Abstract
The dynamic characteristics of structures (beams and plates) can be significantly changed by embossing small out-of-plane patterns in these structures. Recent results in literature show, both numerically and experimentally, that shaping a beam in the geometry of its first mode shape significantly increases the value of the first natural frequency of the beam. This phenomenon also occurs when the beam is shaped in the geometry of other mode shapes, and in the case of plates. This work presents new results (numerical and experimental) regarding the linearization of the forms to be imposed to the structure, focusing on shapes composed of straight regions, which would ease the design of stamping tools for example. The results show that the use of straight regions in the geometry of the beams (linear embossed pattern) has a similar effect to that obtained with curved shapes but requiring bigger distances to the baseline (higher shaping deformations). It is also shown that the linearized shapes can be used to optimize the shape of a beam for desired natural frequencies.
Similar content being viewed by others
References
Arora JS (1989) Introduction to optimum design. Mc-Graw Hill, New York
Ercoli L, Laura PAA, Gil R, Carnicer R, Sanzi HC (1990) Fundamental frequency of vibration of rectangular plates of discontinuously varying thickness with a free edge: analytical and experimental results. J Sound Vib 141:221–229. https://doi.org/10.1016/0022-460X(90)90836-O
Hinton E, Özakça M, Rao NVR (1995) Free vibration analysis and shape optimization of variable thickness plates, prismatic folded plates and curved shells. Part 2: shape optimization. J Sound Vib 181:567–581. https://doi.org/10.1006/jsvi.1995.0158
Maalawi KY, Badr MA (2010) Frequency optimization of a wind turbine blade in pitching motion. Proc IMechE Part A J Power Energy 224:545–554. https://doi.org/10.1243/09576509JPE907
Topal U (2015) Frequency optimization of laminated composite annular sector plates. J Vib Control 21:320–327. https://doi.org/10.1177/1077546313487763
Duan Z, Yan J, Lee I, Wang J, Yu T (2018) Integrated design optimization of composite frames and materials for maximum fundamental frequency with continuous fiber winding angles. Acta Mech Sin 34:1084–1094. https://doi.org/10.1007/s10409-018-0784-x
Ou D, Mak CM (2018) Modification of boundary condition for the optimization of natural frequencies of plate structures with fluid loading. Adv Mech Eng 10:1–11. https://doi.org/10.1177/1687814018796008
Park YH, Park YS (2000) Structure optimization to enhance its natural frequencies based on measured frequency response functions. J Sound Vib 229:1235–1255. https://doi.org/10.1006/jsvi.1999.2591
Lim OK, Lee JS (2000) Structural topology optimization for the natural frequency of a designated mode. KSME Int J 14:306–313. https://doi.org/10.1007/BF03186423
Choi SH, Kim SR, Park JY, Han SY (2007) Multi-objective optimization of the inner reinforcement for a vehicle hood considering static stiffness and natural frequency. Int J Autom Technol 8:337–342 http://www.ijat.net/journal/view.php?number=428
Dong G (2015) Topology optimization for the natural frequency of multibody dynamics systems with multi-functional components. In: ASME 2015 international design engineering technical conferences and computers and information in engineering conference IDETC/CIE 2015, Boston MA, US, August 2–5, DETC2015-47891. https://doi.org/10.1115/DETC2015-47891
Reis DB, Nicoletti R (2010) Positioning of deadeners for dibration reduction in vehicle roof using embedded sensitivity. J Vib Acoust 132:021007. https://doi.org/10.1115/1.4000769
Cheng L, Liang X, Belski E, Wang X, Sietins JM, Ludwick S, To A (2018) Natural frequency optimization of variable-density additive manufactured lattice structure: theory and experimental validation. J Manuf Sci Eng 140:1050002. https://doi.org/10.1115/1.4040622
Fredö CR, Hedlung A (2005) NVH optimization of truck cab floor panel embossing pattern. SAE technical paper 2005-01-2342. https://doi.org/10.4271/2005-01-2342
Silva GAL, Nicoletti R (2017) Optimization of natural frequencies of a slender beam shaped in a linear combination of its mode shapes. J Sound Vib 397:92–107. https://doi.org/10.1016/j.jsv.2017.02.053
Thomson WT, Dahleh MD (1998) Theory of vibration with applications. Prentice Hall, Upper Saddle River
Maia NMM, Silva JMM (1997) Theoretical and experimental modal analysis. Research Studies Press Ltd, Taunton
Acknowledgements
This project was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq (Brazil) under Grant No. 301118/2018-3.
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Wallace Moreira Bessa, D.Sc.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Nicoletti, R. Linearization of embedded patterns for optimization of structural natural frequencies. J Braz. Soc. Mech. Sci. Eng. 41, 545 (2019). https://doi.org/10.1007/s40430-019-2040-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-019-2040-0