Radical deflections of rubber bush mountings of finite lengths

For small radial deformations of bonded cylindrical rubber bush mountings of finite lengths an exact expression is obtained for the applied force. The solution involves the use of Fourier and Fourier-Bessel series and is a generalization of an existing technique applicable to axially symmetric problems. A natural approximation is suggested by the analysis which coincides with the exact solution for small bush lengths and which satisfies all the boundary conditions exactly except the radial displacement boundary conditions which are satisfied in a mean sense over the length of the bush. For both the exact and the approximate solution there is good overall agreement with the limited experimental data that is available. Moreover it would appear that the approximate solution is sufficiently accurate for most engineering purposes. Both solutions agree numerically with those limiting values of the applied force which are obtained for long and short bushes on the assumptions of plane strain and plane stress respectively.     

橡胶筒承受径向载荷时的位移解析解

基于经典弹性理论，利用Euler方程组推导了橡胶筒承受径向载荷时的位移解析解，推导过程中未采用体积不可压缩假设,有限元计算表明，该解析解是正确的。     

Tearing energy for crack growth at the bonds of cylindrical rubber bushes subjected to axial shear

We applied the fracture mechanics approach and the non-linear finite element method to the analysis of interfacial failure in the cylindrical rubber bushes bonded on their outer and inner curved surfaces to rigid metal cylinders. The fracture parameter, tearing energy for rubber bushes was calculated using global energy change. The contact of interfacial crack during deformation was considered. There exist some different results from the previous linear solutions.     

Design and development of engineering component using natural rubber biocomposites

The potential usage of natural rubber biocomposites in engineering products was investigated. The engineering product fabricated is a rubber bush which is widely used in the automobile industry. Three different types of rubber: 25 % mol epoxidised natural rubber, 50 % mol epoxidised natural rubber and deproteinised natural rubber reinforced with eggshell powder and oil palm fibres hybrid biofillers were studied. The mould flow simulation was carried out to study the flow of the rubber in an existing mould cavity. A thermogravimetric analysis was carried out on both the eggshell powder and oil palm fibres and it was observed that the eggshell powder is more stable thermally compared to the oil palm fibres. Static test was conducted to study the static stiffness properties. Dynamic test was also conducted to study the dynamic stiffness and the loss angle. The results of the tests showed promising mechanical properties of the 25 % mol epoxidised natural rubber biocomposites. Further research should be conducted on other biofillers that is capable of improving the properties of the rubber to replace the use of carbon black in the 25 % mol epoxidised natural rubber biocomposite.     

圆锥滑动轴承-转子系统中金属橡胶阻尼器力学性能研究

针对金属橡胶材料优良的阻尼性能,设计了应用于圆锥滑动轴承-转子系统中的金属橡胶阻尼器,制备了专用实验台,在其既承受转子不平衡力等径向载荷又承受轴向载荷作用下,研究了轴向力对金属橡胶阻尼器刚度及能量耗散系数的影响,得到了金属橡胶阻尼器刚度、阻尼性能随变形幅值及轴向载荷的变化关系式,为金属橡胶阻尼器在圆锥滑动轴承-转子系统中的实际应用奠定了基础。     

The transient responses of two-layered cylindrical shells attacked by underwater explosive shock waves

An approximation solution is introduced for the dynamic response of a two-layered cylindrical shell of circular cross-section subjected to an underwater explosive shock wave. The solution is obtained within the framework of the Flugge thin shell theory and the reflected-afterflow-virtual-source (RAVS) method is used to account for the fluid–structure interaction. Detailed numerical computations are carried out, in dimensionless form, for the cases of infinitely long two-layered cylindrical shells. Time histories of nondimensional radial velocity, mid-surface strain, 0th mode radial displacement and 1st mode radial velocity are presented in graphical form and the effects of elastic modulus, shell radius and thickness on the transient response characteristics of the shells are investigated.     

