A damping mechanics model and a beam finite element for the free-vibration of laminated composite strips under in-plane loading

A theoretical framework is presented for predicting the nonlinear damping and damped vibration of laminated composite strips due to large in-plane forces. Nonlinear Green-Lagrange axial strains are introduced in the governing equations of a viscoelastic composite and new nonlinear damping and stiffness matrices are formulated including initial stress effects. Building upon the nonlinear laminate mechanics, a damped beam finite element is developed. Finite element stiffness and damping matrices are synthesized and the static equilibrium is predicted using a Newton-Raphson solver. The corresponding linearized damped free-vibration response is predicted and modal frequencies and damping of the in-plane deflected strip are calculated. Numerical results quantify the nonlinear effect of in-plane loads on structural modal damping of various laminated composite strips. The modal loss-factors and natural frequencies of cross-ply Glass/Epoxy beams subject to in-plane loading are measured and correlated with numerical results.     

Computational prediction of modal damping ratios in thin-walled structures

Modal analysis in finite element packages gives natural frequencies and mode shapes, but not modal damping values. Given a constitutive relation for specific material dissipation, volume integrals of the per cycle dissipation can be used to estimate the modal damping. Here, we adopt a well known power law model for such specific dissipation. We develop a modal damping estimation procedure for thin-walled components using shell elements in a commercial finite element package. We validate our shell element results against both analytical results and a solid elements approach developed elsewhere. Our computational approach allows complex geometries in a study of the effects of shape on damping. Finally, we demonstrate the efficacy of both stress concentrations and small tuned resonant appendages in increasing damping.     

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.     

On the dynamic response at the wheel axle of a pneumatic tire

A method for calculating the steady state displacement response and force transmission at the wheel axle of a pneumatic tire-suspension system due to a steady state force or displacement excitation at the tire to ground contact point is developed. The method requires the frequency responses (or receptances)_of both tire-wheel and suspension units. The frequency response of the tire-wheel unit is obtained by using the modal expansion method. The natural frequencies and mode shapes of the tire-wheel unit are obtained by using a geometrically non-linear, ring type, thin shell finite element of laminate composite. The frequency response of the suspension unit is obtained analytically. These frequency responses are used to calculate the force-input and the displacement-input responses at the wheel axle. This method allows the freedom of designing a vehicle and its tires independently and still achieving optimum dynamic performance.     

Effects of hysteretic and aerodynamic damping on supersonic panel flutter of composite plates

The governing equation for the finite element analysis of the panel flutter of composite plates including structural damping is derived from Hamilton's principle. The first order shear deformable plate theory has been applied to structural modelling so as to obtain the finite element eigenvalue equation. The unsteady aerodynamic load in a supersonic flow is computed by using the linear piston theory. The critical dynamic pressures for composite plates have been calculated to investigate the effects of structural damping on flutter boundaries. The effects are dependent on fiber orientation because flutter mode can be weak or strong in the fiber orientation of composite plates. Structural damping plays an important role in flutter stability with low aerodynamic damping but would not affect the flutter boundary with high aerodynamic damping.     

复杂结构冲击声合成及实验验证

以复杂结构受击振动响应的时域计算为目的, 讨论了结构阻尼的计算方法, 给出一种用于冲击声合成的综合数值方法, 并进行了实验验证. 首先, 考虑到阻尼是影响瞬态振动时变特性的重要因素, 详细讨论了两种模态阻尼的计算方法; 其次, 对阻尼板的受击振动和声辐射进行了时域仿真, 并与时域有限差分法的计算结果进行对比, 显示出两种声音合成方法的计算结果具有高度的一致性; 最后, 针对有限长圆柱壳的受击振动, 将合成声与实验录音进行了对比研究. 结果表明, 合成声与实际录音的时域包络、频谱结构以及衰减趋势基本一致, 证明了采用数值方法进行冲击声合成的有效性. 关键词： 声音合成 模态阻尼 冲击声 数值方法     

Vibration and damping analysis of annular plates with constrained damping layer treatments

The natural frequencies and modal loss factors of annular plates with fully and partially constrained damping treatments are considered. The equations of free vibration of the plate including the transverse shear effects are derived by a discrete layer annular finite element method. The extensional and shear moduli of the viscoelastic material layer are described by the complex quantities. Complex eigenvalues are then found numerically, and from these, both frequencies and loss factors are extracted. The effects of viscoelastic layer stiffness and thickness, constraining layer stiffness and thickness, and treatment size on natural frequencies and modal loss factors are presented. Numerical results also show that the longer constrained damping treatment in radial length does not always provide better damping than the shorter ones.     

