集中载荷作用下不同边界条件的弯曲厚矩形板的受迫振动

运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。     

基于无网格法的Timoshenko曲梁动力分析

曲梁具有外形美观、受力性能良好的优点,故在工程中得到广泛应用。本文基于移动最小二乘近似和一阶剪切变形理论,提出一种对Timoshenko曲梁自由振动和受迫振动进行分析的无网格方法。通过一系列离散点离散曲梁,建立曲梁无网格模型,然后推导曲梁势能和动能方程,通过哈密顿原理给出曲梁自由振动和受迫振动的控制方程,因为本文方法不能直接施加边界条件,所以使用完全转换法处理本质边界条件,最后求解方程得到频率和振动模态。文末通过算例验证了本文方法的有效性,且通过收敛性分析表明本文方法具有较好的收敛性,并进一步分析了不同边界条件、跨高比和变截面变曲率对曲梁自由振动和受迫振动的影响,将计算结果与文献解或ABAQUS解进行对比分析,表明本文方法具有较高的精度,且适用于实际工程情况。     

非均质中厚板的无网格LRPIM动力学分析

用局部加权残值法建立了非均质中厚板的局部径向点插值离散系统方程,采用无网格局部径向点插值法分析了非均质中厚板的自由振动和强迫振动问题。用径向基函数耦合多项式基函数来近似试函数,用四次样条函数做为加权残值法中的权函数。所构造的形函数具有Kronecker delta性质,可以很方便地施加本质边界条件。该方法不需要任何形式的网格划分,所有的积分都在规则形状的子域及其边界上进行。在计算过程中,取积分中的高斯点的材料参数来模拟问题域材料特性的变化。计算结果表明,利用该方法计算非均质中厚板的自由振动和强迫振动问题可以得到具有较高精度的解。     

基于压电振动能量俘获的弯曲结构损伤监测研究

建立了含裂纹损伤的曲梁压电能量俘获系统在强迫振动下的动力学模型. 基于Prescott型压电曲梁力电耦合振动方程的解析解和裂纹截面处的连续性条件, 求解了含裂纹损伤的压电曲梁的格林函数. 根据线性叠加原理, 对含裂纹的力电耦合模型的系统方程解耦, 得到强迫振动下含裂纹损伤的曲梁压电俘能器的输出电压. 在得到模型的强迫振动解析解后, 提出逆方法检测结构中的裂纹损伤, 这一检测方法适用于处于振动状态下的结构. 在数值计算中, 令裂纹深度为零, 通过对比本文的解析解与现有文献中的解析解, 验证了本文解的有效性. 分别分析了含裂纹损伤的压电曲梁的电压响应与裂纹深度、裂纹位置、材料的几何参数以及阻尼之间的关系. 研究结果表明: 裂纹的存在对曲梁式压电俘能器的影响比直梁式更加复杂; 裂纹出现时, 损伤曲梁在健康曲梁的一阶频率值处一定会出现波动并被激励出二阶频率, 此时的二阶频率是开路中健康压电曲梁的一阶频率值; 通过对电压响应的检测可以确定的损伤裂纹的深度和在结构中出现的位置范围; 利用振动问题的解来检测压电曲梁的健康状况是可行且准确的.      

A mixed modal-differential quadrature method for free and forced vibration of beams in contact with fluid

A simple and accurate mixed modal-differential quadrature formulation is proposed to study the dynamic behavior of beams in contact with fluid. Both free and forced vibration problems are considered. The proposed mixed methodology uses the modal technique for the structural domain while it applies the differential quadrature method (DQM) to the fluid domain. Thus, the governing partial differential equations of the beam and fluid are reduced to a set of ordinary differential equations in time. In the case of forced vibration, the Newmark time integration scheme is employed to solve the resulting system of ordinary differential equations. The proposed formulation, in general, combines the simplicity of the modal method and high accuracy and efficiency of the DQM. Its application is shown by solving some beam-fluid interaction problems. Comparisons with analytical solutions show that the present method is very accurate and reliable. To demonstrate its efficiency, the test problems are also solved using the finite element method (FEM). It is found that the proposed method can produce better accuracy than the FEM using less computational time. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.     

