Dynamic characterization of high damping viscoelastic materials from vibration test data

The numerical analysis and design of structural systems involving viscoelastic damping materials require knowledge of material properties and proper mathematical models. A new inverse method for the dynamic characterization of high damping and strong frequency-dependent viscoelastic materials from vibration test data measured by forced vibration tests with resonance is presented. Classical material parameter extraction methods are reviewed; their accuracy for characterizing high damping materials is discussed; and the bases of the new analysis method are detailed. The proposed inverse method minimizes the residue between the experimental and theoretical dynamic response at certain discrete frequencies selected by the user in order to identify the parameters of the material constitutive model. Thus, the material properties are identified in the whole bandwidth under study and not just at resonances. Moreover, the use of control frequencies makes the method insensitive to experimental noise and the efficiency is notably enhanced. Therefore, the number of tests required is drastically reduced and the overall process is carried out faster and more accurately. The effectiveness of the proposed method is demonstrated with the characterization of a CLD (constrained layer damping) cantilever beam. First, the elastic properties of the constraining layers are identified from the dynamic response of a metallic cantilever beam. Then, the viscoelastic properties of the core, represented by a four-parameter fractional derivative model, are identified from the dynamic response of a CLD cantilever beam.     

黏弹细棒中直达波提取及其动态力学参数的宽频测试

黏弹性材料的动态力学参数可通过对材料样品中纵波测试并结合波速法计算得到。由于测试样品尺寸的限制,除了高损耗材料在高频范围外,不管是在样品端头或侧面都难以获得准确的直达波信号,导致参数测量不准确。针对这个问题,对一端固定一端自由的黏弹性细棒中的纵波传播过程进行了分析,提出了黏弹性细棒直达波提取的方法,并实现了黏弹性材料动态力学参数的宽频测试。采用宽带脉冲作为测试激励信号,利用两台激光测振仪对细棒的固定端和自由端的振动速度进行测试,计算得到细棒自由端处的直达波。然后,利用提取出的直达波信号进行波速法计算,得到了黏弹性细棒宽频范围内的储能模量和损耗因子,宽频脉冲测试结果与黏弹仪测试结果相吻合,验证了该方法的有效性。基于直达波提取的宽频测试方法不仅效率高,而且可以使波速法应用于更低的频段。      

冲击动力学研究中实测波信息的解读分析

分析了多点测量技术在解读和分析实测冲击波信息时的重要性和难点,提出了将Lagrange多点测量反分析与Hopkinson压杆技术相结合的新方法,解决了在同一个Lagrange位置上难以同时测量应力和质点速度波形的难题,对试样上不同Lagrange位置处实测质点速度波形进行了解读分析,由n个实测质点速度波形信息得到了各Lagrange位置处的动态应力-应变关系。以有机玻璃和水泥砂浆两种粘弹性试样为例,进行了数值计算,验证了该方法的可行性和有效性。     

Drag reduction by compliant coatings made of a homogeneous material

The possibility of drag reduction due to compliant coatings of viscoelastic silicone rubbers has been tested experimentally. For this purpose, a series of single-layer coatings of various thicknesses was made of a homogeneous material. The experiments were carried out in a high-speed cavitation tunnel of Pusan National University. Dynamic viscoelastic properties of coating materials were carefully measured. The range of flow rates and coating thicknesses was calculated assuming that the coatings can interact intensively with the dynamic structures of the turbulent boundary layer only in the region of frequencies of their maximum compliance. The predicted range of coating parameters and flow velocities, in which the coatings reduce drag, is compared with experimental data.     

Determination of elastic modulus of a beam by using electronic speckle pattern interferometry

This paper proposes a sonic resonance test for an elastic modulus measurement which is based on the electronic speckle pattern interferometry. Previous measurement technique of elastic constant has the limitation of application for thin film or polymer material because contact to specimen affects the result. It has been developed as a non-contact optical measurement technique which can visualize resonance vibration mode shapes with whole field. The maximum vibration amplitude at each vibration mode shape is a clue to find the resonance frequencies. The dynamic elastic constant of test material can be easily determined from vibration of a beam equation using the measured resonance frequencies. The proposed technique is able to give high accurate elastic modulus of materials through a simple experimental set-up and analysis. The experimental result also compared to the theoretical result.     