Receptances of non-proportionally and continuously damped plates-equivalent dampers method

A method for the dynamic analysis of continuously and non-proportionally damped plates is discussed. The method is quite general and suitable for various damping treatments, such as in multilayer plates with damping layers. The transverse vibrations of partially coated plates under harmonic excitation are analyzed by the proposed method. The results of the undamped modal analysis made by classical finite element methods are used in the suggested lumped parameter analysis. The receptance matrices of coated plates have been computed at undamped natural frequencies. The computational results have been verified by comparison with experimental values for partially and fully coated rectangular plates.     

Analysis of wave propagation in a thin composite cylinder with periodic axial and ring stiffeners using periodic structure theory

Wave propagation characteristics of a thin composite cylinder stiffened by periodically spaced ring frames and axial stringers are investigated by an analytical method using periodic structure theory. It is used for calculating propagation constants in axial and circumferential directions of the cylindrical shell subject to a given circumferential mode or axial half-wave number. The propagation constants corresponding to several different circumferential modes and/or half-wave numbers are combined to determine the vibrational energy ratios between adjacent basic structural elements of the two-dimensional periodic structure. Vibration analyses to validate the theoretical development have been carried out on sufficiently detailed finite element model of the same dimension and configuration as the stiffened cylinder and very good agreement is obtained between the analytical and the dense finite element results. The effects of shell material properties and the length of each periodic element on the wave propagation characteristics are also examined based on the current analytical approach.     

Wave propagation characteristics of helically orthotropic cylindrical shells and resonance emergence in scattered acoustic field. Part 1. Formulations

The method of wave function expansion is adopted to study the three dimensional scattering of a plane progressive harmonic acoustic wave incident upon an arbitrarily thick-walled helically filament-wound composite cylindrical shell submerged in and filled with compressible ideal fluids. An approximate laminate model in the context of the so-called state-space formulation is employed for the construction of T-matrix solution to solve for the unknown modal scattering coefficients. Considering the nonaxisymmetric wave propagation phenomenon in anisotropic cylindrical components and following the resonance scattering theory which determines the resonance and background scattering fields, the stimulated resonance frequencies of the shell are isolated and classified due to their fundamental mode of excitation, overtone and style of propagation along the cylindrical axis (i.e., clockwise or anticlockwise propagation around the shell) and are identified as the helically circumnavigating waves.     

数控裁剪机切割刀壳体振动噪声预测分析

高频往复式切割刀是柔性材料数控裁剪机的核心部件.该文对切割刀壳体的振动噪声改进措施进行研究.首先对切割刀进行刚体动力学分析,获取其所受动载荷情况,并通过数值计算验证了切割刀刚体动力学模型的可靠性.其次,基于有限元法获取切割刀壳体模态特性,并通过锤击激振实验验证了有限元模型的准确性.然后基于模态仿真结果进行谐响应分析,将...     

柱壳和锥壳结构自由振动特征的数值计算与校验

为了评估柱壳和锥壳结构自由振动特征数值计算的精度,分析不同边界条件、环肋、纵肋以及流体载荷对自由振动特征的影响,计算并校验了典型壳体结构在空气中、浸没以及浸没并充满水情况下的自由振动特征。结果表明,空气中干模态分析在2 kHz内、单面及双面接触水情况下的流固耦合湿模态分析在500 Hz内的计算精度能够控制在10%以内。壳体流固耦合自由振动分析时可以采用实体单元离散也可以采用壳单元离散的方法,前者精度略高,能够有效保证求解收敛的频带范围更宽,但工作量更大。径长比大于0.2时,浸没于水中的自由振动分析可以转换为内部填充水时的自由振动分析,转换时应保证两者流固耦合湿表面积相等,如半浸水和半充满水,能够有效减小计算量;环肋和流体载荷对壳体自由振动特征的影响明显,环肋使柱壳同阶自振频率增加,流体载荷使柱壳同阶自振频率减小且影响幅度更大,两者均会使得柱壳模态振型呈现错序排列;流固耦合效应对无肋柱壳和环肋柱壳自振频率的影响效果相当;柱壳内外有水相对于单面接触水而言,同阶自振频率进一步减小,模态振型基本不变;流体载荷对环肋锥壳的自振频率和模态振型的影响幅度较对环肋柱壳小。      

