Skip to main content
Log in

Dynamic analysis of olive trees in intensive orchards under forced vibration

  • Original Paper
  • Published:
Trees Aims and scope Submit manuscript

Abstract

The mechanical harvesting of fruit for oil production in an intensive olive tree orchard is generally accomplished by applying vibration to the tree’s trunk. This vibration is consequently transmitted to the branches, causing the fruit to detach. Although this practice is commonly used, the effects on tree behavior under forced vibration are not firmly established. Dynamic analysis was performed on 17 olive trees (Olea europaea L.) growing in an intensively-managed orchard using modal testing techniques. Modal parameter identification was focused inside the range excitation frequency used by the most commonly available trunk shakers on the market. The olive trees featuring a low morphological variability and modal parameters were obtained for a representative olive tree. The first two modes of vibration of the main tree frame were identified with damping ratios of 26.9 and 17.1% and natural frequencies of 20.2 and 37.7 Hz, respectively. A third mode of vibration of less importance was found at a higher frequency. Therefore, many local modes of vibration were detected near these natural frequencies, primarily located on secondary branches. During the testing, the olive trees behaved like a damped harmonic oscillator with predominantly mass damping in these modes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Affeldt HA, Marshall DE, Brown GK (1988) Relative dynamic displacements within a trunk shaker clamp. Trans ASAE 31(2):323–330

    Google Scholar 

  • Allemang RJ, Brown DL (1998) A unified matrix polynomial approach to modal identification. J Sound Vib 211(3):301–322

    Article  Google Scholar 

  • Aristizábal ID, Oliveros CE, Álvarez F (2003) Mechanical harvest of coffee applying circular and multidirectional vibrations. Trans ASAE 46(2):205–209

    Google Scholar 

  • Ayuso Muñoz R (1979) Propiedades biomecánicas de la Madera de olivo. Dissertation, University of Cordoba, Spain

  • Barranco D, Fernández R, Rallo L (2004) El cultivo del olivo. Mundi-Prensa, Madrid

    Google Scholar 

  • Brüchert F, Speck O, Spatz HC (2003) Oscillations of plants stems and their damping: theory and experimentation. Phil Trans R Soc Lond B 358:1487–1492

    Article  Google Scholar 

  • Castro-García S, Gil-Ribes JA, Blanco-Roldán GL, Agüera-Vega J (2007) Mode shape evaluation of trunk shakers used in oil olive harvesting. Trans ASABE 50(3):1–6

    Google Scholar 

  • Chauhan SS, Walker JCF (2006) Variations in acoustic velocity and density with age, and their interrelationships in radiate pine. For Ecol Manage 229:388–394

    Article  Google Scholar 

  • Chowdhury I, Dasgupta SP (2003) Computation of Rayleigh damping coefficients for large systems. EJGE 8C

  • Ciro HJ (2001) Coffee harvesting I: determination of the natural frequencies of the fruit stem system in coffee trees. Appl Eng Agric 17(4):475–479

    Google Scholar 

  • Ewins DJ (2000) Modal testing: theory practice and application. Research Studies Press, England

    Google Scholar 

  • Gil-Ribes JA, Blanco-Roldán GL, Agüera-Vega J (2001) Optimization of the design and use of shaker machines for mechanical harvesting of the olive trees in Spain. ASAE Paper No. 01-1096, Sacramento

  • Hacinen RL, Lemettinen M, Peltola H, Kellomaki D, Gardiner BA (1998) A prism-based system for monitoring the swaying of trees under wind loading. Agric For Meteorol 90:187–194

    Article  Google Scholar 

  • Horvath E, Sitkei G (2005) Damping properties of plum trees shaken at their trunks. Trans ASAE 48(1):19–25

    Google Scholar 

  • James KR (2003) Dynamic loading of trees. J Arboric 29(3):165–171

    Google Scholar 

  • James KR, Haritos N, Ades P (2006) Mechanical stability of trees under dynamic loads. Am J B 93(10):1522–1530

    Article  Google Scholar 

  • Jonsson MJ, Foetzki A, Kalberer M, Lundström T, Ammann W, Stöckli V (2007) Natural frequencies and damping ratios of Norway spruce [Picea abies (L.) Karst] growing on subalpine forested slopes. Trees 21:541–548

    Article  Google Scholar 

  • Kerzenmacher T, Gardiner B (1998) A mathematical model to describe the dynamic response of a spruce tree to the wind. Trees 12:385–394

