Linear dynamical analysis of fractionally damped beams and rods

The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems.     

Stochastic response of fractionally damped beams

This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system.Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional derivative order. Finally, the fractional derivative term introduces in the system dynamics both effective damping and effective stiffness frequency dependent terms.     

Eigenproblem solution of damped structural systems

This article presents an efficient numerical algorithm a complete listing of the associated computer program, developed for the eigenproblem solution of discrete damped structures, including spinning ones. The numerically stable procedure is based on a combined Sturm sequence and inverse iteration technique, which fully exploits the banded form of the relevant matrices and proves to be most substantially economical when compared to similar existing softwares. Numerical results are presented for representative structures, solved by the present computer program written in FORTRAN V for the JPL UNIVAC 1108 computer.     

阻尼结构叶片强迫振动响应分析的改进时频域融合算法

为有效地分析阻尼结构叶片系统的动力学特性,本文对计算非线性动力学系统响应的时频域融合算法进行了改进。引入快速抗混迭傅立叶变换,提高时域与频域间转换运算的精度,减少计算时间;针对阻尼结构叶片系统的局部非线性特点,对线性自由度进行减缩,将迭代求解控制在仅和非线性相关的自由度范围之内;采用混合遗传算法改善计算收敛性。使用改进的时频域融合算法对某真实燃机叶片的非线性强迫振动响应进行了分析。在一定的参数条件下,改进的时频域融合算法计算时间为原算法计算时间的 ,且精度误差不超过 。研究表明：改进的时频域融合算法能够适用于复杂摩擦接触下阻尼结构叶片的振动响应计算。     

Dynamic finite element analysis of viscoelastic composite plates in the time domain

Numerical procedures for analysing transient responses of anisotropic viscoeiastic composite plates have been developed in the time domain using variational principles and a direct time integration method. Recursion relationships have been formulated in order to reduce computer storage substantially. The method developed herein requires only two previous lime solutions to evaluate the next time solution and the necessary storage is independent of the number of the time steps. Verification studies were conducted to evaluate the accuracy and convergence of the present numerical algorithm and they show that the numerical solutions agree well with analytical ones. As examples, dynamic transient responses of viscoeiastic composite plates subjected to unit step loads were calculated using the presently developed procedure.     

Time‐domain integration methods of exponentially damped linear systems

In this paper, three new kinds of time‐domain numerical methods of exponentially damped systems are presented, namely, the simplified Newmark integration method, the precise integration method, and the simplified complex mode superposition method. Based on the traditional Newmark integration method and transforming the equation of motion with exponentially damping kernel functions into an equivalent second‐order equation of motion by using the internal variables technique, the simplified Newmark integration method is developed by using a decoupling technique to reduce the computer run time and storage. By transforming the equation of motion with exponentially damping kernel functions into a first‐order state‐space equation, the precise integration technique is used to numerically solve the state‐space equation. Based on a symmetric state‐space equation and the complex mode superposition method, a delicate and simplified general solution of exponentially damped linear systems, completely in real‐value form, is developed. The accuracy and efficiency of the developed numerical methods are compared and discussed by two benchmark examples.     

约束阻尼板的有限元动力分析

基于虚功原理，提出了一种新的建立约束阻尼板结构动力学模型的方法。该方法将坐标系建立在板的中性面，采用层合理论推导出约束阻尼板结构的动力方程，并结合GHM(Golla—Hughes—McIavish)方法引人辅助的耗散坐标，来描述粘弹性材料随频率变化的特性。通过算例同实验结果和ANSYS计算值作比较验证了其有效性。结果表明，本方法分析约束阻尼结构具有良好的计算精度。也可以用来计算类似的约束阻尼结构。     

Finite Element Dynamic Analysis of Laminated Viscoelastic Structures

This work is concerned with the dynamic behavior of laminated beam, plate and shell structures consisting of a viscoelastic damping layer constrained between two structural layers. Finite element models for modal, harmonic and transient analyses are developed. The dynamic interlaminar shear stresses are determined and presented under harmonic and transient loads. The effect of the damping ratio of the viscoelastic material is investigated. It is found that the viscoelastic material damping reduces the interlaminar stresses. The results also show the dependency of the viscoelastic material on frequency, hence, the effect of the viscoelastic material appears significantly under harmonic loading. In transient analysis, the importance of the viscoelastic material is observed in absorbing the impact and returning the structure to its original configuration.     