Forced capillary-gravity wave motion of two-layer fluid in three-dimensions

A class of problems associated with forced capillary-gravity wave motion in a channel are analyzed in the presence of surface and interfacial tensions in a two-layer fluid in both the cases of finite and infinite water depths. The two and three-dimensional Green functions associated with the capillary-gravity wave problems in the presence of surface and interfacial tensions are derived using the fundamental source potentials. Using the two-dimensional Green function along with Green’s second identity, the expansion formulae for the velocity potentials associated with the capillary-gravity wavemaker problems in two-dimensions are obtained. The two-dimensional results are generalized to derive the expansion formulae for the velocity potentials associated with the forced capillary-gravity wave motion in the presence of surface and interfacial tensions in three-dimensions. Certain characteristics of the eigen-system associated with the expansion formulae are derived. The velocity potentials associated with the free oscillation of capillary-gravity waves in a closed basin and semi-infinite open channel in the presence of surface and interfacial tensions are obtained. The utility of the forced motion in a channel is demonstrated by analyzing the capillary-gravity wave reflection by a wall in a channel in the presence of surface and interfacial tensions. Long wave equations associated with capillary-gravity wave motion in the presence of surface and interfacial tensions are derived under shallow water approximation and the associated dispersion relation are obtained. Various expansion formulae and Green functions derived in the present study will be useful for analyzing a large class of physical problems in ocean engineering and mathematical physics.     

Nonlinear vibration analysis by an extended averaged equation approach

The paper presents an extended averaged equation approach to the investigation of nonlinear vibration problems. The proposed method is applied to some free and self-excited oscillators, the Duffing's forced oscillators including main resonance, subharmonic resonance and super harmonic resonance. The results in analyzing the vibration systems with arbitrary non-linearity show advantages of the method.     

Reciprocal theorem method for the forced vibration of elastic thick rectangular plates

I.IntroductionTheproblelllsofthefol.cedvibrationofelasticthickrectallgularplatestobesolvedareofgreattheoreticalsignificanceandpractical\7altle.Asthevibratinggoverningequationofthethickplateismorecomplicatedthallthatofthinplate.itisdil'ficulttoso]\'einmathematics.Manyscholarshat,eresearchedintotheseproblemsalldadvancedvariousspecialapproximations.Suchassuperpositionmethod.initialfLinctiollnletllod.thecombinedseriesot'theeigenftlnctionsofdeepbeamabouttilecorrespondillgboulldarycollditions.eller…     

结构谐振动力响应的有限元、动凝聚、迁移子结构法

本文扩展了FETM法思想,结合子结构、动凝聚及Riccati变换理论,直接求解谐和激励下结构的受迫动力响应,从而节省了运行时间,严格控制了计算精度。本文编制了程序,并以振型叠加法运行结果为参照,对不同算例的运算效率作了比较。结果表明:本文方法在理论上、实践上是切实可行的。     

考虑径向惯性力时圆柱的非线性强迫振动

研究了考虑径向惯性力时弹性圆薄板大挠度非线性强迫振动问题，提出了一个类似修正迭代法的求解方法，并以固支圆板为例作了具体的求解     

阻尼耗能减振框架结构地震作用振动方程求解及地震反应分析Calculation of vibration equation and analysis of seismic response for damping energy dissipation frame structure

研究了设置耗能阻尼器框架的地震作用振动方程求解及该结构的地震反应。框架结构设置耗能阻尼器后,振动方程的阻尼矩阵不再对振型具有正交性,本文对该振动方程给出了状态方程直接积分法,并与传统强制解耦法进行了比较分析,结果表明强制解耦法对结构第一阶振动反应求解偏差较小,而对于高阶振动反应差别较大,并且强制解耦法高估了阻尼器的减震效果。继而采用状态方程直接积分法对设置有粘滞阻尼器的框架结构进行了地震反应分析,探讨了阻尼器位置对框架结构地震反应的影响,结果表明设置有阻尼器的楼层减振效果明显,未设置阻尼器的楼层减振效果差别较大,甚至有可能出现楼层层间侧移增大的现象,由此提出耗能阻尼器应在结构中合理设置。     

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part II: applications and validation

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. In Part I the governing equations of the aforementioned problem have been derived, leading to the formulation of five boundary value problems with respect to the transverse displacements, to the axial displacement and to two stress functions. These problems are numerically solved using the Analog Equation Method, a BEM based method. In this Part II, numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. Thus, the results obtained from the proposed method are presented as compared with those from both analytical and numerical research efforts from the literature. More specifically, the shear deformation effect in nonlinear free vibration analysis, the influence of geometric nonlinearities in forced vibration analysis, the shear deformation effect in nonlinear forced vibration analysis, the nonlinear dynamic analysis of Timoshenko beams subjected to arbitrary axial and transverse in both directions loading, the free vibration analysis of Timoshenko beams with very flexible boundary conditions and the stability under axial loading (Mathieu problem) are presented and discussed through examples of practical interest.

     

An investigation on primary resonance phenomena of elastic medium based single walled carbon nanotubes

In this paper, the geometrically nonlinear free and forced oscillations of simply supported single walled carbon nanotubes (SWCNTs) are analytically investigated on the basis of the Euler–Bernoulli beam theory. The nonlinear frequencies of SWCNTs with initial lateral displacement are discussed. Equations have been solved using an exact method for free vibration and multiple times scales (MTS) method for forced vibration and some analytical relations have been obtained for natural frequency of oscillations. The numerical results reveal that the nonlinear free and forced vibration of nanotubes is effected significantly by both surrounding elastic medium and CNT aspect ratio.     

