Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass

In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlin- ear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of mul- tiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequen- cies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.

Design of a new kind of chemical experiment container with virtual reality fusion

Background At present,the teaching of experiments in primary and secondary schools is affected by cost and security factors.Existing research on virtual experiment platforms has alleviated these problems.However,the lack of real experimental equipment and use of a single channel to understand user intentions weaken these platforms operationally and degrade the naturalness of interactions.Methods To solve these problems,we propose an intelligent experimental container structure and a situational awareness algorithm,both of which are verified and applied to a chemical experiment involving virtual-real fusion.First,the acquired images are denoised in the visual channel using the maximum diffuse reflection chroma to remove overexposure.Second,container situational awareness is realized by segmenting the image liquid level and establishing a relation-fitting model.Then,strategies for constructing complete behaviors and making priority comparisons among behaviors are adopted for information complementarity and independence,respectively.A multichannel intentional understanding model and an inter-active paradigm that integrates vision,hearing,and touch are proposed.Results The experimental results show that the accuracy of the intelligent container situation awareness proposed in this paper reaches 99%,and the accuracy of the proposed intention understanding algorithm reaches 94.7%.The test shows that the intelligent experimental system based on the new interaction paradigm also has better performance and a more realistic sense of operation experience in terms of experimental efficiency.Conclusion The results indicate that the proposed experimental container and algorithm can achieve a natural level of human-computer interaction in a virtual chemical experiment platform,enhance the user′s sense of operation,and achieve high levels of user satisfaction.