方口径电磁轨道发射装置参数选择对系统动态响应的影响

将方口径电磁轨道发射装置的导轨及壁板在发射状态下的力学分析简化为在集中荷载和均布荷载同步作用下双层弹性地基梁的动力响应问题,在建立双层弹性基础梁的动力学平衡方程的基础上,依据边界约束条件设定振动模态,得到了导轨（上梁）和壁板（下梁）的动位移和动应力的解析解,并通过算例分析了不同的结构参数、材料参数及运动参数对导轨和壁板动态响应的影响。结果表明：导轨宽度及厚度、壁板厚度、上下梁之间支撑的弹性常数、发射速度的变化对系统动态响应的影响较大;导轨和壁板的弹性模量、壁板宽度、导轨和壁板的密度、下梁与地基间的弹性常数的变化所带来的影响较小。研究结果可为方口径电磁发射装置的动特性分析和结构设计提供依据。     

机械荷载与热荷载共同作用下变厚度梁的热弹性力学解

本文研究了两端简支变厚度梁受机械荷载与热荷载共同作用下的热弹性力学解.温度场用调和级数展开,通过求解热传导方程可首先确定温度沿梁厚度方向的非线性分布情况.从二维热弹性力学理论的基本方程出发,导出满足控制微分方程和两端简支边界条件的位移函数的一般解,对上下表面的边界方程作傅立叶正弦级数展开确定待定系数,数值结果与商业有限元软件ANSYS进行了比较,显示出很高的精度.本文方法可直接应用于对应力和位移分析要求较高的工程问题,如航空航天和微型机械的设计.     

考虑尺度效应的微梁静态弯曲数值分析

基于修正偶应力理论及表面弹性理论,本文提出了一种新的双曲线剪切变形梁模型,用于均匀微尺度梁的静态弯曲分析。该理论可以直接利用本构关系获得横向剪切应力,满足梁顶部和底部的无应力边界条件,避免了引入剪切修正因子。根据广义Young-Laplace方程建立了梁的内部与表面层的应力连续性条件,单一的变量场可以描述梁的位移模式。通过在位移场中考虑表面层厚度以及表面层的应力连续条件,可以使新模型能够更准确地预测微尺寸和表面能相关的尺度效应。通过Hamilton原理推导出了梁的控制方程和边界条件。应变能除了考虑经典弹性理论,还要考虑微结构效应和表面能。Navier-type的解析解适用于简支边界条件,而基于拉格朗日插值的微分求积法(DQEM)可以研究在不同边界条件下的力学响应。把该数值解与Navier方法得出的解析解作了对比,得出:微尺度梁在考虑表面能或微尺寸效应、不同载荷和梁高变化下的响应一致;当不考虑微结构相关性和表面能效应时,该模型退化为经典的欧拉梁模型。     

弹性机翼阵风响应数值计算方法

建立了求解弹性机翼阵风响应的计算方法.在计算中,通过采用数值方法求解三维非定常Euler方程来获得气动特性;采用模态叠加的方法考虑弹性影响,实现了流体力学和弹性力学的耦合计算.通过对刚性机翼在攻角突然增大的阵风作用下的响应历程计算和二维NLR7301翼型的极限环振荡计算,对计算方法进行了验证.此后在"1-cos"阵风响应的计算中考虑弹性效应影响,先是只考虑了结构变形的前三个基本模态,弹性机翼气动力响应的计算结果与刚性机翼的响应计算结果有比较大的区别,弹性机翼阵风响应的升力峰值低于刚性机翼,这与文献中的结果是一致的.最后在计算中考虑了高阶弹性模态,计算结果表明:考虑高阶模态后,机翼气动力计算结果的总体变化趋势与只考虑前三个模态时基本一致,但结果中出现了高频的波动,波动的频率与高阶模态本身的频率有关.     

