Approximate analytical determination of vibrodiagnostic parameters of a cracked elastic body under subharmonic resonance. Part 1. Weak resonance

The paper discusses an approximate analytical method for the calculation of vibrodiagnostic parameters of an elastic body with a closing crack, which is modeled by an elastic system with a single degree of freedom at a bilinear asymmetric characteristic of the restoring force, in the region of a weak 1/2-order subharmonic resonance. __________ Translated from Problemy Prochnosti, No. 2, pp. 26–40, March–April, 2008.     

Approximate analytical determination of vibrodiagnostic parameters of the presence of a crack in an elastic body under superharmonic resonance

We discuss an approximate analytical method for calculating the main parameter of nonlinearity of vibration of an elastic body with a closing crack, which is simulated by a single-degree-of-freedom system with an asymmetric bilinear characteristic of the restoring force, under a strong 2nd-order superharmonic resonance.     

Approximate Analytical Determination of Vibrodiagnostic Parameters of Non-Linearity of Elastic Bodies Due to the Presence of a Closing Crack. Part 1. Available and Proposed Methods of Solution

The paper discusses the available analytical methods and the results of investigation of vibrations of elastic bodies with a bilinear asymmetric characteristic of restoring force that simulates the behavior of a local discontinuity in a material in the form of a closing fatigue crack. An approximate analytical method is put forward for the determination of vibrodiagnostic parameters of the vibration process of the nonlinear system under study in the range of weak superharmonic resonances.     

Vibrodiagnostic parameters of fatigue damage in rectangular plates. Part 1. A procedure of determination of damage parameters

We describe a procedure of approximate analytical determination of fatigue damage parameters of rectangular plates. As an initial damage characteristic we apply the relative value of the plate potential-strain-energy variation due to availability of a Mode I crack, and, based on this value, we find relations for determination of the plate natural frequency variation, as well as parameters of distortion of monoharmonic oscillations in the modes of main resonance and superharmonic resonance of the 2nd order.Translated from Problemy Prochnosti, No. 6, pp. 5–16, November–December, 2004     

Approximate Analytical Determination of Vibrodiagnostic Parameters of Non-Linearity of Elastic Bodies Due to the Presence of a Closing Crack. Part 2. Determination of Diagnostic Parameters in Principal and 2-nd Order Superharmonic Resonances

Using the constitutive equations derived by the author, variously approximated analytical expressions have been obtained for the determination of principal- and superharmonic-resonance vibrodiagnostic parameters of fatigue damage in the form of a Mode I closing crack in an elastic body. The reliability of the analytical solution is assessed by comparing the calculated and the numerical solution results.     

受机械力作用金属／陶瓷功能梯度板的亚谐共振研究

研究机械力作用下金属，陶瓷功能梯度薄板1／3次亚谐共振问题。按照功能梯度薄板的非线性动力学方程，得到金属，陶瓷功能梯度薄板受横向机械力作用的非线性振动方程。应用非线性振动的多尺度法得到系统1／3次亚谐共振近似解并进行数值计算。分析阻尼、激励、几何尺寸等参数对系统1／3次亚谐共振幅频响应曲线的影响。     

球轴承变柔度1/2阶亚谐共振的滞后特性及其分岔机理

滚动轴承变柔度(varying compliance, VC)振动是转子系统不可避免的激励形式,属于轴承-转子动力学领域的基本科学问题。由于Hertzian接触非线性、间隙(轴承游隙)非线性和时变柔度参激非线性的耦合作用,系统具有显著的VC滞后共振特性,影响轴承自身乃至其支承转子系统运动的稳定性和安全性,相关问题得到持续关注。根据非线性振动基本理论,参激系统往往具有丰富的主共振、内共振、超谐、亚谐和组合共振行为。然而,相对于国内外大量有关滚动轴承VC参激主共振的研究,其他共振类型的研究甚少。基于此,该研究将针对球轴承-刚性Jeffcott转子系统VC振动亚谐共振问题展开研究。采用谐波平衡-频时转换(harmonic balance and alternating frequency/time domain, HB-AFT)方法追踪系统的VC周期运动分枝,并结合Floquet理论分析了系统亚谐共振行为的演化机制,发现系统1/2阶亚谐共振同样具有滞后跳跃行为。在此基础上,指出系统1/2阶亚谐运动包含复杂的1∶2和1∶4内共振现象,会引起球轴承不同自由度方向强烈的耦合振动。另外,研究发现在亚...     

