As highly sensitive to structural parameter variations, it is necessary to study relations between derivatives of displacement modes and structural design parameters. This paper proposes an integral technique for obtaining the analytical solutions of slope and curvature modes of arbitrary cross-section inhomogeneous cantilever beam. The method is validated by comparing the computation results of modal frequencies and shapes with both numerical and analytical solutions. Furthermore, based on the presented method, we have established explicit expressions for the structural parameters sensitivity of the slope/curvature mode shapes. An example of parameter design is also presented for a cantilever beam with the proposed sensitivity analysis method.
- Dynamic Systems and Control Division
Derivatives and Parameter Designs of Arbitrary Cross-Section Inhomogenous Beams’ Modes Available to Purchase
Xing, JW, & Zheng, GT. "Derivatives and Parameter Designs of Arbitrary Cross-Section Inhomogenous Beams’ Modes." Proceedings of the ASME 2013 Dynamic Systems and Control Conference. Volume 1: Aerial Vehicles; Aerospace Control; Alternative Energy; Automotive Control Systems; Battery Systems; Beams and Flexible Structures; Biologically-Inspired Control and its Applications; Bio-Medical and Bio-Mechanical Systems; Biomedical Robots and Rehab; Bipeds and Locomotion; Control Design Methods for Adv. Powertrain Systems and Components; Control of Adv. Combustion Engines, Building Energy Systems, Mechanical Systems; Control, Monitoring, and Energy Harvesting of Vibratory Systems. Palo Alto, California, USA. October 21–23, 2013. V001T06A001. ASME. https://doi.org/10.1115/DSCC2013-3725
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