Experimental analysis of the linear and nonlinear behaviour of composites with delaminations

An analysis of the linear and nonlinear vibration responses of composites with delaminations is presented. The effect of delamination size on the linear and nonlinear vibration response is studied. The composite material used in this paper is a glass fibre reinforced plastic (GFRP) having delaminations at the plies interfaces. The experimental procedure consists in inducing the specimen on its resonance flexural modes with different excitation levels (amplitudes) for six bending modes and for each delamination length. The presence of the nonlinearity introduced by the delamination was clearly identified by the variation of natural frequencies for increasing excitation levels. Then, nonlinear elastic parameters for progressive delamination length were determined and discussed for the first six bending modes. The linear and the nonlinear elastic parameters were compared in their sensitive modes.     

Large-amplitude nonlinear vibrations of a Mooney–Rivlin rectangular membrane

An analysis of the linear and nonlinear vibration response and stability of a pre-stretched hyperelastic rectangular membrane under harmonic lateral pressure and finite initial deformations is presented in this paper. Geometric nonlinearity due to finite deformations and material nonlinearity associated with the hyperelastic constitutive law are taken into account. The membrane is assumed to be made of an isotropic, homogeneous, and incompressible Mooney–Rivlin material. The results for a neo-Hookean material are obtained as a particular case and a comparison of these two constitutive models is carried out. First, the exact solution of the membrane under a biaxial stretch is obtained, being this initial stress state responsible for the membrane stiffness. The equations of motion of the pre-stretched membrane are then derived. From the linearized equations, the natural frequencies and mode shapes of the membrane are analytically obtained for both materials. The natural modes are then used to approximate the nonlinear deformation field using the Galerkin method. A detailed parametric analysis shows the strong influence of the stretching ratios and material parameters on the linear and nonlinear oscillations of the membrane. Frequency–amplitude relations, resonance curves, and bifurcation diagrams, are used to illustrate the nonlinear dynamics of the membrane. The present results are compared favorably with the results evaluated for the same membrane using a nonlinear finite element formulation.     

Multi-mode nonlinear resonance ultrasound spectroscopy for defect imaging: an analytical approach for the one-dimensional case

A nonlinear version of the resonance ultrasound spectroscopy (RUS) theory is presented as an extension of the RUS formalism to the treatment of microdamage characterized by nonlinear constitutive equations. General analytical equations are derived for the one-dimensional case, describing the excitation amplitude dependent shift in the resonance frequency and the generation of harmonics resulting from the interaction between bar modes due to the presence of either localized or volumetrically distributed nonlinearity. Solutions are obtained for classical cubic nonlinearity, as well as for the more interesting case of hysteresis nonlinearity. The analytical results are in excellent quantitative agreement with numerical calculations from a multiscale model. Finally, the analytical formulas are exploited to infer critical information about damage position, degree of nonlinearity, and width of the damage zone either from the shifts in resonance frequency occurring at different excitation modes, or from the shift and the harmonics predicted at a single mode. Unlike other techniques, the multi-mode-nonlinear RUS method does not require a spatial scan to locate the defect, as it lets different excitation modes, with different vibration patterns, probe the structure. Two general methods are suggested for inverting experimental data.     

Resonance frequency response of geometrically nonlinear micro-switches under electrical actuation

This paper presents an analytical study on the forced vibration of electrically actuated micro-switches near resonance region, taking into consideration the intermolecular force, axial residual stress, and geometrical nonlinearity due to mid-plane stretching. The micro-switch is made of either homogeneous material or non-homogeneous functionally graded materials with two material phases and subjected to a time-varying applied voltage consisting of a DC component and a small AC component. The perturbation-based method of averaging is employed to solve the nonlinear partial differential governing equations to obtain the resonance frequency responses of both the vibration amplitude and phase angle. The present analysis is validated through direct comparisons with published experimental results and excellent agreement has been achieved. A parametric study is conducted to show the effects of geometrical nonlinearity, intermolecular Casimir force, the electrostatic force due to DC voltage, the AC voltage induced harmonic force, quality factor, axial residual stress and material composition on the frequency response characteristics.     

