Vibration of clamped elliptical plates using exact circular plate modes as shape functions in Rayleigh-Ritz method

The vibration of clamped uniform elliptical plates is investigated using the exact modes of circular plates as shape functions in the Rayleigh-Ritz method. This paper investigates the behaviour of clamped elliptical plates using modified polar coordinates and the exact modes of circular plates in terms of Bessel and modified Bessel functions. The elements of the mass and stiffness matrices are expressed in closed form using Lommel integrals. The accuracy and the convergence of this approach are validated, and numerical results for natural frequencies for various plate aspect ratios are presented.     

Scattering of flexural wave in a thin plate with multiple circular inclusions by using the multipole method

The multipole method is presented to analytically solve the scattering of flexural wave by multiple circular inclusions in an infinite thin plate. The near-field dynamic moment concentration factor (DMCF) and the far-field scattering pattern are both investigated in this paper. The former has a connection with the fatigue failures and the defects in plate-like structures can be detected by the latter. Owing to the addition theorem, the multipole expansion for the multiple scattering fields can be transformed into one coordinate system centered at one circle where continuity conditions are required. In this way, a coupled infinite linear algebraic system is derived as an analytical model for an infinite thin plate with multiple circular inclusions subject to an incident flexural wave. The convergence analysis is conducted to provide the guideline of usage for the proposed method. The effects of the size and thickness of the flexible inclusion, and the central distance between inclusions on the near-field DMCF and the far-field scattering pattern are investigated in the numerical experiments. It shows that the scattering pattern correlates closely with the size and thickness of weakness, indicating the importance of the scattering pattern to detect the various defects. In addition, the DMCF of two corrosion defects is larger than that of one. Therefore, it is essential to evaluate structural safety when multiple circular defects are very close to each other. The effect of the space between the inclusions on the near-field DMCF is different from that on the far-field scattering pattern.     

Vibration of a three-layered viscoelastic sandwich circular plate

The equations of motion for a three-layer sandwich circular plate with viscoelastic core are derived. The Donnell–Mushtari–Vlasov assumptions follow to simplify. For the case of iso-symmetric annular plate, five equations are further reduced to three equations. The assumed-mode method then yields the free and the forced solutions being characterized by six generalized coordinates for each circumferential wave number n. Due to the splitting of transversal and in-plane terms the study of vibration response can be reduced to the consideration of the SDOF linear oscillator with hysteretic damping. Numerical results first illustrated the frequency response function (FRF) for two different visco models and slight difference is observed. The effects of frequencies changes and damping due to viscoelastic material (VEM) core for several core-to-face thickness ratios are studied. The results, via the FRF's, show that a relatively thin visco (VEM) core can reduce vibration effectively, but as the core thickness exceeds it the damping gradually reduces. The embedded VEM core decreases the frequencies as expected. The damping effects upon individual modes are looked into as well. The results show that the n=0 mode is affected the most by VEM core.     

Natural mode analysis of a telescopic boom system with multiple sections using the Rayleigh-Ritz method

Journal of Mechanical Science and Technology - A truck crane, a type of construction machine, contains a boom consisting of several strips with different cross-sectional data. A set of the overall...     

一种新的圆光栅偏心参数自标定方法

圆光栅安装偏心误差对圆光栅编码器的角度测量精度有较大影响,对偏心误差进行补偿可以有效提高测量结果的精度。为了对圆光栅的安装偏心参数进行辨识,建立了双读数头的偏心误差模型,推导出了基于双读数头的圆光栅偏心参数的自标定公式。通过实验利用对径安装的两个读数头对圆光栅的偏心参数进行自标定,求解出了相关的偏心参数,并使用正十二面棱体搭建的实验装置,对自标定参数的补偿效果进行了验证。实验结果表明,用双读数头自标定公式标定出的偏心参数对单读数头的测量结果进行偏心误差补偿后,圆光栅的平均误差从补偿前的0.046 4°减小到了0.003 7°。     

Transverse vibration of completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method

The Rayleigh-Ritz method using characteristic orthogonal polynomials has been applied to study the problem of transverse vibration of completely-free elliptic and circular plates of uniform thickness. A sequence of successive approximations has been generated to work out the frequencies and mode shapes. The process is continued until at least the first four frequencies converge to five significant digits. It has been found that the results agree completely with the known results for a circular plate. A comparison has also been made with some known experimental and theoretical results for an elliptic plate.     