非均匀加筋圆柱薄壳圆截面内振动的径向模态机械阻抗分析

提出圆柱薄壳的圆截面内运动假设,从声学角度将环肋对壳体的作用等效为径向作用力,根据Hamilton原理建立了简支非均匀加筋圆柱壳的振动控制方程,利用驻波形式解对其径向模态机械阻抗进行了研究。分析表明:对于加筋圆柱壳,环肋与圆柱薄壳的径向模态机械阻抗具有串联连接方式,通过调整环肋的几何参数增大环肋自身的径向模态机械阻抗,可以达到壳体减振降噪的目的,并指出了利用环肋的反共振特性进行加筋圆柱壳结构减振的设计方向。     

On the deformation of circular cylindrical rubber bars under axial thrust

Summary The axisymmetric bulging of circular cylindrical rubber bars under end thrust is investigated. The results for different forms of the strain energy function are compared with experimental results.With 2 Figures     

副车架计算模态分析中衬套动刚度的当量方法

针对副车架计算模态分析中橡胶衬套的处理问题,在有限元分析软件中以CBUSH单元模拟橡胶衬套,并以橡胶衬套动刚度的当量值作为CBUSH单元的刚度赋值。从动刚度与静刚度之比的角度出发,提出一种基于橡胶衬套静刚度的动刚度当量方法,称之为"橡胶衬套动刚度的修正系数当量方法"。运用正交试验设计,通过试验模态与计算模态的对比验证所提橡胶衬套动刚度当量方法的有效性,同时,明确不同位置的橡胶衬套对模型精度的影响规律,可应用于相关建模分析中。     

复杂边界条件圆柱壳自由振动特性分析

提出一种半解析法来分析圆柱壳结构自由振动特性。将圆柱壳壳结构在轴向方向分解为若干壳段,用沿轴向的Jacobi多项式和沿周向的Fourie r级数来表示各个壳段的位移函数,并采用罚参数法对圆柱壳结构的边界条件和壳段间的连续性条件进行模拟;最后,基于Rayleigh-Ritz法求得圆柱壳结构的自由振动频率。研究表明,该方法具有较好的收敛性,与公开发表文献一致性较高,研究成果可为复杂边界条件下圆柱壳结构自由振动特性分析提供数据积累和方法依据。     

Buckling of functionally graded circular columns including shear deformation

An analysis of the stability of circular cylindrical columns/beams composed of functionally graded materials is made where shear deformation is taken into account. In this study, a new approach is carried out. Different from the assumption of uniform shear stress at the cross-section adopted in the Timoshenko beam theory, proposed model provides a new approach for treating the problem. Based on the traction-free surface condition, two coupled governing equations for the deflection and rotation are derived, and a single governing equation is further obtained. A comparison of buckling loads derived from the proposed circular column model and the Timoshenko and Euler–Bernoulli theories of beams is made. Moreover, the effects of radial gradient on buckling loads of elastic columns with circular cross-section made of functionally graded materials are elucidated. Finally, the stability of double-walled carbon nanotubes is considered and critical stress is determined and compared with existing results. The results obtained by the proposed model show very good agreement with the results of the Timoshenko beam theory or Reddy–Bickford beam theory.     

Stress and strain concentration factors for tension bars of circular cross-section with semicircular groove

In this paper, the elastic stresses and strains in the circular cross-section bars with semicircular groove subjected to uniaxial tension are systematically examined using the finite element method. It is shown that the stress and strain concentration factors are different even if the material is in the elastic state. Poisson’s ratio can have a significant effect on the strain concentration factor. The relation of stress and strain concentration factors is also obtained for stress concentration region in cylindrical coordinates. This relation depends on Poisson’s ratio, the radial stress factor and the triaxial stress constraint factor.     

橡胶隔振器非线性动力学模型理论与实验研究

基于静态压缩实验、广义胡克定律和应变能密度推导了描述橡胶超弹性的本构关系,进而获得了橡胶隔振器静态刚度模型;在此基础上,提出基于动态激振实验的动态刚度模型,该模型由橡胶隔振器静态刚度、位移系数和频率系数组成。在此基础上,对单自由度质量-隔振器系统进行数值仿真和实验测试,二者获得的系统的固有频率基本吻合,验证了所提出的橡胶隔振器动力学模型的正确性。研究结果为获得橡胶隔振器静、动态刚度模型提供了简洁、实用的思路,并为研究含有隔振器的动力系统的动力学特性提供了理论基础。     

