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Structural Dynamics of Planar Linkages

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Design of Special Planar Linkages

Part of the book series: Springer Tracts in Mechanical Engineering ((STME))

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Abstract

In this chapter, we propose a structural dynamics method for foldable linkages based on transfer matrix. The foldable stair and deployable wing are all typical planar linkages which are made up of a number of identical units. For each unit, every link is supposed to be an Euler-Bernoulli beam. Therefore, the dynamics of each segment beam between every two adjacent revolute joints can be precisely expressed by the transfer matrix of the segment with the variables of boundary conditions of the joints. In this way, the structural dynamics of the whole structure can be built using the least number of variables compared with the traditional methods. In addition, this algorithm avoids the problem of the traditional transfer-matrix method that the number of variables greatly increases when there are a huge number of cross joints within a structure.

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References

  1. Mirats Tur JM, Juan SH (2009) Tensegrity frameworks: dynamic analysis review and open problems. Mech Mach Theory 44(1):1–18

    Article  MATH  Google Scholar 

  2. Escrig F, Valcarcel P (1993) Geometry of expandable space structures. Int J Space Struct 8(1-2):71–84

    Google Scholar 

  3. Kaveh A, Davaran A (1996) Analysis of pantograph foldable structures. Comput Struct 59(1):131–140

    Article  MATH  Google Scholar 

  4. Chen Y, You Z, Tarnai T (2005) Threefold-symmetric Bricard linkages for deployable structures. Int J Solids Struct 42(8):2288–2301

    Article  Google Scholar 

  5. Seffen KA, You Z, Pellegrino S (2000) Folding and deployment of curved tape springs. Int J Mech Sci 42(10):2055–2073

    Article  MATH  Google Scholar 

  6. Mirats Tur JM, Juan SH (2008) Tensegrity frameworks: static analysis review. Mech Mach Theory 43(7):859–881

    Article  MATH  Google Scholar 

  7. Xu LJ, Tian GY, Duan Y, Yang SX (2001) Inverse kinematic analysis for triple-octahedron variable-geometry truss manipulators. Proc Inst Mech Eng C J Mech Eng Sci 215(2):248–251

    Article  Google Scholar 

  8. Gan WW, Pellegrino S (2006) Numerical approach to the kinematic analysis of deployable structures forming a closed loop. Proc Inst Mech Eng C J Mech Eng Sci 220(7):1045–1056

    Article  Google Scholar 

  9. Park SW (2001) Analytical modelling of viscoelastic dampers for structural and vibration control. Int J Solids Struct 38(44-45):8065–8092

    Article  MATH  Google Scholar 

  10. Tarnai T (2003) Zero stiffness elastic structures. Int J Mech Sci 45(3):425–431

    Article  MATH  Google Scholar 

  11. Impollonia N (2006) A method to derive approximate explicit solutions for structural mechanics problems. Int J Solids Struct 43(22-23):7082–7098

    Article  MATH  Google Scholar 

  12. Nohmi M, Matsumoto K, Ueno H, Yoshida T (2001) Deployable truss operation by ETS-VII robot arm using force accommodation control. Comput Aided Civ Infrastruct Eng 16(3):169–179

    Article  Google Scholar 

  13. Talebinejad I, Fischer C, Ansari F (2011) Numerical evaluation of vibration-based methods for damage assessment of cable-stayed bridges. Comput Aided Civ Infrastruct Eng 26(3):239–251

    Article  Google Scholar 

  14. Jafarkhani R, Masri SF (2011) Finite element model updating using evolutionary strategy for damage detection. Comput Aided Civ Infrastruct Eng 26(3):208–224

    Article  Google Scholar 

  15. Kim Y, Hurlebaus S, Langari R (2010) Model-based multi-input, multi-output supervisory semi-active nonlinear fuzzy controller. Comput Aided Civ Infrastruct Eng 25(5):387–393

    Article  Google Scholar 

  16. Cortés F, Elejabarrieta MJ (2008) Structural vibration of flexural beams with thick unconstrained layer damping. Int J Solids Struct 45(22-23):5805–5813

    Article  MATH  Google Scholar 

  17. Mohan Rao AR, Shyju PP (2010) A meta-heuristic algorithm for multi-objective optimal design of hybrid laminate composite structures. Comput Aided Civ Infrastruct Eng 25(3):149–170

    Article  Google Scholar 

  18. Liu Y, Xu L, Grierson DE (2010) Influence of semi-rigid connections and local joint damage on progressive collapse of steel frameworks. Comput Aided Civ Infrastruct Eng 25(3):184–204

    Article  Google Scholar 

  19. Chang SY (2010) A new family of explicit methods for linear structural dynamics. Comput Struct 88(11-12):755–772

    Article  Google Scholar 

  20. Aldemir U (2010) A simple active control algorithm for earthquake excited structures. Comput Aided Civ Infrastruct Eng 25(3):218–225

    Article  Google Scholar 

  21. Koh CG, Chen YF, Liaw CY (2003) A hybrid computational strategy for identification of structural parameters. Comput Struct 81(2):108–118

    Article  Google Scholar 

  22. Correa FN, Jacob BP, Mansur WJ (2010) Formulation of an efficient hybrid time-frequency domain solution procedure for linear structural dynamic problems. Comput Struct 88(5-6):331–346