Machining of gears with circular teeth by means of an eccentric modifier

The formation of circular teeth surfaces is considered, in cases where the influence of an eccentric modifier is taken approximately and precisely into account. The limitations on the modifier parameters are established. The modified motion ensures localized contact, with less likelihood of manufacturing and assembly errors when smaller-diameter cutter heads are employed in gear shaping.     

Free vibration analysis of a thin rectangular plate with multiple circular and rectangular cut-outs

The present work is to investigate the variation in the natural frequency of a rectangular plate with the change in position of cut outs of different sizes along its diagonal and major axis line by considering different aspect ratios of plates. In this regard the free vibration analysis of an isotropic rectangular plate of various aspect ratios with different sizes of multiple circular and rectangular cut-outs is carried out by using an Independent coordinate coupling method (ICCM) under simply supported boundary condition. The ICCM utilizes independent coordinates separately for plate domain and hole domain, in which the reduced mass and stiffness matrices can be derived, by matching the deflection conditions for each hole imposed on the expressions. The resulting equation is useful for the calculation of the Eigen values. The position, size, and number of cutouts have been varied in all the possible ways to investigate their effects on the natural frequency of the rectangular plate.     

Vibration of circular membrane backed by cylindrical cavity

The natural vibration of a circular membrane backed by a cylindrical air cavity is investigated using the multimodal approach. The cavity-backed membrane is modeled as a dynamical system composed of two subsystems, and their modal receptance or “inverse receptance” characteristics are used to study the system vibration. The natural frequencies of the system are determined for four typical cases and the results show that the resulting modes can be categorized into three groups depending on the strength of the sybsystem interaction.     

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded orthotropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.     

Vibration of circular Mindlin plates with concentric elastic ring supports

This paper studies the vibration behaviour of circular Mindlin plates with multiple concentric elastic ring supports. Utilizing the domain decomposition technique, a circular plate is divided into several annular segments and one core circular segment at the locations of the elastic ring supports. The governing differential equations and the solutions of these equations are presented for the annular and circular segments based on the Mindlin-plate theory. A homogenous equation system that governs the vibration of circular Mindlin plates with elastic ring supports is derived by imposing the essential and natural boundary and segment interface conditions. The first-known exact vibration frequencies for circular Mindlin plates with multiple concentric elastic ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented. The influence of the elastic ring support stiffness, locations, plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed.     

Vibration of skew plates by the MLS-Ritz method

This paper presents a study on the vibration of skew plates by a numerical method, the moving least square Ritz (MLS-Ritz) method which was proposed by the authors in a previous study [Zhou L, Zheng WX. A novel numerical method for the vibration analysis of plates. Computational mechanics WCCM VI in conjunction with APCOM’04, Beijing, China, 5-10 September 2004; Zhou L, Zheng WX. MLS-Ritz method for vibration analysis of plates. Journal of Sound and Vibration 2006;290(3-5):968-90]. One of the most challenging numerical difficulties in analysing the vibration of a skew plate with a large skew angle is the slow convergence due to the stress singularities at the obtuse corners of the plate. The MLS-Ritz method is employed in this paper to address such problem. This method utilises the moving least square technique to establish the trial function for the transverse displacement of a skew plate and the Ritz method is applied to derive the governing eigenvalue equation for the skew plate. The boundary conditions of the plate are enforced through a point substitution technique that forces the MLS-Ritz trial function satisfying the essential boundary conditions along the plate edges. Due to the flexibility of the arrangement of the MLS-Ritz grid points, more grid points can be placed around the obtuse corners of a skew plate so as to address the stress singularity problem at the corners. A series of cases for rhombic plates of various edge support conditions are presented to demonstrate the efficiency and accuracy of the MLS-Ritz method.     

