piezoelectric actuator. While the fiber sample vibrates around a flexural eigenfrequency, structural damping is determined from the measurement of the curve of phase difference between excitation and motion. This technique does not require the amplitude of the fiber motion to be determined. The phase curve is inferred from the periodic disturbance occurring when the fiber acts as a shutter for a light beam. This method can be applied to fibers of arbitrary shape and material. Examples are shown of measurements with polymer and metallic fibers. Flexural damping is evaluated at atmospheric pressure and in vacuum. The technique is validated by a comparison with polypropylene damping measurements from standard dynamic mechanical thermal analysis techniques.     

On the number of cells for flexural vibration suppression in periodic beams

Meccanica - Vibration suppression is an important topic for many engineering applications. There are different techniques, typically involving passive and active controllers. However, it can...     

On the size-dependent flexural vibration characteristics of unbalanced couple stress-based micro-spinning beams

On the basis of the modified couple stress theory, some analytical results are obtained for vibrational parameters of micro-spinning Rayleigh beams with an axial mass-eccentricity distribution. The modified couple stress theory is a nonclassical continuum theory capable to capture the size effects in small-scale structures. After writing the governing equations of motion, they are transformed to the complex form. Then by utilizing the Galerkin method, analytical expressions for natural frequencies of the micro-spinning beam in forward and backward whirl motions are obtained. Critical speeds are also analytically presented in the two whirl motions for different modes. Moreover, the vibrational amplitude of the micro-spinning beam with axial mass eccentricity distribution is determined. Some numerical results are presented to study the effect of the length scale parameter on the vibrational characteristics.     

The hybrid control of vibration of thin plate with active constrained damping layer

This paper concerns in the active and passive hybrid control of vibration of the thin plate with Local Active Constrained damping Layer (LACL). The governing equations of system are formulated based on the constitutive equations of elastic, viscoelastic, piezoelectric materials. Galerkin method and GHM method are employed to transform partial differential equations into ordinary ones with a lower dimension. LQR method of classical control theory is used in simulating calculation. Numeral results show that the active and passive hybrid control manner obtained in this paper is a better one for vibration control of the plate. Project supported by the National Science Foundation of China (19632001) and the Research Foundation of Xian Jiaotong University     

Continuum modelling of piezoelectromechanical truss beams: an application to vibration damping

Summary We call piezoelectromechanical (PEM) truss beam a truss modular beam coupled with a transmission electrical line when the coupling is obtained by piezoelectric actuators which act as bars in the module and as capacitances in the electrical line. The truss module length is assumed negligible with respect to the considered wave lengths. The transmission electrical line is assumed continuously distributed along the truss beam. Applying the method of virtual power as expounded in [2] we formulate a continuum model for PEM truss beams and we prove that there exists a critical value for the transmission electrical impedance in the neighborhood of which the electromechanical modal coupling is maximum and the possible electrical dissipation of mechanical energy is relevant. Accepted for publication 1 June 1997     

Analysis of frequency-domain vibration response of thin plate attached with viscoelastic free layer damping

To predict the vibration response of viscoelastic composite structure, two key issues need to be conducted, one is introducing the constitutive model of viscoelastic material into the analysis model and the other is describing the real damping behavior of viscoelastic composite structure. The emphasis of this study is to obtain the effects of frequency dependence on the vibration response of viscoelastic composite structure and the method of introducing two kinds of damping (viscoelastic material damping and remaining equivalent viscous damping). Vibration response analysis in frequency domain was investigated for viscoelastically damped plate. A cantilever plate attached with the ZN_1 viscoelastic free layer damping (FLD) was chosen to demonstrate the developed method. Frequency-domain response of the composite plate were solved and the obtained results were compared with the experimental values for the purpose of assessing the rationality of the proposed method. In addition, in order to obtain the effects of viscoelastic material parameters on vibration response of viscoelastic composite structure, a detailed parametric analysis was performed. This study shows that the frequency dependent characteristic of viscoelastic material has significant influence on the vibration response in the resonant region and acceptable results can be achieved in the non-resonant region if frequency dependent parameters are substituted by average values of the viscoelastic parameters reasonably in the analysis process.     

局部约束阻尼开口柱壳的减振分析及优化

为了缩减开口柱壳结构的振动,本文基于Lagrange方程以及Sanders薄壳理论建立了局部约束阻尼开口柱壳的动力学模型,分析了粘弹性单元分段数和厚度、阻尼单元占空比以及约束层敷设角和厚度对结构前三阶模态损耗因子和固有频率的影响,得到了各参数对结构振动特性的影响规律.并以前三阶损耗因子为目标,应用NSGA-Ⅱ遗传算法对...     

