According to the mapping theory in complex plane,the geometric features of eigen fre-quency loci of systems undergoing free vibrations are investigated.It is concluded that the phenomenaof curve coalescence and veering can be described in a unified manner from the singularities of map-ping from the complex parameter plane onto the complex frequency plane.The formation of a branchpoint in the parameter space is the foundation of explaining localization and veering phenornena.Bythe use of condensation to reduce the dimension of a system,the scope of application of the geometrictheory is widely expanded.The theory is applied to examples to verify the validity of the proposed ap-proach.The present work is an improvement and extension of recent work by M.S.Traintafyllou etal., 相似文献
The ordinary differential constitutive equations of endochronic theory are extended to simulate elasto-plastic deformation in the range of finite strain using the concept of corotational rate. Different corotational stress rates (Jaumann, Cotter-Rivlin, Truesdell, Dienes and Mandel) are incorporated into the theory. In addition, a new formulation of the plastic spin, which can be used in the Mandel stress rate, is derived. Theoretical simulations of the axial effects for various materials subjected to simple and pure torsional loading cases are discussed in this study. It is shown that the endochronic theory incorporated with the Mandel stress rate yields the most satisfactory result, as indicated from comparison with the experimental data found in literature.
Finally, theoretical investigation of the deformation subjected to finite proportional and non-proportional biaxial compression is presented. The true relationship between stress and strain can be converted to a nominal stress-strain relationship for biaxial loading through the explicit transformation equations derived in this paper. Experimental data tested by Khan and Wang [1990] (“An Experimental study of Large finite Plastic Deformation in Annealed 1100 Aluminum During Proportional and Non-proportional Biaxial Compression” Int. J. Plasticity, 6, 485) are suitably described by the theory demonstrated from a comparison with the theoretical prediction according to rigid-plastic and elastic-plastic models employed by Huang and Khan [1991]. “An Analysis of Finite Elastic-Plastic Deformation under Biaxial Compression”, Int. J. Plasticity, 7, 219). 相似文献
This paper discusses the effect of intensity pattern noise on the displacement measurement precision of digital image correlation
(DIC). Through mathematical deduction, a formula is presented to estimate the displacement measurement error caused by intensity
pattern noise. The resulting formula synthetically reflects the effects of the variance of noise, the intensity variance and
the subset size on the displacement measurement precision. To verify the correctness of the resulting formula, two experiments
are done. The first one is a real self-correlation experiment, and aims to analyze the effect of the subset size, while the
second is a numerical self-correlation experiment, and is to analyze to the effect of the different noise levels. The experimental
results are in good agreement with the theoretical predictions.
The project is supported by the National Science Foundation of China (10572103). 相似文献