变分原理分析开裂简支箱梁剪力滞效应

变分原理通常应用于箱形截面梁剪力滞效应弹性分析,本文基于换算截面法,运用变分原理推导了预应力混凝土简支箱梁均布荷载作用、钢筋混凝土简支箱梁集中荷载作用的剪力滞系数计算公式,考虑了混凝土开裂对箱梁剪力滞效应的影响,并与试验结果和规范方法进行了对比分析。变分原理分析开裂混凝土箱梁剪力滞效应方法力学概念明确,是其弹性分析适用范围的拓展,亦可推广应用到混凝土连续箱梁开裂后的剪力滞效应分析,具有广阔的应用前景。     

有限长Timoshenko梁弹性碰撞接触瞬间的动态特性

给出了质点与有限长Timoshenko梁横向弹性碰撞接触问题的半解析解,分析了该碰撞问题在碰撞接触瞬间的动态响应特性：揭示了其中的波传播现象．     

黏弹性地基上功能梯度材料板的振动分析

为研究黏弹性地基上功能梯度材料板的自由和强迫振动特性,基于Reddy高阶剪切变形理论以及由Shen导得的广义Karman型方程,用双重Fourier级数法推导了三参数黏弹性地基上四边简支功能梯度材料板自由振动和动力响应的解析解,计算了各模态自振频率和半波冲击载荷作用下的动力响应,讨论了材料组分指数、黏弹性地基参数、边厚比等因素对自由振动和动力响应的影响.结果表明,黏弹性地基的剪切和压缩刚度显著提升了功能梯度材料板的振动频率,减小了动力响应;另外,地基的黏性对振动频率和动力响应也有一定的影响.     

INVESTIGATIONS ON THE MECHANICAL CHARACTERISTICS OF NANOBEAMS BASED ON THE NONLOCAL STRAIN GRADIENT THEORY1)

基于非局部应变梯度理论,建立了一种具有尺度效应的高阶剪切变形纳米梁的力学模型. 其中,考虑了应变场和一阶应变梯度场下的非局部效应. 采用哈密顿原理推导了纳米梁的控制方程和边界条件,并给出了简支边界条件下静弯曲、自由振动和线性屈曲问题的纳维级数解. 数值结果表明,非局部效应对梁的刚度产生软化作用,应变梯度效应对纳米梁的刚度产生硬化作用,梁的刚度整体呈现软化还是硬化效应依赖于非局部参数与材料特征尺度的比值. 梁的厚度与材料特征尺度越接近,非局部应变梯度理论与经典弹性理论所预测结果之间的差异越显著.     

非局部应变梯度理论下纳米梁的力学特性研究

基于非局部应变梯度理论,建立了一种具有尺度效应的高阶剪切变形纳米梁的力学模型.其中,考虑了应变场和一阶应变梯度场下的非局部效应.采用哈密顿原理推导了纳米梁的控制方程和边界条件,并给出了简支边界条件下静弯曲、自由振动和线性屈曲问题的纳维级数解.数值结果表明,非局部效应对梁的刚度产生软化作用,应变梯度效应对纳米梁的刚度产生硬化作用,梁的刚度整体呈现软化还是硬化效应依赖于非局部参数与材料特征尺度的比值.梁的厚度与材料特征尺度越接近,非局部应变梯度理论与经典弹性理论所预测结果之间的差异越显著.     

含尺度效应的功能梯度三明治微梁振动、弯曲与屈曲特性研究

基于修正的应变梯度理论和精化的高阶剪切变形理论,提出了一种含尺度效应的功能梯度三明治微梁模型。功能梯度材料的等效弹性参数由Mori-Tanaka均匀化方法描述。针对微梁的高阶边值问题,融合微分求积和Gauss-Lobatto求积准则,建立了一种2节点18自由度的微分求积有限元。通过对比性研究,验证了理论及数值模型的有效性。最后,讨论了边界条件、材料尺度参数、功能梯度指数、长细比、各层厚度比等对功能梯度三明治微梁静动态特性的影响。结果表明,功能梯度三明治微梁的静力响应、振动频率、屈曲荷载以及模态均呈现出显著的尺度效应,所得结果有望为微机电系统中承载器件的设计提供数据积累和方法依据。     

Theoretical analysis of transient waves in a simply-supported Timoshenko beam by ray and normal mode methods