四角点支撑纳米板稳态受迫振动解析解

本文基于非局部弹性理论及辛叠加方法,得到放置在黏弹性介质上四角点支撑矩形纳米板稳态受迫振动问题的解析解．将纳米板受迫振动问题导入哈密顿体系,得到哈密顿控制方程,在无需任何预设函数的情况下可直接对哈密顿控制方程进行求解,得到简支纳米板稳态受迫振动问题在辛空间展开形式的解析解．进而通过边界叠加,可求出四角点支撑纳米板稳态受迫振动的解析解．数值算例中验证了本文应用辛叠加方法得到解析解的准确性,并以石墨烯纳米板为例,分析了非局部参数和黏弹性介质参数对四角点支撑石墨烯纳米板稳态受迫振动的影响．结果表明,非局部参数和黏弹性介质参数的变化会影响石墨烯纳米板的共振频率及共振幅值．     

Constrained parameter-splitting perturbation method for the improved solutions to the nonlinear vibrations of Euler–Bernoulli cantilevers

In this paper, a new method named constrained parameter-splitting perturbation method for improving the solutions obtained from the parameter-splitting perturbation method is proposed for solving the problems in some extremal cases, such as the strongly nonlinear vibration of an Euler–Bernoulli cantilever. The proposed method takes the advantages of both the perturbation method and the harmonic balance method. The idea is that the solution obtained by the parameter-splitting perturbation method is substituted into the equation of motion and then the accumulative error of the equation is minimized for determining the unknown splitting parameters under the constraints constructed under the frame of harmonic balance method. The forced vibration of an oscillator with cubic geometric nonlinearity and inertia nonlinearity and the forced vibration of a planar microcantilever beam with a lumped tip mass are studied as examples to reveal the efficacy of the proposed method. The inspection of the steady-state response including its stability is conducted by means of comparing the frequency-response curves obtained by the proposed method with those obtained by the numerical continuation method and harmonic balance method, respectively, to show the efficacy and the advantages of the proposed method. Meanwhile, the nonlinear ordering effect on the solutions of the proposed method is also studied by comparing the results obtained by using different nonlinear orderings in the systems. In the last, we found through convergence examinations that it is necessary to have corrections to the erroneous solution which are obtained by harmonic balance method and Floquet theory in stability analysis.

     

Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs

The piezoelectric materials are used to investigate the active vibration control of ordered/disordered periodic two-span beams. The equation of motion of each sub-beam with piezoelectric patches is established based on Hamilton's principle with an assumed mode method. The velocity feedback control algorithm is used to design the controller. The free and forced vibration behaviors of the two-span beams with the piezoelectric actuators and sensors are analyzed. The vibration properties of the disordered two-span beams caused by misplacing the middle support are also researched. In addition, the effects of the length disorder degree on the vibration performances of the disordered beams are investigated. From the numerical results, it can be concluded that the disorder in the length of the periodic two-span beams will cause vibration localizations of the free and forced vibrations of the structure, and the vibration localization phenomenon will be more and more obvious when the length difference between the two sub-beams increases. Moreover, when the velocity feedback control is used, both the forced and the free vibrations will be suppressed. Meanwhile, the vibration behaviors of the two-span beam are tuned.     

Free and forced vibration of repetitive structures

In this paper, the vibration problems of some repetitive structures, including symmetric, cyclic periodic, linear periodic, chain, and axi-symmetric structures is investigated. Eigen-value problems derived from the vibration equations of these structures are established based on their continuous models. The special properties of the structural modes of these structures are deduced. Applying these properties can provide effective reduction approach to solving the natural and forced vibration problems of these structures by either numerical or experimental methods. Furthermore, these properties can be applied in other aspects such as evaluating the reasonableness of the discrete models of these repetitive structures.     

GREEN QUASIFUNCTION METHOD FOR FREE VIBRATION OF CLAMPED THIN PLATES

The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the...     

双层石墨烯系统稳态受迫振动问题中的辛方法

针对悬臂石墨烯系统提出一种求解其稳态受迫振动问题的辛解析方法。基于Eringen非局部理论,将石墨烯层板受迫振动问题导入哈密顿体系。采用边界条件分解技术,将问题化为三种边界条件的子问题。通过辛解析方法,得到由辛本征值和辛本征解表示的双层石墨烯系统受迫振动问题的解析解表达式。数值结果表明,辛本征解级数具有很好的收敛性和精度,并与文献结果吻合;在一定的外载激励下可发生同向振动模式和反向振动模式;在一定的参数下,得到一些新的现象和结论。