Vibrodiagnostic parameters of fatigue damage in rectangular plates. Part 3. Through-the-thickness and surface semi-elliptical cracks

The paper addresses the analytical determination of vibrodiagnostic parameters that describe the presence of normal-rupture flat through-the-thickness and surface semi-elliptical central cracks in a rectangular homogeneous plate of constant thickness for various plate fixing conditions and vibration modes. It is shown that the most sensitive vibrodiagnostic damage parameter of a plate is the variation of the logarithmic decrement in the case of a through-the thickness crack and the second-harmonic ratio of the vibration process in superharmonic resonance in the case of a surface crack. __________ Translated from Problemy Prochnosti, No. 5, pp. 27–47, September–October, 2006.     

Improving the accuracy of determination of the elastic and inelastic characteristics of high-damping materials by resonance methods

The paper presents a brief analysis of the amplitude-frequency characteristics at a variable frequency of vibration excitation in a specimen and constant temperature and at a constant frequency of vibration excitation and variable temperature. The error of determination of the elastic and inelastic characteristics of high-damping materials is estimated by the resonance methods.Translated from Problemy Prochnosti, No. 1, pp. 144–152, January–February, 2005.     

Vibrodiagnostic parameters of fatigue damage in rectangular plates. Part 2. Straight cracks of constant depth

The paper discusses the results of analytical determination of vibrodiagnostic parameters of fatigue damage in the form of Mode I straight cracks of constant depth in a rectangular homogeneous uniform-thickness plate with various plate fastening conditions and vibration modes. It is demonstrated that, in the range of the relative crack depth up to 0.3, the parameter of distortion of vibration monoharmonicity in the 2nd-order superharmonic resonant mode is one-two orders of magnitude higher than the value of a relative change of the plates natural frequency.Translated from Problemy Prochnosti, No. 1, pp. 43–59, January–February, 2005.     

On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 1. analytical approach

We consider a perfectly elastic cantilever beam with a crack. The influence of the crack depth and location on the vibration mode of the beam is simulated by a local change in the cross section. This problem is solved by the Rayleigh method. Fairly simple formulas for the determination of the natural frequency of the first mode of bending and longitudinal vibrations of a cantilever beam with an open and closing crack are derived. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 35–44, March–April, 1999.     

On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 2. Experimental and calculation results

The results of experimental investigation of the relationship between the natural frequency of the first mode bending and longitudinal vibrations of titanium alloy and alloyed steel cantilever beams and the crack parameters (crack depth and location) are presented together with the data on calculation of the relative change of the vibration frequency of cracked beams, which are obtained by the proposed analytical approaches. Based on a comparative analysis, we choose fairly simple and sufficiently accurate formulas for calculating the frequencies of bending and longitudinal vibrations of a cantilever beam with an open or closing crack. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 45–53, May–June, 1999.     

外激励作用下输流管道伴随内共振的非线性振动分析

利用多元L-P法研究外部周期激励下两端固定输流管道伴随内共振的非线性受迫振动问题。外激励流固耦合系统固有频率第二阶约为第一阶3倍且激励频率接近前两阶固有频率中间值时会发生伴随强烈内部共振的组合共振,并用多元L-P法求解振动响应,分析前两模态运动及外激励幅值对内共振的影响。数值算例揭示出系统因内共振发生的更丰富、复杂的动力学行为,随激励幅值增大内共振发生趋势降低,响应形式亦发生变化。用多元L-P法研究非线性动力学便捷、高效。     

Primary and secondary resonance analysis of FG/lipid nanoplate with considering porosity distribution based on a nonlinear elastic medium