Transverse vibration of a circular plate with arbitrary thickness variation

Rayleigh-Ritz method has been employed to obtain approximations to frequencies and mode shapes of circular plates with variable thickness. The boundary is either clamped, simply supported or completely free. The main distinguishing feature of the present investigations is that the thickness approximation is done by measuring thickness at a suitable set of sample points and then using interpolation to get the approximating polynomial. Thus, unlike other methods already available in literature where either linear or quadratic variation of thickness has been examined, here one can have a polynomial of arbitrary degree depending upon the number and locations of the sample points. The results have been tabulated in a large number of cases and three-dimensional mode shapes have been plotted for some selected cases. Comparison has been made with available results. A short tables are also given to depict the rate of convergence with the order of approximation.     

利用附加因素降低含圆孔矩形板的应力集中

应力集中是机械工程中常见的问题,一般出现在构件形状急剧变化的地方,如缺口、孔洞、沟槽及有刚性约束处.对于常见的含孔板,利用附加因素降低板的应力集中是一种很好的方法.含一个圆孔的受拉薄板,若在拉伸方向靠近该孔附加一些圆孔,使之成为圆孔群,则对于降低应力集中是相当有效的.使用有限元法分别对附加圆孔半径、圆孔间距及圆孔数对含圆孔矩形薄板应力集中系数的影响进行了分析,并与光弹性实验结果进行了比较,两者基本一致.研究结果表明:在孔数一定时,对于不同的孔间距,存在不同的孔径比最佳值,使应力集中得到最有利的缓和.文中还给出最有利于降低应力集中的孔径和孔距条件.     

偏心轴承外圆磨削方法探讨

将原偏心轴承外圆磨削方法进行详细分析,并针对其不足之处提出了相应改进办法。     

Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters.     

Transverse vibration of a circular plate with unidirectional quadratic thickness variation

Free transverse vibration of a circular plate with thickness varying as (1 + α× + βx²) has been studied when the edge of the plate is clamped or simply-supported. The Rayleigh—Ritz method with suitable choice of basis functions satisfying the essential boundry conditions, has been employed to find the fundamental frequency and the associated mode shapes for various values of α and β with different boundary conditions. The convergence of results is ensured by working out several approximations till the results converge to the desired accuracy. The results for uniform thickness, linear and parabolic variation of thickness have been obtained as special cases. Tables and graphs are given for frequency, mode shapes and for depicting the effect of parameters α and β on the frequency.     

Frequencies of circular plate with concentric ring and elastic edge support

Exact solutions for the flexural vibrations of circular plates having elastic edge conditions along with rigid concentric ring support have been presented in this paper. Values of frequency parameter for the considered circular plate are computed for different sets of values of elastic rotational and translation restraints and the radius of internal rigid ring support. The results for the first three modes of plate vibrations are computed and are presented in tabular form. The effects of rotational and linear restraints and the radius of the rigid ring support on the vibration behavior of circular plates are studied over a wide range of non-dimensional parametric values. The values of the exact frequency parameter presented in this paper for varying values of restraint parameters and the radius of the rigid ring support can better serve in design and as benchmark solutions to validate the numerical methods obtained by using other methods of solution.     

气动肌腱驱动的形封闭偏心轮机构和杠杆式压板的绿色夹具

介绍了一种由气动肌腱驱动的形封闭偏心轮机构与杠杆式压板串联结合的绿色夹具的性能特点和工作原理,给出了相应的力学计算公式.通过计算分析,该夹具将得到一个相当于气动肌腱收缩力约42倍的输出力.该夹具具有结构紧凑、力传递效率高且输出力大等优点.