The dynamic transient responses of a simply-supported Timoshenko beam subjected to an impact force are investigated by two theoretical approaches – ray and normal mode methods. The mathematical methodology proposed in this study for the ray method enable us to construct the solution for the interior source problem and to extend to solve the complicated problem for the multi span of the Timoshenko beam. Numerical results based on these two approaches are compared. The comparison in this study indicates that the normal mode method is more computationally efficient than the ray method except for very short time after the impact. The long-time transient responses are easily calculated using the normal mode method. It is shown that the average long-time transient response converges to the corresponding static value. The Timoshenko beam theory is more accurate than the Bernoulli–Euler beam theory because it includes shear and rotary inertia. This study also provides the slender ratio for which the Bernoulli–Euler beam can be used for the transient-response analysis of the displacement. Moreover, the resonant frequencies obtained from finite element calculation based on the three-dimensional model are compared with the results calculated using the Timoshenko beam and Bernoulli–Euler beam theories. It is noted in this study that the resonant frequency can be accurately determined by the Timoshenko beam theory if the slender ratio is larger than 100, and by the Bernoulli–Euler beam theory if the slender ratio is larger than 400.     

Transient wave analysis of a cantilever Timoshenko beam subjected to impact loading by Laplace transform and normal mode methods

This study applies two analytical approaches, Laplace transform and normal mode methods, to investigate the dynamic transient response of a cantilever Timoshenko beam subjected to impact forces. Explicit solutions for the normal mode method and the Laplace transform method are presented. The Durbin method is used to perform the Laplace inverse transformation, and numerical results based on these two approaches are compared. The comparison indicates that the normal mode method is more efficient than the Laplace transform method in the transient response analysis of a cantilever Timoshenko beam, whereas the Laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi-span Timoshenko beam. Furthermore, a three-dimensional finite element cantilever beam model is implemented. The results are compared with the transient responses for displacement, normal stress, shear stress, and the resonant frequencies of a Timoshenko beam and Bernoulli–Euler beam theories. The transient displacement response for a cantilever beam can be appropriately evaluated using the Timoshenko beam theory if the slender ratio is greater than 10 or using the Bernoulli–Euler beam theory if the slender ratio is greater than 100. Moreover, the resonant frequency of a cantilever beam can be accurately determined by the Timoshenko beam theory if the slender ratio is greater than 100 or by the Bernoulli–Euler beam theory if the slender ratio is greater than 400.     

无约束修正Timoshenko梁的冲击问题

介绍了修正后的Timoshenko梁运动方程，并比较了修正Timoshenko梁与经 典Timoshenko梁的运动方程. 推导了考虑剪切变形引起的转动惯量的修正Timoshenko 梁的正交条件，推导了集中质量对无约束修正Timoshenko梁的正碰撞对梁所引起的瞬态冲 击响应公式，并用算例进行了分析，且与集中质量对经典的无约束Timoshenko梁的正碰撞 对梁所引起的冲击响应进行了比较，另外还用算例分析了梁的刚度的变化和冲击质量比对其 冲击响应产生的影响.     

A microstructure-dependent Timoshenko beam model based on a modified couple stress theory

A microstructure-dependent Timoshenko beam model is developed using a variational formulation. It is based on a modified couple stress theory and Hamilton's principle. The new model contains a material length scale parameter and can capture the size effect, unlike the classical Timoshenko beam theory. Moreover, both bending and axial deformations are considered, and the Poisson effect is incorporated in the current model, which differ from existing Timoshenko beam models. The newly developed non-classical beam model recovers the classical Timoshenko beam model when the material length scale parameter and Poisson's ratio are both set to be zero. In addition, the current Timoshenko beam model reduces to a microstructure-dependent Bernoulli-Euler beam model when the normality assumption is reinstated, which also incorporates the Poisson effect and can be further reduced to the classical Bernoulli-Euler beam model. To illustrate the new Timoshenko beam model, the static bending and free vibration problems of a simply supported beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported beam predicted by the new model are smaller than those predicted by the classical Timoshenko beam model. Also, the differences in both the deflection and rotation predicted by the two models are very large when the beam thickness is small, but they are diminishing with the increase of the beam thickness. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the new model is higher than that by the classical model, with the difference between them being significantly large only for very thin beams. These predicted trends of the size effect in beam bending at the micron scale agree with those observed experimentally. Finally, the Poisson effect on the beam deflection, rotation and natural frequency is found to be significant, which is especially true when the classical Timoshenko beam model is used. This indicates that the assumption of Poisson's effect being negligible, which is commonly used in existing beam theories, is inadequate and should be individually verified or simply abandoned in order to obtain more accurate and reliable results.     

