A GEOMETRIC THEORY IN INVESTIGATION ON MODE LOCALIZATION AND FREQUENCY LOCI VEERING PHENOMENA

According to the mapping theory in complex plane, the geometric features of eigen frequency loci of systems undergoing free vibrations are investigated. It is concluded that the phenomena of curve coalescence and veering can be described in a unified manner from the singularities of mapping from the complex parameter plane onto the complex frequency plane. The formation of a branch point in the parameter Space is the foundation of explaining localization and veering phenomena. By the use of condensation to reduce the dimension of a system, the scope of application of the geometric theory is widely expanded. The theory is applied to examples to verify the validity of the proposed approach. The present work is an improvement and extension of recent work by M. S. Traintafyllou et al..

Curve Veering in Torsional Systems with Stepped Shafts

In this study, the influence of geometrical parameters on the curve veering phenomenon in a tor-sional system with stepped shaft is investigated. Three approximate solutions including finite el-ement, Rayleigh-Ritz and discretization methods, along with an exact solution are employed to obtain the natural frequencies of the structure. The study reveals that, under specific circumstances, the results obtained by approximate methods are very close to the exact solution. The curve veering behavior is manifested irrespective of the method employed. It is concluded that for the structure studied the curve veering behavior is not because of the approximate techniques used to compute the natural frequencies, and is an inherent behavior of the structure.

Natural vibration of cantilever porous twisted plate with variable thickness in different directions

In this paper,the blade is assumed to be a rotating variable thickness cantilever twisted plate structure,and the natural vibrations of variable thickness cantilever twisted plate made of metal porous material are studied.It is assumed that the thickness of the plate changes along spanwise direction and chordwise direction,respectively,and it changes in both directions.The classical thin shell theory,the first and second fundamental forms of surface and von Karman geometric relationship are employed to derive the total potential energy and kinetic energy of the cantilever twisted plate,in which the centrifugal force potential due to high rotational speed is included.Then,according to the Rayleigh-Ritz procedure and applying the polynomial functions which satisfy the cantilever boundary conditions,the dynamic system expressed by equations of motion is reduced to an eigenvalue problem.By numerical simulation,the frequency curves and the mode shapes of the twisted plate can be obtained to reveal the internal connection between natural vibration and the parameters.A series of comparison studies are performed to verify the accuracy of the present formulation and calculations,in which compared data come from experimental,finite element method and theoretical calculation,respectively.The influence of pre-twist angle,three different forms of thickness taper ratio and rotational speed on natural vibration,mode exchange and frequency veering phenomenon of the system is discussed in detail.In addition,the approach proposed here can efficiently extract analytical expressions of mode functions for rotating variable thickness cantilever twisted plate structures.

中印比较视野下的现代性、民族主义、精神与世俗——Peter van der Veer思想述评

本文述评了Peter van der Veer比较印度和中国的现代性经验的研究,即关于自殖民时期到后殖民时期,两国民族主义、现代性努力、宗教和世俗势力之间的纠缠和演化的研究。本文认为van der Veer的中印比较研究对曾占支配地位的"现代化理论范式"进行了反思,他主要挑战了将欧美的现代性作为理想型、而非西方社会的现代性只是对西方现代性的模仿的观念,以及世俗化的观念。本文介绍了他相关思想的几个重要方面,尤其"帝国的现代性"情境下中印民族主义与宗教的关系、世俗化作为国家工程在两国的发展和两国表征在身体上的民族精神即瑜伽和气功。本文最后指出了van der Veer中印比较研究中的一些不足,但仍然认为他的思想是开拓性的,他对世俗化理论和其背后的现代化理论的挑战和反思代表着这个领域最先进的理念。

Testing method for veer of table tennis ball

Under the premise of fully respecting Technical Leaflet T3developed by the International Table Tennis Federation(I T T F),this paper proposes an effective method for testing the veer degree of the table tennis ball based on airflow suspension and machine vision.By sequentially capturing the images of the ball in the stable state of spinning and suspension,a set of fitting circle centres from different circular sections can be obtained by circle fitting through the least square method.The minimum circumscribed circle(MCC)diameter of these centres is served as a basic parameter to evaluate the veer degree of the ball.Experimental results show that this diameter can effectively reflect the veer degree of the ball.The method proposed in this papercan provide a technical basis for the veer online testing of the table tennis ball.