Ultrasonic interferometry for the measurement of shear velocity and attenuation in viscoelastic solids

A method for the measurement of the shear properties of solid viscoelastic materials is presented. The viscoelastic material is cut into a cylindrical sample which is clamped between two rods. The transmission and reflection coefficient spectra of the fundamental torsional mode through the sample are measured by means of two pairs of piezoelectric transducers placed at the free ends of the rod-sample-rod system. Such spectra exhibit maxima and minima which occur approximately at the resonance frequencies of the free viscoelastic cylinder. Therefore, the shear velocity can be obtained by measuring the frequency interval between two consecutive maxima or minima. The shear attenuation is derived by best fitting the analytical expression of the reflection and transmission coefficients to the experimental spectra. The test is very quick to set up as the sample is simply clamped between the two rods.     

Measurement of dynamic properties of viscoelastic materials

A new method for measurement of viscoelastic properties of materials, based on the exact solution of the problem of the forced oscillations of a flat sample loaded by inertial mass, is proposed. The device for these measurements is described. The elasticity modulus and loss tangent are measured within the frequency range from 100 Hz to 10 kHz at relative deformation of a sample below 1%. The approximate formulas for calculation of viscoelastic properties are derived, and the conditions of their applicability are determined. The methods for expansion of the frequency range and measurement of materials with extremely high loss tangent are proposed. The proposed method is compared with the current Standard. It is shown that the new method has the higher accuracy and expanded range of parameter measurements, and the construction of device is easy and reliable, since it does not require the knowledge on the oscillation properties of vibration source. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 06-08-00193-a).     

Transfer function method for investigating the complex modulus of acoustic materials: Rod-like specimen

The complex Young's modulus of acoustic materials as a function of frequency is generally investigated by using a cylindrical or prismatic specimen of the material excited into longitudinal harmonic vibration at one end, the other end being loaded by a mass. The transfer function method is the most advantageous to use for the investigation, which involves the measurement of the vibration amplitudes of the specimen ends and the phase angle between them. In this paper, the transfer function method is analyzed theoretically and experimentally in that frequency range where the specimen can essentially be modelled by a longitudinally vibrating rod (rod-like specimen). The analysis includes the measurability of the transfer function, the role of the measurement errors, the frequency range of the method and the maximum dynamic strain of the specimen. A special application of the method is developed for investigating the complex modulus of low loss materials at the extremes of the absolute value of the transfer function, without measuring the phase angle. Experimental results obtained by both methods are presented.     

Stability of flat plate boundary layer over monolithic viscoelastic coatings

It is well known that compliant coatings of a wetted surface can affect the stability of hydrodynamic flows. The mechanism of this influence is related to viscoelastic properties of the coatings particularly to their reaction on the disturbing impact. However, the majority of corresponding studies are devoted to investigation of the effect of soft compliant coatings which are unpractical. Moreover, up to now only model computations of flow stability over the compliant coatings have been performed, as experimental data on viscoelastic properties (the modulus of elasticity E characterizing the elastic features, and the loss tangent ?? characterizing the viscous or damping features) as functions of frequency for the coatings promising from the point of view of their practical application have been absent. Such data were obtained only last years for some materials (silicon rubbers) in a series of studies [1?C3]. The coatings are prospective first of all because of their adequate stiffness (about 1 MPa). In the present paper, results of computations of boundary layer stability performed for the first time for the flow developed over compliant coatings with real properties.     

Vibration and dynamic stability of a traveling sandwich beam

The vibration and dynamic stability of a traveling sandwich beam are studied using the finite element method. The damping layer is assumed to be linear viscoelastic and almost incompressible. The extensional and shear moduli of the viscoelastic material are characterized by complex quantities. Complex-eigenvalue problems are solved by the state-space method, and the natural frequencies and modal loss factors of the composite beam are extracted. The effects of stiffness and thickness ratio of the viscoelastic and constrained layers on natural frequencies and modal loss factors are reported. Tension fluctuations are the dominant source of excitation in a traveling sandwich material, and the regions of dynamic instability are determined by modified Bolotin's method. Numerical results show that the constrained damping layer stabilizes the traveling sandwich beam.     

Vibrations of three layered damped sandwich plate composites

Theoretical and experimental results are presented and discussed for the transverse driving point mechanical impedances, as well as for the transfer impedances, of damped composite plates made up of a thin viscoelastic layer sandwiched between two elastic layers. Analytical results are determined by finite element approximations. Due to the elements used and the system to be modeled, several fundamental assumptions or restrictions usually adopted in analytical investigations are removed. The dependence on frequency and temperature of the dynamic properties of the viscoelastic materials is taken into consideration. A companion experiment was conducted, for comparison purposes, on such damped composite plates suspended in air by lightweight elastic shock cords and driven at the center by an electromechanical vibration shaker. Good correlations between the test data and analytical solutions are obtained over a wide frequency range for two configurations.     