Experimental study of nonlinear acoustical effects in limestone

Results of an experimental and theoretical study of nonlinear acoustic effects (amplitude-dependent loss, resonance frequency shift, second and third harmonic generation, and sound by sound damping) in a limestone bar resonator are reported. The observed effects are analytically described in the framework of phenomenological equations of state with allowance for the low-frequency hysteretic nonlinearity and the high-frequency dissipative nonlinearity. Experimental and analytical dependences of nonlinear effects are compared to find the parameters of the hysteretic and dissipative nonlinearities of the limestone sample studied.     

Experimental investigations of nonlinear acoustic phenomena in polycrystalline zinc

The results of experimental and theoretical investigations of nonlinear acoustic phenomena (nonlinear losses, shift of resonance frequency, generation of the third harmonic, and nonlinear sound-by-sound damping) in polycrystalline zinc nonannealed and annealed resonating rods are presented. The measurements were carried out in the 10(-7)-10(-5) strain range at a frequency of about 3 kHz; the frequency of the weak ultrasonic pulse was about 270 kHz. The experimentally observed phenomena are described in frames of phenomenological equations of state containing elastic hysteresis and dissipative nonlinearity. The nonlinear acoustic parameters of these equations are determined by comparison between theoretical dependencies and experimental results. The influence of structural changes in zinc due to annealing on the nonlinear acoustic phenomena is shown.     

考虑弯曲和轴向振动模态的一维梁压电阻抗模型及试验研究

同时考虑一维梁结构的弯曲和轴向振动,对其压电阻抗模型进行建模分析和试验验证。在0.02～42 kHz频段内区分并标记了一维钢梁弯曲振动模态前18阶及轴向振动模态前3阶。结果表明:在0.02～7.5kHz频段内,数值计算和试验结果中谐振峰对应频率的相对误差较大:11.7%～16.5%,其原因可能是低频时振动能量较低且波的传播受结构阻尼、边界条件及环境噪音等因素影响较为明显;在7.5～42kHz范围内,两者谐振峰位置符合良好,相对误差较小:0.11%～2.31%,表明该模型在高频段具有较好的适用性;轴向振动模态对应频率大于弯曲振动模态。本研究为结构健康监测过程中检测频段的选取及损伤信息的提取提供参考。     

Properties of cementitious composites containing polypropylene fiber waste

The carpet waste fibers and waste glass that create a serious environmental problem can be converted into useful products. The use of these waste materials in a cement-based composite can be a promising direction for waste reduction and resources conservation. In this study, several tests have been carried out to investigate the performance of control mortar using recycled glass and fibers as a fraction of aggregates in a cement-based composite. These tests included compressive strength, flexural strength, flexural toughness and water absorption. The results revealed that carpet waste fiber and waste glass could be reused as substitutes for conventional materials in cement-based composites.     

The influence of localized damage in a sample on its resonance spectrum

A nonlinear version of resonance ultrasound spectroscopy (RUS) theory is presented. This is important for NDT-purposes as damage manifests itself more pronounced and in an earlier stage by changes in the nonlinear elastic constants. General equations are derived for the 1-D case, describing the interaction between the modes due to the presence of nonlinearity. An analytical solution of these equations is derived which predicts the shift of the resonance frequency versus amplitude in a bar with localized damage. The damage was modelled as a finite region, having a constant cubic nonlinearity, in an otherwise linear 1-D bar. The analytical expressions for the shifts in resonance frequency at different modes were used to infer information about the position, nonlinearity and width of the damage. Unlike other techniques, the proposed method does not require scanning to locate the defect, as it lets the different modes, each with a different vibration pattern, probe the structure.     

High-accuracy acoustic detection of nonclassical component of material nonlinearity

The aim is to assess the nonclassical component of material nonlinearity in several classes of materials with weak, intermediate, and high nonlinear properties. In this contribution, an optimized nonlinear resonant ultrasound spectroscopy (NRUS) measuring and data processing protocol applied to small samples is described. The protocol is used to overcome the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic nonlinearity. External temperature fluctuation is identified as a primary source of measurement contamination. For instance, a variation of 0.1?°C produced a frequency variation of 0.01%, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to overcome environmental effects, the reference frequency measurements are repeated before each excitation level and then used to compute nonlinear parameters. Using this approach, relative resonant frequency shifts of 10(-5) can be measured, which is below the limit of 10(-4) often considered as the limit of NRUS sensitivity under common experimental conditions. Due to enhanced sensitivity resulting from the correction procedure applied in this work, nonclassical nonlinearity in materials that before have been assumed to only be classically nonlinear in past work (steel, brass, and aluminum) is reported.     