Frequency Veering of Rotating Metal Porous Twisted Plate with Cantilever Boundary Using Shell Theory

The frequency veering of a metal porous rotating cantilever twisted plate with twist angle and stagger angle is investigated.Metal porous materials may have the characteristics of gradient or uniform distribution along the thickness direction.Based on the classical shell theory,considering the influence of centrifugal force produced by high-speed rotation,the free vibration equations of a rotating cantilever twisted plate are derived.Through the polynomial function and Rayleigh-Ritz method,the natural frequencies and mode shapes of the metal porous cantilever twisted plate in both static and rotating states are derived.The accuracy of the present theory and calculation results is confirmed by a comparison between them and the results available from the literature and those obtained from Abaqus.The influences of the thickness ratio,porosity,twist angle,stagger angle and rotational velocity on the frequency veering and mode shape shift of the rotating cantilever twisted plate with porous material under three different distributions are analyzed.It should be mentioned that the frequency veering accompanied by mode shape shift occurs in both static and dynamic states.

Characterization of forced localization of disordered weakly coupled micromechanical resonators

The mode localization phenomenon of disordered weakly coupled resonators(WCRs)is being used as a novel transduction scheme to further enhance the sensitivity of micromechanical resonant sensors.In this paper,two novel characteristics of mode localization are described.First,we found that the anti-resonance loci behave as a linear function of the stiffness perturbation.The antiresonance behavior can be regarded as a new manifestation of mode localization in the frequency domain,and mode localization occurs at a deeper level as the anti-resonance approaches closer to the resonance.The anti-resonance loci can be used to identify the symmetry of the WCRs and the locations of the perturbation.Second,by comparing the forced localization responses of the WCRs under both the single-resonator-driven(SRD)scheme and the double-resonator-driven(DRD)scheme,we demonstrated that the DRD scheme extends the linear measurement scale while sacrificing a certain amount of sensitivity.We also demonstrated experimentally that the amplitude ratio-based sensitivity under the DRD scheme is approximately an order of magnitude lower than that under the SRD scheme,that is,the amplitude ratio-based sensitivity is−70.44%(Nm^(−1))^(−1) under the DRD scheme,while it is−785.6%(Nm^(−)1)^(−1) under the SRD scheme.These characteristics of mode localization are valuable for the design and control of WCR-based sensors.

Revisited dynamic modeling and eigenvalue analysis of the cable-stayed beam

In this study,the Hamilton’s principle is applied to revisit the dynamic modeling of the cable-stayed beam,and the motion equations governing the nonlinear response of the cable-stayed beam are derived.The corresponding boundary terms are transformed to the dynamic equilibrium conditions through the continuity of the displacement at the anchoring point.Following the standard condensation procedure,the condensed model of the cable-stayed beam is determined.The eigenvalue analysis is performed to determine the closed-form eigenvalue solution of the linear problems,and two types of eigenvalue solution are obtained.It is shown that the frequency spectrum of the cable-stayed beam exhibits the curve veering and crossover phenomena.Corresponding to these phenomena,the mode shapes of the cable-stayed beam may exhibit the coupling characteristic.Finally,the discrete model of the cable-stayed beam is determined,and the possible nonlinear interactions are discussed.

BUCKLING LOADS AND EIGENFREQUENCIES OF A BRACED BEAM RESTING ON AN ELASTIC FOUNDATION

The eigenvalue problems of the buckling loads and natural frequencies of a braced beam on an elastic foundation are investigated. sented. The eigenvalues vary with the different The exact solutions for the eigenvalues are preparameters and are especially sensitive to the brace location. As the beam of a continuous system has infinite eigenvalues and these eigenvalues are influenced differently by a brace, the eigenvalues show rich variation patterns. Because these eigenvalues physically correspond to the structure buckling loads and natural frequencies, the study on the eigenvalues variation patterns can offer a design guidance of using a lateral brace of translation spring to strengthen the structure.