    Article  Google Scholar 

  • LMS (1996) Leuven measurements system. CADA-Pc Ver 2.0. Leuven, Belgium

    Google Scholar 

  • MAPYA (2005) Agricultural statistics. Ministerio de Agricultura, Pesca y Alimentación. Spain. Available at: http://www.mapa.es. Accessed 20 April 2007

  • Mayer H (1987) Wind-induced tree sways. Trees 1:195–206

    Article  Google Scholar 

  • Milne R (1991) Dynamics of swaying of Picea sitchensis. Tree Physiol 9:383–399

    PubMed  Google Scholar 

  • Moore JR, Maguire DA (2004) Natural sway frequencies and damping ratios of trees: concepts, review and synthesis of previous studies. Trees 18:195–203

    Google Scholar 

  • Moore JR, Maguire DA (2005) Natural sway frequencies and damping ratios of trees: influence of crown structure. Trees 19:363–373

    Article  Google Scholar 

  • Niklas KJ (1992) Plant biomechanics: an engineering approach to plant form and function. University of Chicago Press, Chicago

    Google Scholar 

  • Peltola H (1996) Swaying of trees in response to wind and thinning in a stand of Scots pine. Bound Layer Meteor 77:285–304

    Article  Google Scholar 

  • Polat R, Gezer I, Guner M, Durson E, Erdogan D, Bilim HC (2007) Mechanical harvesting of pistachio nuts. J Food Eng 79:1131–1135

    Article  Google Scholar 

  • Richardson M, Schwarz B (2003) Modal parameter estimation from operating data. Sound and Vibration. January, pp 1–8

  • Rosa UA, Lee BS, Diezma-Iglesias B, Thompson JF (2005) Modeling transient response of fruitful branch for sensing of fruit removal. ASAE Paper No. 05–1081. Tampa

  • Sellier D, Fourcaud T (2005) A mechanical analysis of the relationship between tree oscillations of Pinus pinaster Ait. saplings and their aerial architecture. J Exp Bot 56(416):1563–1573

    Article  PubMed  CAS  Google Scholar 

  • Sellier D, Fourcaud T, Lac P (2006) A finite element model for investigating effects of aerial architecture on tree oscillations. Tree Physiol 26:799–806

    PubMed  Google Scholar 

  • Spatz HC, Speck O (2002) Oscillation frequencies of tapered plant stems. Am J Bot 89(1):1–11

    Article  Google Scholar 

  • Spatz HC, Beismann H, Brüchert F, Emanns A, Speck T (1997) Biomechamics of the giant red Arundo donax. Phil Trans R Soc Lond B 352:1–10

    Article  Google Scholar 

  • Spatz HC, Brüchert F, Pfisterer J (2007) Multiple resonance damping or how do trees escape dangerously large oscillations? Am J Bot 94(10):1603–1611

    Article  Google Scholar 

  • Speck O, Spatz HC (2004) Damped oscillations of the giant reed Arundo donax (Poaceae). Am J Bot 91:789–796

    Article  Google Scholar 

  • Thomson WT (1993) Theory of vibration with applications, 4th edn. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Torregrosa A, Martin B, Ortiz C, Chaparro O (2006) Mechanical harvesting of processed apricots. Appl Eng Agric 22(4):499–506

    Google Scholar 

  • Watt MS, Moore JR, Façon JP, Downes GM, Clinton PW, Coker G, Davis MR, Simcock R, Parfitt RL, Dando J, Mason EG, Bown HE (2006) Modelling the influence of stand structural, edaphic and climatic influence on juvenile Pinus radiata dynamic modulus of elasticity. For Ecol Manage 229:136–144

    Article  Google Scholar 

  • Whitney JD, Hartmond U, Kender WJ, Burns JK, Salyani M (2000) Orange removal with trunk shakers and abscission chemical. Appl Eng Agric 16(4):367–371

    Google Scholar 

Download references

Acknowledgments

The authors acknowledge the financial support from the Spanish Ministry of Science and Technology (project AGL2007-61533). Furthermore, they express gratitude to the three anonymous reviewers that provided many useful comments for the improvement of this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jesús A. Gil-Ribes.

Additional information

Communicated by D. Treutter.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Castro-García, S., Blanco-Roldán, G.L., Gil-Ribes, J.A. et al. Dynamic analysis of olive trees in intensive orchards under forced vibration. Trees 22, 795–802 (2008). https://doi.org/10.1007/s00468-008-0240-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00468-008-0240-9

Keywords

Navigation