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.
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References
Affeldt HA, Marshall DE, Brown GK (1988) Relative dynamic displacements within a trunk shaker clamp. Trans ASAE 31(2):323–330
Allemang RJ, Brown DL (1998) A unified matrix polynomial approach to modal identification. J Sound Vib 211(3):301–322
Aristizábal ID, Oliveros CE, Álvarez F (2003) Mechanical harvest of coffee applying circular and multidirectional vibrations. Trans ASAE 46(2):205–209
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
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
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
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
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
Ewins DJ (2000) Modal testing: theory practice and application. Research Studies Press, England
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
Horvath E, Sitkei G (2005) Damping properties of plum trees shaken at their trunks. Trans ASAE 48(1):19–25
James KR (2003) Dynamic loading of trees. J Arboric 29(3):165–171
James KR, Haritos N, Ades P (2006) Mechanical stability of trees under dynamic loads. Am J B 93(10):1522–1530
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
Kerzenmacher T, Gardiner B (1998) A mathematical model to describe the dynamic response of a spruce tree to the wind. Trees 12:385–394
LMS (1996) Leuven measurements system. CADA-Pc Ver 2.0. Leuven, Belgium
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
Milne R (1991) Dynamics of swaying of Picea sitchensis. Tree Physiol 9:383–399
Moore JR, Maguire DA (2004) Natural sway frequencies and damping ratios of trees: concepts, review and synthesis of previous studies. Trees 18:195–203
Moore JR, Maguire DA (2005) Natural sway frequencies and damping ratios of trees: influence of crown structure. Trees 19:363–373
Niklas KJ (1992) Plant biomechanics: an engineering approach to plant form and function. University of Chicago Press, Chicago
Peltola H (1996) Swaying of trees in response to wind and thinning in a stand of Scots pine. Bound Layer Meteor 77:285–304
Polat R, Gezer I, Guner M, Durson E, Erdogan D, Bilim HC (2007) Mechanical harvesting of pistachio nuts. J Food Eng 79:1131–1135
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
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
Spatz HC, Speck O (2002) Oscillation frequencies of tapered plant stems. Am J Bot 89(1):1–11
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
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
Speck O, Spatz HC (2004) Damped oscillations of the giant reed Arundo donax (Poaceae). Am J Bot 91:789–796
Thomson WT (1993) Theory of vibration with applications, 4th edn. Prentice-Hall, Englewood Cliffs
Torregrosa A, Martin B, Ortiz C, Chaparro O (2006) Mechanical harvesting of processed apricots. Appl Eng Agric 22(4):499–506
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
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
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.
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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
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DOI: https://doi.org/10.1007/s00468-008-0240-9