Energy and phase velocity considerations required for attenuation and velocity measurements of anisotropic composites

Viscoelastic fibre-reinforced composite materials have a number of possible advantages for use in underwater acoustic applications. In order to exploit these materials it is important to be able to measure their complex stiffness matrix in order to determine their acoustic response. Ultrasonic transmission measurements on parallel-sided samples, employing broadband pulsed transducers at 2.25 MHz and an immersion method, have been used to determine the viscoelastic properties of a glass-reinforced composite with uniaxially aligned fibres. The composite measured was constructed from Cytecfiberite's CYCOM 919 E-glass. The theory of acoustic propagation in anisotropic materials shows that the direction of energy propagation is, in general, different from that given by Snell's Law. At 15 degrees incidence, Snell's Law implies a refracted angle of 40 +/- 2 degrees, whereas the energy direction is observed to be 70 +/- 2 degrees. Despite this, the experimental data indicates that the position of the receiving transducer has relatively little effect on the apparent phase velocity measured. The phase velocities measured at positions determined from the refracted angle and energy direction are 3647 and 3652 +/- 50 m s(-1), respectively. However, the amplitude of the received signal, and hence estimate of attenuation, is highly sensitive to the receiver position. This indicates that the acoustic Poynting vector must be considered in order to precisely determine the correct position of the receiving transducer for attenuation measurements. The beam displacement for a 17.6 mm sample at 15 degrees incidence is 9.5 and 40 mm by Snell's Law and Poynting's Theorem, respectively. Measured beam displacements have been compared with predictions derived from material stiffness coefficients. These considerations are important in recovering the complex stiffness matrix.     

Analytical model for nanoscale viscoelastic properties characterization using dynamic nanoindentation

In the last few decades, nanoindentation has gained widespread acceptance as a technique for materials properties characterization at micron and submicron length scales. Accurate and precise characterization of material properties with a nanoindenter is critically dependent on the ability to correctly model the response of the test equipment in contact with the material. In dynamic nanoindention analysis, a simple Kelvin–Voigt model is commonly used to capture the viscoelastic response. However, this model oversimplifies the response of real viscoelastic materials such as polymers. A model is developed that captures the dynamic nanoindentation response of a viscoelastic material. Indenter tip-sample contact forces are modelled using a generalized Maxwell model. The results on a silicon elastomer were analysed using conventional two element Kelvin–Voigt model and contrasted to analysis done using the Maxwell model. The results show that conventional Kelvin–Voigt model overestimates the storage modulus of the silicone elastomer by ~30%. Maxwell model represents a significant improvement in capturing the viscoelastic material behaviour over the Voigt model.     

Shells on nanowires detected by analytical TEM

Nanostructures in the form of nanowires or filled nanotubes and nanoparticles covered by shells are of great interest in materials science. They allow the creation of new materials with tailored new properties. For the characterisation of these structures and their shells by means of analytical transmission electron microscopy (TEM), especially by energy dispersive X-ray spectroscopy (EDXS), and electron energy loss spectroscopy (EELS), the accurate analysis of linescan intensity profiles is necessary. A mathematical model is described, which is suitable for this analysis. It considers the finite electron beam size, the beam convergence, and the beam broadening within the specimen. It is shown that the beam size influences the measured result of core radius and shell thickness. On the other hand, the influence of the beam broadening within the specimen is negligible. At EELS, the specimen thickness must be smaller than the mean free path for inelastic scattering. Otherwise, artifacts of the signal profile of a nanowire can pretend a nanotube.     

黏弹性材料的动态力学特性及其对覆盖层吸声性能的影响

本文利用标准化动态力学测量手段获得了某种高分子聚合物的动态杨氏模量,并根据时温等效原理对动态杨氏模量与声学测量在频段上的差异加以分析和转换,得到了500—7500 Hz频率范围内该黏弹性材料杨氏模量随频率变化的特性.基于所测得动态杨氏模量,采用有限元方法分析了均匀黏弹材料的吸声性能,并将仿真结果与样品声管实验数据进行对比,验证了测试所得参数的准确性.进一步仿真分析了含有局域共振结构的声学覆盖层吸声性能,并讨论了黏弹性材料的动态特性对其吸声性能的影响,提出了改进水声覆盖层低频宽带吸声特性的建议.     

