Abstract
The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies' problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown.
Highlights
The solution of nonlinear differential equations for spherical pendulum swaying requires the introduction of modern numerical computational analysis techniques
Abdel-Rahman and Nayfeh [1] have studied the dynamic problem for a “crane boom tip-payload” mechanical system focused on the reduction of payload lateral vibrations by reeling and unreeling the hoist cable
The present paper focuses on the Lagrange mechanicsbased description of small oscillations for a spherical pendulum with a uniformly rotating suspension center
Summary
The solution of nonlinear differential equations for spherical pendulum swaying requires the introduction of modern numerical computational analysis techniques. The authors have derived two- and three-dimensional models for a spherical pendulum taking into account the linearity of transport motion. Blajer et al [9] have simulated a two-tier framed human arm model with segments of equal length The application of this model seems to be very useful for the dynamic analysis of a swaying load in the horizontal plane during rotation of a crane boom. Mitrev [17] has applied his generalized approach with the introduction of an inertia force vector to the case of linear transport motion of the pendulum pivot center. The prime novelty statement of the present paper is based on the rational introduction of a Cartesian coordinate system for study of small relative swaying of a payload and substantiation of uniformity of crane boom rotation
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