ANALYSIS ON TRANSVERSE IMPACT RESPONSE OF AN UNRESTRAINED TIMOSHENKO BEAM

A moving rigid-body and an unrestrained Timoshenko beam, which is subjected to the transverse impact of the rigid-body, are treated as a contact-impact system. The generalized Fourier-series method was used to derive the characteristic equation and the characteristic function of the system. The analytical solutions of the impact responses for the system were presented. The responses can be divided into two parts : elastic responses and rigid responses. The momentum sum of elastic responses of the contact-impact system is demonstrated to be zero, which makes the rigid responses of the system easy to evaluate according to the principle of momentum conservation.     

经典理论与一阶理论之间简支梁特征值的解析关系

利用Euler-Bernoulli梁理论(EBT)和Timoshenko梁理论(一阶理论,TBT)之间,梁的特征值问题在数学上的相似性,研究了不同梁理论之间特征值的关系。将特征值问题的求解转化为一个代数方程的求解,并导出了不同梁理论之间梁的特征值之间的精确解析关系。因此,只要已知梁的经典结果(临界载荷和固有频率),便很容易从这些关系中获得一阶梁理论下的相应结果。这些解析结果清楚地显示了横向剪切变形对经典结果影响的本质特点。另外,从这些关系中获得的含有剪切变形影响的结果,可以用于检验一阶理论下梁特征值数值结果的有效性、收敛性以及精确性等问题。     

THERMAL POST-BUCKLING OF FUNCTIONALLY GRADED MATERIAL TIMOSHENKO BEAMS

Analysis of thermal post-buckling of FGM (Functionally Graded Material) Timoshenko beams subjected to transversely non-uniform temperature rise is presented. By accurately considering the axial extension and transverse shear deformation in the sense of theory of Timoshenko beam, geometrical nonlinear governing equations including seven basic unknown functions for functionally graded beams subjected to mechanical and thermal loads were formulated. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using a shooting method, the obtained nonlinear boundary value problem was numerically solved and thermal buckling and post-buckling response of transversely non-uniformly heated FGM Timoshenko beams with fixed-fixed edges were obtained. Characteristic curves of the buckling deformation of the beam varying with thermal load and the power law index are plotted. The effects of material gradient property on the buckling deformation and critical temperature of beam were discussed in details. The results show that there exists the tension-bend coupling deformation in the uniformly heated beam because of the transversely non-uniform characteristic of materials.     

复合材料叠层梁和金属梁的固有振动特性

对根据三种梁理论得到的金属梁和复合材料叠层梁的固有振动特性进行了对比性的研究对常用的三种梁理论在弹性碰撞分析中的应用进行了分析和比较     

A micro scale Timoshenko beam model based on strain gradient elasticity theory

A micro scale Timoshenko beam model is developed based on strain gradient elasticity theory. Governing equations, initial conditions and boundary conditions are derived simultaneously by using Hamilton's principle. The new model incorporated with Poisson effect contains three material length scale parameters and can consequently capture the size effect. This model can degenerate into the modified couple stress Timoshenko beam model or even the classical Timoshenko beam model if two or all material length scale parameters are taken to be zero respectively. In addition, the newly developed model recovers the micro scale Bernoulli–Euler beam model when shear deformation is ignored. To illustrate the new model, the static bending and free vibration problems of a simply supported micro scale Timoshenko beam are solved respectively. Numerical results reveal that the differences in the deflection, rotation and natural frequency predicted by the present model and the other two reduced Timoshenko models are large as the beam thickness is comparable to the material length scale parameter. These differences, however, are decreasing or even diminishing with the increase of the beam thickness. In addition, Poisson effect on the beam deflection, rotation and natural frequency possesses an interesting “extreme point” phenomenon, which is quite different from that predicted by the classical Timoshenko beam model.