Finite Element Dynamic Analysis of Laminated Viscoelastic Structures

This work is concerned with the dynamic behavior of laminated beam, plate and shell structures consisting of a viscoelastic damping layer constrained between two structural layers. Finite element models for modal, harmonic and transient analyses are developed. The dynamic interlaminar shear stresses are determined and presented under harmonic and transient loads. The effect of the damping ratio of the viscoelastic material is investigated. It is found that the viscoelastic material damping reduces the interlaminar stresses. The results also show the dependency of the viscoelastic material on frequency, hence, the effect of the viscoelastic material appears significantly under harmonic loading. In transient analysis, the importance of the viscoelastic material is observed in absorbing the impact and returning the structure to its original configuration.     

《洗衣机滚筒的有限元动态分析》

针对某型号滚筒洗衣机的滚筒结构特点,运用Pro/E软件和有限元软件ANSYS对洗衣机在高速脱水工况下进行结构动力分析,并进行离心载荷作用下的模态分析,得到受力和变形情况以及固有频率和振型。根据分析结果,得出危险位置和临界转速,并对滚筒组件提出了改进建议。     

Finite Element Techniques for Dynamic Crack Analysis in Piezoelectrics

This paper deals with numerical methods, developed to analyze plane stationary cracks in piezoelectric structures under dynamic electromechanical loading conditions. In the first part an explicit finite element scheme is presented, which has been developed to solve the transient coupled electromechanical boundary value problem. A special technique is implemented in the algorithm, accounting for the limited electrical permeability of the crack. In contrast to well known algorithms for static calculations it does not require any iteration. In order to calculate dynamic stress and electric displacement intensity factors for arbitrary crack configurations, the interaction integral is generalized for electromechanical problems. The efficient applicability and the high accuracy of the implementations are demonstrated by numerical examples, giving insight into several effects occuring with dynamically loaded cracks in piezoelectrics     

Finite difference time domain methods for piezoelectric crystals

The numerical simulation of acoustic wave propagation through piezoelectric crystals using the finite-difference time-domain (FDTD) method is introduced. The update equations for the velocity and stress fields are derived and applied to the propagation of ultrasonic waves in three substrates. The concept of the perfectly matched layer (PML), first introduced for the simulation of electromagnetic waves, is extended to the simulation of mechanical waves. The technique is shown to be effective for some crystals, but the PML is found to exhibit numerical instabilities for others.     

结构时域识别的超单元法

在实际应用中 ,传感器数目通常远远小于结构模型自由度的数目。而为了实现识别结果的唯一性 ,一般的时域识别方法要求测量信息是完备的。由于超单元法的分散识别能力 ,使得该方法可以在传感器数目有限的情况下实现大型结构的识别。首先建立了超单元模型 ,其次提出了对超单元模型进行参数化的方法 ,针对结构识别中的荷载未知问题对超单元的划分进行了讨论。最后用大型结构的识别算例对整体识别方法和超单元识别方法进行了比较。结果表明 :超单元法不但可以在传感器数目有限的情况下实现结构参数的完整识别 ,而且其识别效率远远高于一次完成型算法。     

陀螺转子动力学系统的时间有限元内点法

将保辛的时间有限元法(FEM)应用于陀螺转子动力学系统,给出了陀螺转子动力学系统时间有限元法的时间单元刚度阵列式和非齐次外力的表达式,以及辛时间传递矩阵。在此基础上,提出了精度更高的时间有限元内点法(IDTFEA),该方法既继承了时间有限元保辛的优良特性,又大大提高了数值计算精度,具有非常明显的优越性。算例给出了该方法和Newmark方法的比较结果,表明该方法的优越性。     