    Article  Google Scholar 

  23. Langbecker T (1999) Kinematic analysis of deployable scissor structures. Int J Space Struct 14(1):1–15

    Article  Google Scholar 

  24. Chen Y, You Z (2007) Spatial 6R linkages based on the combination of two Goldberg 5R linkages. Mech Mach Theory 42(11):1484–1489

    Article  MATH  Google Scholar 

  25. Liu SY, Chen Y (2009) Myard linkage and its mobile assemblies. Mech Mach Theory 44(10):1950–1963

    Article  MATH  Google Scholar 

  26. Kang SC, Miranda E (2009) Numerical methods to simulate and visualize detailed crane activities. Comput Aided Civ Infrastruct Eng 24(3):169–185

    Article  Google Scholar 

  27. Graf W, Freitag S, Kaliske M, Sickert JU (2010) Recurrent neural networks for uncertain time-dependent structural behaviour. Comput Aided Civ Infrastruct Eng 25(5):322–333

    Article  Google Scholar 

  28. Lin CC, Chen CL, Wang JF (2010) Vibration control of structures with initially accelerated passive tuned mass dampers under near-fault earthquake excitation. Comput Aided Civ Infrastruct Eng 25(1):69–75

    Article  Google Scholar 

  29. Schoefs F, Yáñez-Godoy H, Lanata F (2011) Polynomial chaos representation for identification of mechanical characteristics of instrumented structures. Comput Aided Civ Infrastruct Eng 26(3):173–189

    Article  Google Scholar 

  30. Shigley JE, Uicher JJ (1980) Theory of machines and mechanisms. McGraw-Hill Companies, Inc, New York

    Google Scholar 

  31. Gantes CJ, Konitopoulou E (2004) Geometric design of arbitrarily curved bi-stable deployable arches with discrete joint size. Int J Solids Struct 41(20):5517–5540

    Article  MATH  Google Scholar 

  32. Adeli H (1988) Interactive microcomputer-aided structural steel design. Prentice Hall, Englewood Cliffs

    Google Scholar 

  33. Kaveh A, Shojaee S (2007) Optimal design of scissor-link foldable structures using ant colony optimization algorithm. Comput Aided Civ Infrastruct Eng 22(1):56–64

    Article  Google Scholar 

  34. Adeli H (1994) Advances in design optimization. Chapman & Hall, London

    Google Scholar 

  35. Adeli H, Soegiarso R (1999) High-performance computing in structural engineering. CRC Press, London

    Google Scholar 

  36. Hachem C, Karni E, Hanaor A (2005) Evaluation of biological deployable systems. Int J Space Struct 20(4):189–200

    Article  Google Scholar 

  37. Ragavan V, Made AM (2001) An algorithm for nonlinear stability analysis of an expandable self-erecting structure. Comput Struct 79(29-30):2588–2593

    Article  Google Scholar 

  38. Ando K, Mitsugi J, Senbokuya Y (2000) Analyses of cable-membrane structure combined with deployable truss. Comput Struct 74(1):21–39

    Article  Google Scholar 

  39. Chen WJ, Luo LY, Fu GY, Gong JH, Dong SL (2001) A study on space masts based on octahedral truss family. Int J Space Struct 16(1):75–82

    Article  Google Scholar 

  40. Hanaor A, Levy R (2001) Evaluation of deployable structures for space enclosures. Int J Space Struct 16(4):211–229

    Article  Google Scholar 

  41. Bolander JE, Hong GS, Yoshitake K (2000) Structural concrete analysis using rigid-body-spring networks. Comput Aided Civ Infrastruct Eng 15(2):120–133

    Article  Google Scholar 

  42. Niu H, Wu Z (2005) Numerical analysis of debonding mechanisms in FRP-strengthened RC beams. Comput Aided Civ Infrastruct Eng 20(5):354–368

    Article  Google Scholar 

  43. Adeli H, Sierakowski RL (1991) Mechanics computing in 1990’s and beyond, vol 1. American Society of Civil Engineers, New York

    Google Scholar 

  44. Adeli H, Sierakowski RL (1991) Mechanics computing in 1990’s and beyond, vol 2. American Society of Civil Engineers, New York

    Google Scholar 

  45. Pestel EC, Leckie FA (1963) Matrix method in elastomechanics. McGraw-Hill Book Company, New York

    Google Scholar 

  46. Rui X, Yun L, Lu Y, He B, Wang G (2008) Transfer matrix method of multibody system and its applications. Chinese Science Publishing House, Beijing

    Google Scholar 

  47. Ying L, Salari E (2010) Beamlet transform-based technique for pavement crack detection and classification. Comput Aided Civ Infrastruct Eng 25(8):572–580

    Article  Google Scholar 

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Authors and Affiliations

  1. Tsinghua University, Beijing, China, People’s Republic

    Jingshan Zhao, Zhijing Feng, Ning Ma & Fulei Chu

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  1. Jingshan Zhao
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  2. Zhijing Feng
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  3. Ning Ma
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  4. Fulei Chu
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© 2014 Springer-Verlag Berlin Heidelberg

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Zhao, J., Feng, Z., Ma, N., Chu, F. (2014). Structural Dynamics of Planar Linkages. In: Design of Special Planar Linkages. Springer Tracts in Mechanical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38448-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-38448-6_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38447-9

  • Online ISBN: 978-3-642-38448-6

  • eBook Packages: EngineeringEngineering (R0)

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