Abstract

In this study, the nonlinear vibration analysis of the new generation nanostructures is investigated. The composite nanoplate is fabricated from the functional-graded (FG) core and two lipid layers on top and bottom of the FG core as face sheets. The nonlinear vibration analysis is studied in the presence of the external harmonic excitation force. The porosity effect on the free and force vibration analysis of the composite nanoplate is investigated. The nonlocal elasticity theory is utilized to obtain the nonlinear differential governing equation. The Kelvin–Voigt model is used to model the viscoelastic effect of the lipid layers. The Hamilton's principle is utilized to obtain the differential governing equation. The Galerkin's method is used to discrete the nonlinear partial differential governing equation to a nonlinear ordinary differential equation. The multiple scale method is used to solve the ordinary differential equation. The numerical results are compared with the reported results in the literature. A comparison between the presented numerical results and the Runge–Kutta results is done and good agreement is obtained. In the presence and absence of the porosity, the system vibration behavior is studied in the primary and secondary resonance cases. The results show that the porosity distribution types play an important role in the mechanical behavior of the composite nanoplate. Also, the numerical results show that the nonlinear frequency of the system decreases by passing time. This study can be useful to product the sensors and devices at the nanoscale with high biocompatibility.     

Experimental-numerical investigation of the dynamic stability of flexural-torsional vibrations of compressor blades under conditions of attached and separated flow. Part 2. Cross aerodynamic characteristics

We consider the results of investigation of cross aerodynamic characteristics of compressor blades and their dynamic stability under flexural-torsional vibrations for the cases of attached and separated flows in broad ranges of variations of the phase shift, the ratio of amplitudes of the translational and angular components of displacements, the angle of attack, the reduced frequency of vibrations, and the geometry of the blade cascade. Translated from Problemy Prochnosti, No. 4, pp. 89–100, July–August, 2009.     

Experimental-numerical investigation of the dynamic stability of flexural-torsional vibrations of compressor blades under conditions of attached and separated flow. Part 1. Procedure and equipment for the determination of nonstationary aerodynamic characteristics

We present the results of investigations of the aerodynamic stability of flexural-torsional vibrations of compressor blades under conditions of attached and separated flow with regard for the cross and mutual aerodynamic links of the blades in a broad range of variations of the phase shift, the ratio of the amplitudes of translational and angular components of their displacements, and the angle of attack. A procedure and equipment used for the experimental determination of the nonstationary aerodynamic characteristics of the blades are described on the basis of the model of flat-plate airfoil cascades. __________ Translated from Problemy Prochnosti, No. 2, pp. 129–142, March–April, 2007.     

Computational model of the ultimate hardening of materials under high-cycle fatigue and determination of its parameters. Part 2. Computational description of the kinetics of inelastic cyclic deformation

The ultimate hardening model of materials, described by the authors earlier, which is based on allowance for hardening in the zone of localization of inelastic strains, is applied to the estimation of the high-cycle life of materials. A method for the determination of local inelastic strain for the simple case of loading has been developed. The prospects for the use of the model for various complex cases of loading are shown.     

Nonlinear Dynamic Finite Element Analysis of Thick Transversely Flexible Sandwich Panel on Elastic Foundation with Account of Damage Progression in Time. Part 2. 3D Analysis and Time Integration

A plate theory for a thick transversely compressible sandwich plate with composite laminated face sheets is constructed using the simplified assumptions earlier described in Part 1. An algorithm, which takes account of damage progression in dynamic problems, is incorporated into the computational scheme based on the geometrically nonlinear formulation and applied to failure analysis of a sandwich plate under ground impact. __________ Translated from Problemy Prochnosti, No. 4, pp. 95 – 112, July – August, 2005.     

Quantification of effects of stochastic feature parameters of yarn on elastic properties of plain-weave composite – Part 2: Statistical predictions vs. mechanical experiments

This paper presents a linear discretized theoretical model on the basis of the ideal theoretical model to evaluate elastic constants of plain-weave composite by using the statistics of the feature parameters of yarn measured from Micro CT data. A finite element method is utilized to calculate the elastic constants of the composite using the modified and global mean feature parameters of yarn, respectively. Uniaxial tensile and in-plane shear experiments are then completed to measure in-plane elastic constants of the composite. Finally, comparisons among the predictions of two theoretical models, FEM and experimental results are conducted. The results show that the stochastic fluctuations of yarn feature parameters decrease the in-plane elastic moduli and increase the in-plane shear moduli and Poisson’s ratios of the plain-weave composite. The discretized theoretical model with taking account of real yarn stochastic features can predict more accurate elastic constants of the composite than deterministic models.