Effect of Fractal Tree Structures on Fruit’s Vibration Amplitude in Mechanical Harvesting Process

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی مکانیک بیوسیستم، دانشکده بناب، دانشگاه آزاد اسلامی واحد بناب. بناب. ایران

2 گروه مهندسی مکانیک بیوسیستم، دانشکده کشاورزی، دانشگاه آزاد اسلامی واحد تبریز. تبریز. ایران

چکیده

 Tree structures are complex and random in nature but they follow some specific rules according to their various kinds. The objective of this work is to model three fractal trees’ dynamic behavior in the mechanical shaking process and study the effect of the bifurcation ratio and the length-order ratio (pruning ratio) on the frequency response and the percentage of the harvested fruit. Experimentally the static loadings are carried out on the trunk and branches of the tree to obtain their important elastic properties. In order to obtain viscoelastic properties of the tree, its dynamic free vibration is examined. The fractal trees are modeled with an equivalent multi degree of freedom mass-spring models and the governing equations of motion are derived by means of Newton’s second law; then, they are solved numerically for some sample fractal trees. Consequently, for different values of the bifurcation ratio and the length-order ratio (fractal dimension), the displacement of the fruit is calculated and the displacement amplitude of the fruit is obtained. Also, the effects of the tree structures and pruning ratios on the displacement amplitude of the fruit are discussed. 

کلیدواژه‌ها


عنوان مقاله [English]

اثر ساختارهای فراکتال درختان روی دامنه ارتعاش میوه در فرآیند برداشت مکانیکی

نویسندگان [English]

  • Behzad Mohammadi-Alasti 1
  • Adel Nabian 2
  • Mohammad Homaei 1
1 Department of Mechanical Engineering of Biosystems, Bonab Branch, Islamic Azad University, Bonab, Iran.
2 Department of Mechanical Engineering of Biosystems, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
چکیده [English]

ساختارهای درختی در طبیعت پیچیده و تصادفی هستند اما با توجه به انواع مختلف شان از قوانین خاصی پیروی می کنند. هدف از این کار مدل سازی رفتار دینامیکی سه درخت فراکتال در فرآیند تکان دادن مکانیکی و مطالعه تأثیر نسبت دو شاخه شدن و نسبت هرس بر پاسخ فرکانسی و درصد میوه‌های برداشت شده، هست. به طور تجربی برای بدست آوردن خواص مهم الاستیکی، بارهای استاتیکی بر روی تنه و شاخه های درخت وارد می شوند. همچنین برای به دست آوردن خواص ویسکوالاستیک درخت، ارتعاش آزاد دینامیکی آن بررسی می شود. درختان فراکتال با مدل‌های معادل جرم-فنر چند درجه آزادی مدل سازی می‌شوند و معادلات حاکم بر حرکت با استفاده از قانون دوم نیوتن به دست می‌آیند؛ سپس، آنها به صورت عددی برای برخی از درختان فراکتال نمونه حل می شوند. در نتیجه برای مقادیر مختلف نسبت انشعاب و نسبت هرس (بعد فراکتال)، جابجایی میوه محاسبه شده و دامنه جابجایی میوه به دست می آید. همچنین اثرات ساختارهای درختی و نسبت های هرس بر دامنه جابجایی میوه مورد بحث قرار می‌گیرد.   

کلیدواژه‌ها [English]

  • ساختارهای فراکتالی
  • بعد فراکتال
  • نسبت دو شاخه شدن
  • نسبت هرس و پاسخ فرکانسی
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