The Molecular Dynamic Finite Element Method (MDFEM)

In order to understand the underlying mechanisms of inelastic material behavior and nonlinear surface interactions, which can be observed on macroscale as damping, softening, fracture, delamination, frictional contact etc., it is necessary to examine the molecular scale. Force fields can be applied to simulate the rearrangement of chemical and physical bonds. However, a simulation of the atomic interactions is very costly so that classical molecular dynamics (MD) is restricted to structures containing a low number of atoms such as carbon nanotubes. The objective of this paper is to show how MD simulations can be integrated into the finite element method (FEM) which is used to simulate engineering structures such as an aircraft panel or a vehicle chassis. A new type of finite element is required for force fields that include multi-body potentials. These elements take into account not only bond stretch but also bending, torsion and inversion without using rotational degrees of freedom. Since natural lengths and angles are implemented as intrinsic material parameters, the developed molecular dynamic finite element method (MDFEM) starts with a conformational analysis. By means of carbon nanotubes and elastomeric material it is demonstrated that this pre-step is needed to find an equilibrium configuration before the structure can be deformed in a succeeding loading step.     

多铁性复合材料动态耦合响应的有限元分析

多铁性材料在实际应用中往往需要考虑多场动态耦合效应。为研究磁电多铁性复合材料的动态耦合效应及其界面的影响,建立了在动态激励下磁电耦合响应的有限元分析模型,其中采用内聚力模型单元模拟压电和压磁材料间界面,以表征其刚度和强度。对多个算例进行了磁电动态耦合响应分析,考察了界面刚度以及边界条件对动态磁电耦合响应的影响。结果显示,界面刚度和边界约束对磁电多铁性复合材料的动态耦合效应有较大影响,界面刚度越大,耦合效应越强。     

Dynamic Analysis of Stochastic Finite Element Based on Sensitivity Computation

In this paper, material properties, geometry parameters and applied loads are assumed to be stochastic, sensitivity computation of structural vibration is presented. The vibration equation of a system is transformed to a static problem by using the Newmark method, and the Taylor expansion stochastic finite element method (TSFEM) is extended for the structural vibration analysis. An example is given, and the calculation results show the validity of the proposed method.     

粘弹阻尼结构动态性能的有限元分析

考虑到阻尼材料的频率依赖性,提出了一种研究粘弹阻尼结构动态力学性能的迭代有限元模拟分析方法。用这种迭代算法计算了几种典型阻尼结构 悬臂梁和压筋板的模态参数,计算结果与试验模态分析结果或理论解析计算的结果基本一致。此外,还探讨了有限元模拟单元的类型对计算结果的影响。     

Dynamic Finite Element Analysis of Extensional-Torsional Coupled Vibration in Nonuniform Composite Beams

The application of a Dynamic Finite Element (DFE) technique to the extensional-torsional free vibration analysis of nonuniform composite beams, in the absence of flexural coupling, is presented. The proposed method is a fusion of the Galerkin weighted residual formulation and the Dynamic Stiffness Matrix (DSM) method, where the basis functions of approximation space are assumed to be the closed form solutions of the differential equations governing uncoupled extensional and torsional vibrations of the beam. The use of resulting dynamic trigonometric interpolation (shape) functions leads to a frequency dependent stiffness matrix, representing both mass and stiffness properties of the beam element. Assembly of the element matrices and the application of the boundary conditions then leads to a frequency dependent nonlinear eigenproblem, which is solved to evaluate the system natural frequencies and modes. Two illustrative examples of uniform and tapered cantilevered, Circumferentially Uniform Stiffness (CUS), hollow, composite beams are presented. The influence of ply fibre-angle on the natural frequencies is also studied. The correctness of the theory and the superiority of the proposed DFE over the contrasting DSM and conventional FEM methods are confirmed by the published results and numerical checks. The discussion of results is followed by some concluding remarks.