On the Form of the Contact Reaction in a Solid Circular Plate Simply Supported Along Two Antipodal Edge Arcs and Deflected by a Central Transverse Concentrated Force

A static, purely flexural mechanical analysis is presented for a Kirchhoff solid circular plate, deflected by a transverse central force, and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. Two kinds of contact reactions are considered, namely the case of distributed reaction force alone, and the situation in which the distributed force is added to a distributed couple of properly selected profile. For both cases this plate problem is formulated in terms of an integral equation of the Prandtl type, coupled with two constraint conditions. The existence of solutions in an appropriate scaled weighted Sobolev space is discussed, and the behaviour of the solution at the endpoints of the support is exhibited. This revised version was published online in June 2006 with corrections to the Cover Date.     

基于有限元方法对人工径向裂纹薄圆板振动辐射声场的研究

在有限元模态分析的基础上，提取了含人工径向裂纹的周界固定薄圆板各单元的相关参数，并将瑞利积分离散化后进而计算了裂纹圆板辐射声场的轴向声压分布和r=0．5m球面上声场指向性。结果表明，径向裂纹不仅使模态裂解为关于裂纹的对称模态和反对称模态，而且使声场分布有显著的变化。通过完整圆板辐射声场计算验证了本文提出方法的正确性。可用于求解任意形状穿透裂纹薄圆板辐射声场的计算。     

Two Kinds Equal Frequency Circuits to Achieve Locally Resonant Band Gap of a Circular Plate Attached Alternately by Piezoelectric Unimorphs

A circular thin plate is proposed for vibration attenuation,which is attached alternately by annular piezoelectric unimorphs with resonant shunt circuits.Two kinds of equal frequency resonant shunt circuits are designed to achieve an integrated locally resonant(LR)band gap(BG) with a much smaller transmission factor:(1) the structure is arrayed periodically while the resonant shunt circuits are aperiodic;(2) the resonant shunt circuits are periodic while the structure is aperiodic.The transmission factor curve is calculated,which is validated by the finite element method.Dependences of the LR BG performance upon the geometric and electric parameters are also analyzed.     

Deformation of a Convex Hydrogel Shell by Parallel Plate and Central Compression

To characterize the materials parameters and deformation of a convex shell of axial symmetry, a hydrogel contact lens is mechanically deformed by two loading configurations: (a) compression between two parallel plates and (b) central load applied by a shaft with a spherical tip. A universal testing machine with nano-Newton and submicron resolutions is used to measure the applied force, F, as a function of vertical displacement of the plate/shaft, w ₀, while a homemade laser aided topography system records the in-situ deformed shell profile and the contact radius or central dimple, a. A nonlinear shell theory and an iterative finite difference method are used to account for the large elastic deformation, the central buckling for the central load compression, and the interrelationship between the measureable quantities (F, w ₀, a).     

Shear and Bending Response of a Rigid Plastic Circular Plate Struck Transversely by a Mass*

ABSTRACT

A theoretical analysis is presented for the dynamic plastic behavior of a fully clamped rigid, perfectly plastic circular plate struck transversely by a rigid mass at the center. It is shown that the maximum permanent transverse deformation predicted by a theoretical solution, with combined transverse shear and bending, is similar to that from a bending-only solution when the ratio of shear strength to bending capacity υ is sufficiently large. However, when the strength parameter υ is small, the transverse shear deformation dominates the response and the maximum deformation from a combined shear and bending solution increases sharply with a decrease in υ. It is also found that the transverse shear deformation becomes more important with an increase in the dimensionless mass ratio β and is sensitive to the dimensionless radius ρ₀ of the impact area.