Dynamic viscoelastic effects on sound wave scattering by an eccentric compound circular cylinder

The classical method of separation of variables in conjunction with the translational addition theorem for cylindrical wave functions are employed to obtain an exact solution for two-dimensional interaction of a harmonic plane acoustic wave with an infinitely long (visco)elastic circular cylinder which is eccentrically coated by another (visco)elastic material and is submerged in an ideal unbounded acoustic medium. The novel features of Havriliak-Negami model for dynamic viscoelastic material behaviour are used to take the rheological properties of the coating (and/or core) material into consideration. The analytical results are illustrated with numerical examples in which a steel rod eccentrically coated with (an eccentric steel shell filled with) dissipative materials of distinct viscoelastic properties is insonified by plane sound waves at selected angles of incidence. The effects of incident wave frequency, angle of incidence, core eccentricity and dynamic viscoelastic material properties on the backscattered form function spectra are examined. Limiting cases are considered and fair agreements with available solutions are obtained.     

黏弹材料动力学参数的宽频测试

利用改进的波速法,对黏弹性材料连续宽频范围的动力学参数进行测试。利用有限元方法,对波速法的测试过程进行了仿真,验证了利用长短棒波速法测量宽频动力学参数的有效性。采用可控脉冲生成技术,在激振器上产生了用于宽频测试的短脉冲信号。黏弹性长短棒在上述宽带短脉冲激励下作纵向强迫振动,利用激光测振仪测量长短两棒自由端的纵向振动速度,从而可得两振动信号在连续宽频范围的幅值比和相位差,进而可根据波速法原理计算得到材料在连续宽频范围的储能模量和损耗因子。测试结果表明,该系统通过较少次数测试,可直接计算得到1~5 kHz连续宽频范围的动力学参数,测试结果与黏弹仪数据吻合。通过对幅值比和相位差进行线性最小二乘拟合,可以进一步拓展测量的频率范围。该方法准确可靠、简便快速,具有实际应用价值。      

Transfer function method for investigating the complex modulus of acoustic materials: Spring-like specimen

The complex modulus of acoustic materials has to be known as a function of frequency. Among many methods for investigating the complex modulus, it is advantageous to use the transfer function method for detailed frequency analysis. In this method, a cylindrical or prismatic specimen is excited into longitudinal vibration at one end, the other end being loaded by a mass. The complex modulus can be calculated after having measured the transfer function: i.e., the vibration amplitudes of the specimen ends and the phase angle between them. In this paper the transfer function and its measurability are investigated theoretically and experimentally in that frequency range where the specimen can essentially be modelled by lumped parameter mechanical elements. The role of the measurement errors is analyzed and it is shown that the smaller the loss factor the higher the measurement accuracy that is needed. Furthermore, it is shown that disregarding the longitudinal wave motion of the specimen at higher frequencies leads to an apparent increase of the dynamic modulus and to an apparent decreases of the loss factor. This effect may be compensated up to a certain frequency by the lateral wave motion of the specimen. Experimental results supporting the theoretical predictions are presented.     

A finite element model for sandwich viscoelastic beams: Experimental and numerical assessment

Among the passive control systems for attenuation of vibrations in structures, those that use viscoelastic materials as a damping core in laminated-plate-like components are focused herein. In the present work an assessment of a time-domain formulation for numerical modelling of viscoelastic materials is made. This formulation, which is called Golla–Hughes method (GHM), is based on a second-order time-domain realization of Laplace-domain motion equations. The GHM parameters used in the characterization of a viscoelastic material are experimentally determined and a sandwich GHM-based finite element model is presented and validated through numerical comparisons with classic formulation results. Finally, a time-domain simulation of an experimentally tested sandwich beam is carried out.     

Determination of the complex Young and shear dynamic moduli of viscoelastic materials

The Young and shear dynamic moduli of viscoelastic materials are determined from laser vibrometric measurements of the surface motion of a three-dimensional sample excited by a piezoelectric actuator inside a chamber with controllable temperature and static pressure. The moduli are estimated from an inversion code that minimizes the difference between the data and the predictions from a finite element model in which the elastic moduli are the adjustable parameters. The technique is first used to measure the dynamic properties of homogeneous samples and the results are compared with those obtained by the standard rod resonance technique. Results are then obtained with microvoided samples in the 0.5-3 kHz frequency range, at temperatures ranging from 7 to 40 degrees C, and static pressures ranging from ambient to 34 atm (3.45 MPa or 500 psi). The limitations of the technique are discussed.