含损伤黏弹性阻尼加筋层合板声功率和指向性变异*

该文旨在研究损伤位置和程度对自由阻尼加筋层合板声辐射功率和指向性的影响。基于Mindlin和Timoshenko梁理论,建立了自由阻尼层合板-梁组合结构有限元模型。数值求解四边简支边界条件自由阻尼加筋层合板振动响应,继而通过Rayleigh积分计算加筋层合板辐射声功率和指向性。将计算得到的前4阶模态固有频率、声辐射功率与指向性与已有文献进行了对比基本一致,验证了数值模型的正确性。最后,详细讨论了损伤位置和程度对自由阻尼加筋层合板固有频率、振型、声辐射功率和指向性的影响,结果表明：随着结构损伤程度的增大,声辐射功率峰值向低频移动,在更多角度上出现明显的指向性;声辐射功率和指向性对损伤位置比损伤程度更加敏感。     

Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method

Modal parameters of structures are often used as inputs for finite element model updating, vibration control, structural design or structural health monitoring (SHM). In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the eigenfrequencies and modal damping coefficients under the form of a Gaussian perturbation, while the uncertainty on the mode shapes is modeled in the form of independent Gaussian noise at each measured location. A more rigorous approach consists however in adding uncorrelated noise on the time domain responses at each sensor before proceeding to an operational modal analysis. In this paper, we study in detail the resulting uncertainty when modal analysis is performed using the stochastic subspace identification method. A Monte-Carlo simulation is performed on a simply supported beam, and the uncertainty on a set of 5000 modal parameters identified with the stochastic subspace identification method is discussed. Next, 4000 experimental modal identifications of a small clamped–free steel plate equipped with 8 piezoelectric patches are performed in order to confirm the conclusions drawn in the numerical case study. In particular, the results point out that the uncertainty on eigenfrequencies and modal damping coefficients may exhibit a non-normal distribution, and that there is a non-negligible spatial correlation between the uncertainty on mode shapes at sensors of different locations.     

A computational approach to calculating frequency-dependent structural operators using the spectral finite element method and a wavenumber-based gridding technique

Spectral finite element methods are used to compute exact vibration solutions of structural models at specific frequencies. The applicability of these methods to certain areas of structural dynamics is limited by two major factors: the lack of separate structural operators (mass, damping, and stiffness matrices), and the subsequent difficulty in computing mode shapes via eigenvalue decomposition. In the work presented in this article, a method is investigated to accurately calculate spectral finite elements while overcoming these limitations. The approach incorporates a two-dimensional, discrete solution utilizing a wavenumber-based gridding technique to compute frequency-dependent local mass, damping, and stiffness matrices which can be assembled into the global structural operators. Computed models are able to be used for precise vibration analysis as well as modal analysis via eigenvalue decomposition of the structural operators.     

DYNAMICS BEHAVIOR OF AXISYMMETRIC AND BEAM-LIKE ANISOTROPIC CYLINDRICAL SHELLS CONVEYING FLUID

The flow-induced vibration characteristics of anisotropic laminated cylindrical shells partially or completely filled with liquid or subjected to a flowing fluid are studied in this work for two cases of circumferential wave number, the axisymmetric, where n=0 and the beam-like, where n=1. The shear deformation effects are taken into account in this theory; therefore, the equations of motion are determined with displacements and transverse shear as independent variables. The present method is a combination of finite element analysis and refined shell theory in which the displacement functions are derived from the exact solution of refined shell equations based on orthogonal curvilinear co-ordinates. Mass and stiffness matrices are determined by precise analytical integration. A finite element is defined for the liquid in cases of potential flow that yields three forces (inertial, centrifugal and Coriolis) of moving fluid. The mass, stiffness and damping matrices due to the fluid effect are obtained by an analytical integration of the fluid pressure over the liquid element. The available solution based on Sanders' theory can also be obtained from the present theory in the limiting case of infinite stiffness in transverse shear. The natural frequencies of isotropic and anisotropic cylindrical shells that are empty, partially or completely filled with liquid as well as subjected to a flowing fluid, are given. When these results are compared with corresponding results obtained using existing theories, very good agreement is obtained.     

Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks

The objective of this work is to present the finite element modeling of laminate composite plates with embedded piezoelectric patches or layers that are then connected to active-passive resonant shunt circuits, composed of resistance, inductance and voltage source. Applications to passive vibration control and active control authority enhancement are also presented and discussed. The finite element model is based on an equivalent single layer theory combined with a third-order shear deformation theory. A stress-voltage electromechanical model is considered for the piezoelectric materials fully coupled to the electrical circuits. To this end, the electrical circuit equations are also included in the variational formulation. Hence, conservation of charge and full electromechanical coupling are guaranteed. The formulation results in a coupled finite element model with mechanical (displacements) and electrical (charges at electrodes) degrees of freedom. For a Graphite-Epoxy (Carbon-Fibre Reinforced) laminate composite plate, a parametric analysis is performed to evaluate optimal locations along the plate plane (xy) and thickness (z) that maximize the effective modal electromechanical coupling coefficient. Then, the passive vibration control performance is evaluated for a network of optimally located shunted piezoelectric patches embedded in the plate, through the design of resistance and inductance values of each circuit, to reduce the vibration amplitude of the first four vibration modes. A vibration amplitude reduction of at least 10 dB for all vibration modes was observed. Then, an analysis of the control authority enhancement due to the resonant shunt circuit, when the piezoelectric patches are used as actuators, is performed. It is shown that the control authority can indeed be improved near a selected resonance even with multiple pairs of piezoelectric patches and active-passive circuits acting simultaneously.     

Transmission loss of periodically stiffened laminate composite panels: shear deformation and in-plane interaction effects

This paper investigates the transmission loss of symmetric and asymmetric laminate composite panels periodically reinforced by composite stiffeners. A comprehensive model based on periodic structure theory is developed. First order shear deformation theory is used and the coupling of the in-plane motion of the panel with its out-of-plane motion is taken into account. Stiffeners interact with the panel through three forces (two in-plane, one out-of-plane) and a torsion moment. Three types of cross sections are investigated for the composite stiffeners: I-shaped, C-shaped, and omega-shaped cross-sections. The model is validated numerically by comparison with the finite element/boundary element method. Experimental validations are also conducted. In both cases, excellent agreement is obtained. Numerical results show that the in-plane coupling effect is increased by increasing the panel thickness and the stiffener's eccentricity. The in-plane coupling effect is also found to increase with frequency.     

Hybrid finite element method applied to supersonic flutter of an empty or partially liquid-filled truncated conical shell

In this study, aeroelastic analysis of a truncated conical shell subjected to the external supersonic airflow is carried out. The structural model is based on a combination of linear Sanders thin shell theory and the classic finite element method. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for pressure loading. The influence of stress stiffening due to internal or external pressure and axial compression is also taken into account. The fluid-filled effect is considered as a velocity potential variable at each node of the shell elements at the fluid-structure interface in terms of nodal elastic displacements. Aeroelastic equations using the hybrid finite element formulation are derived and solved numerically. The results are validated using numerical and theoretical data available in the literature. The analysis is accomplished for conical shells of different boundary conditions and cone angles. In all cases the conical shell loses its stability through coupled-mode flutter. This proposed hybrid finite element method can be used efficiently for design and analysis of conical shells employed in high speed aircraft structures.     

Errors in shell finite element models for the vibration of circular cylinders

Four commonly used shell theories, membrane, thin, thick and proportional theories, are compared with an accurate triangular torus cubic finite element method in their ability to predict the natural frequencies and mode shapes of infinite and free-free finite length solid and hollow circular cylinders. In the computation each shell theory is replaced by a finite element approximation which satisfies the same basic assumptions as the shell theory. Error curves are given for the first two axial-shear, torsional-shear and radial-stretch modes of infinite cylinders. Error contours are given for the first symmetric and first antisymmetric mode of cylinders for circumferential wave numbers n = 0, 1, 2.