Moderately large flexural vibrations of composite plates with thick layers

In this paper moderately large amplitude vibrations of a polygonally shaped composite plate with thick layers are analyzed. Three homogeneous and isotropic layers with a common Poisson’s ratio are perfectly bonded and their arbitrary thickness and material properties are symmetrically disposed about the middle plane. Mindlin–Reissner kinematic assumptions are implemented layerwise, and as such model both the global and local response. Geometric nonlinear effects arising from longitudinally constrained supports are taken into account by Berger’s approximation of nonlinear strain–displacement relations. Overall cross-sectional rotations are defined and subsequently a correspondence of this complex problem to the simpler case of a homogenized shear-deformable nonlinear plate with effective stiffness and hard hinged boundary conditions is found. The nonlinear steady-state response of composite plates subjected to a time-harmonic lateral excitation is investigated and the phenomena of nonlinear resonance are studied and evaluated.     

Effect of debonding in active constrained layer damping patches on hybrid control of smart beams

A new model for a smart beam with a partially debonded active constrained layer damping (ACLD) patch is presented, and the effects of the debonding of the ACLD patch on both passive and hybrid control are investigated. In this model, both shear and compressional vibrations of the viscoelastic material (VEM) layer are considered. The moment inertia and the transverse shear effect are also taken into account based on the Timoshenko’s beam theory. The adhesive layer between the host beam and the piezoelectric sensor patch is modeled as an elastic load transferring media. The debonding of the ACLD patch is approximated by removing the VEM between the constraining layer and the host beam in the debonding region, and the continuity conditions are imposed based on displacement continuity and force balance. A modal velocity observer-based modal control scheme is also given to perform the active modal control of the beam. In order to examine the effects of part debonding of the ACLD patch, the characteristic equation of the beam treated with an ACLD patch is derived. The simulation example results show that an edge debonding of the ACLD patch can significantly affect both passive and hybrid control. It is also found that the additional mode induced by the debonding has unique effects on the modal damping ratios and frequencies of both open-loop and closed-loop system.     

On the modal equations of large amplitude flexural vibration of beams,plates, rings and shells

In a simple and straight forward manner the modal equations applicable for the large amplitude flexural vibrations of plates and shells are obtained by the Lagrange's method. These equations can easily be specialised to obtain the corresponding equations applicable for beams and rings. The basic nature of the modal equations for beams and plates on the one hand and rings and shells on the other hand are shown to exhibit hard and soft spring characteristics, respectively.     

Effects of compressive load and support damping on the propagation of flexural waves in beams resting on elastic foundation

The contributions of compressive load and support damping are included into the formulation of flexural wave motion in beams lying on elastic (Winkler) foundation. The beam is modeled by both Euler–Bernoulli’s and Timoshenko’s theories. First, dispersion analysis is performed, which reveals that, for a fixed wavenumber, phase velocity decreases as the intensity of the compressive force or the value of the support damping is increased. Secondly, the transverse displacement of a semi-infinite beam excited by a velocity step pulse at its finite end is examined in the transient regime by adopting Laplace transform approach. This latter study sustains the validity of the dispersion analysis outcomes and shows that compressive load and support damping cause an amplification and a diminution, respectively, of the displacement amplitudes at the various positions of the beam.     

On flexural vibration of hemispherical shell

This paper makes detailed analyses for the flexural vibration(frequency)of the hemispherical shell and presents the varying laws of frequency with the varying boundary angles and the wall thickness of the above shell.It is an important value to develop the instrument,such as hemispherical resonator gyro(HRG),whose sensing component is a hemispherical shell.     

Damage detection method in complicated beams with varying flexural stiffness

A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method (SSEM), and its applicability condition is introduced. For a beam with the continuously varying flexural stiffness and an edge crack, the SSEM is used to detect the crack location effectively by numerical modal shapes. As a complicated beam, the glass fiber-reinforced composite model of a wind turbine blade is studied based on an experimental modal analysis. The SSEM is used to calculate the damage index from the measured modal parameters and locate the damage position in the blade model successfully. The results indicate that the SSEM based on the modal shapes can be used to detect the damages in complicated beams or beam-like structures for engineering applications.     

State-vector equation with damping and vibration analysis of laminates

Based on the modified mixed Hellinger-Reissner(H-R)variational principle for elastic bodies with damping,the state-vector equation with parameters is directionally derived from the principle.A new solution for the harmonic vibration of simply supported rectangular laminates with damping is proposed by using the precise integration method and Muller method.The general solutions for the free vibration of underdamping,critical damp and overdamping of composite laminates are given simply in terms of the linear damping vibration theory.The effect of viscous damping force on the vibration of com- posite laminates is investigated through numerical examples.The state-vector equation theory and its application areas are extended.