Concrete damage diagnosed by using non-classical nonlinear acoustic method

<正>It is known that the strength of concrete is seriously affected by damage and cracking.In this paper,six concrete samples under different damage levels are studied.The experimental results show a linear dependence of the resonance frequency shift on strain amplitude at the fundamental frequency,and approximate quadratic dependence of the amplitudes of the second and third harmonics on strain amplitude at the fundamental frequency as well.In addition,the amplitude of the third harmonics is shown to increase with the increase of damage level,which is even higher than that of the second harmonics in samples with higher damage levels.These are three properties of non-classical nonlinear acoustics.The nonlinear parameters increase from 10~6 to 10~8 with damage level,and are more sensitive to the damage level of the concrete than the linear parameters obtained by using traditional acoustics methods.So,this method based on non-classical nonlinear acoustics may provide a better means of non-destructive testing(NDT) of concrete and other porous materials.     

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.     

On cubic nonlinearity of cracked media

An equation of state with cubic nonlinearity has been obtained for the model of a cracked medium. It is shown that cracks in a solid can lead not only to a strong change of the cubic nonlinearity parameter but also to the sign reversal of the latter. We describe the experiment on the measurement of a nonlinear shift in the resonance frequency of a bar resonator of glass with cracks where the positive shift of the resonance frequency was observed. We estimate the effective parameter of the cubic nonlinearity for such a resonator by comparing theoretical and experimental dependences. Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 7, pp. 897–902, July. 1997.     

高温高应变率下混凝土材料的损伤演化方程

采用?74 mm大口径分离式霍普金森压杆(SHPB)对不同温度(20、200、400℃)下的C45混凝土材料进行动态力学性能实验,得到了不同温度、不同应变率下混凝土材料的应力-应变曲线。实验结果表明:在20~400℃温度范围内,混凝土材料具有温度硬化和应变率硬化现象。基于上述实验数据给出了损伤变量关于塑性应变的关系式,并通过相关实验数据确定了不同温度、不同应变率下损伤演化方程的材料参数。将该损伤演化方程应用于混凝土材料的本构关系中,预测结果与实验数据具有较好的一致性,证明了所提出的高温、高应变率下混凝土材料损伤演化方程的合理性。     

On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator

There are many systems which consist of a nonlinear oscillator attached to a linear system, examples of which are nonlinear vibration absorbers, or nonlinear systems under test using shakers excited harmonically with a constant force. This paper presents a study of the dynamic behaviour of a specific two degree-of-freedom system representing such a system, in which the nonlinear system does not affect the vibration of the forced linear system. The nonlinearity of the attachment is derived from a geometric configuration consisting of a mass suspended on two springs which are adjusted to achieve a quasi-zero stiffness characteristic with pure cubic nonlinearity. The response of the system at the frequency of excitation is found analytically by applying the method of averaging. The effects of the system parameters on the frequency-amplitude response of the relative motion are examined. It is found that closed detached resonance curves lying outside or inside the continuous path of the main resonance curve can appear as a part of the overall amplitude-frequency response. Two typical situations for the creation of the detached resonance curve inside the main resonance curve, which are dependent on the damping in the nonlinear oscillator, are discussed.     

Design of vibration isolators by exploiting the beneficial effects of stiffness and damping nonlinearities

The present study is concerned with the design of a new type of single degree of freedom (sdof) nonlinear vibration isolation system that can deal with harmonic excitations and take advantage of both spring and damping nonlinearities. For typical design requirements expressed in terms of a transmissibility envelope, the proposed design makes use of a recently developed method called the output frequency response function (OFRF) approach, which provides a direct relationship between the system output frequency response and parameters that define the system nonlinearity. Taking all output harmonics into account, a detailed step-by-step procedure is developed to systematically determine the nonlinear parameters from a small set of simulation or experimental data. Simulation studies are conducted to verify the results and demonstrate that the design can effectively achieve all the three requirements for a vibration isolation system of a low resonant peak, low high frequency transmissibility, and a large isolation range.