橡胶支座与柱串联体系的动力特性分析

针对工程界比较关注的橡胶隔震支座与柱串联的隔震体系,研究了串联隔震体系横向振动的固有频率,探讨了轴向压力和不同隔震支座等效弯曲刚度对串联隔震系统固有频率的影响。考虑横截面转动和剪切变形以及轴向压力的影响,建立了串联隔震系统横向自由振动的数学模型;采用微分求积单元法（DQEM）对所得控制方程和边界条件进行离散处理,避免了繁琐的偏微分方程求解;数值求解固支—自由边界条件下串联隔震体系的横向固有频率,并得到该系统横向固有频率参数随压力变化的曲线。数值结果表明：轴向力的增加将显著降低串联隔震系统的低阶固有频率;在总高度一定的情况下,隔震支座尺寸的增大对串联隔震体系的力学特性也有显著的影响。     

On the stability of thin-walled, corrugated, circular cylindrical shells under external pressure

Summary Thin-walled, corrugated, circular cylindrical shells under external pressure have repeatedly buckled at much lower values than has been predicted from simple orthotropic shell theory, where a flexural mode of buckling is assumed, in-plane to the cross-section of the tube. In the present paper it is shown that there exists always a combined, torsional–flexural, out-of-plane mode of buckling, frequently corresponding to an extremely low critical pressure. The need to design these tubes also with respect to torsional stiffness is emphasized, and a formula for the buckling pressure is proposed. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

Finite element method applied to the supersonic flutter of circular cylindrical shells

The application of the finite element method to the supersonic flutter of circular cylindrical shells subjected to internal pressure and axial compression is presented. A circular cylindrical shell element is used. The element stiffness, mass and initial stiffness matrices are given. The element aerodynamic matrix is derived based on a first order high Mach number approximation to the linear potential flow theory. The eigenvalue problem is solved by the QR algorithm. Numerical results are presented and these are compared with analytical solutions and experimental data.     

弱刚性机匣橡胶减振柔性夹具研究

薄壁机匣的径向刚度低,在加工过程中易出现颤振,影响工件表面加工质量和加工效率。因此,设计了一种橡胶减振柔性夹具,其可大面积地支撑工件内壁,从而提高工件的加工刚度。建立了工件?夹具系统等效动力学模型,通过机匣铣削实验验证了模型的准确性。对比分析了橡胶减振柔性夹具与传统夹具的减振性能,研究了铣削力加载频率、压板压力、T形压板压力和推动块压力对工件?夹具系统的振动影响。结果表明：工件在采用减振夹具工况下加速度有效值相较于采用传统夹具减小了43.33%;采用橡胶减振柔性夹具后,工件可以避开400~900 Hz范围内剧烈振动的频率区间,振动幅度大大减小;随着压板压力的增大,工件加速度有效值先减小后增大;针对不同高度工件,应采用不同的压板压力,以减小加工过程中工件的振动;在实际加工中,T形压板压力应超过3.56 MPa,推动块压力应超过0.26 MPa,即液压缸推力超过20 kN。研究结果对橡胶减振柔性夹具的现场应用具有重要的指导意义。     

Calculating the pressure force of the non-paraxial cylindrical Gaussian beam exerted upon a homogeneous circular-shaped cylinder

Forces exerted upon a dielectric cylinder of infinite length and arbitrary, or circular, cross-section by the non-paraxial cylindrical Gaussian beam are considered. The projections of the vector of the light force pressure exerted upon a dielectric cylinder of arbitrary and circular cross-section are expressed analytically. In particular, the pressure force is expressed through the coefficients of decomposition of the non-paraxial Gaussian beam into the cylindrical functions. Using numerical examples, a possibility to optically trap a circular-shaped cylinder in two oppositely directed Gaussian beams or a single non-paraxial Gaussian beam is demonstrated.     

橡胶隔振器加速疲劳试验谱的编制方法研究

通过大量的橡胶动静刚度试验和疲劳试验,分别获取了某填充型天然橡胶材料在各试验条件下的动静比数据表和疲劳寿命数据表。以发动机悬置为例,在充分考虑橡胶材料动态特性的基础上,建立了道路载荷值与应变值的转换关系。对采集的道路载荷谱进行雨流计数,根据Miner线性损伤累积理论与损伤等效原则,编制得到最终的加速疲劳试验谱。用该加速疲劳试验谱对发动机悬置进行疲劳试验,试验结果表明：用该方法编制的加速疲劳试验谱可成功应用于悬置等橡胶隔振器零件的疲劳试验,并且较大程度地缩短了试验与产品开发周期。