On the kinematic model approximation of granular dampers under vertical vibration

Öz

Granular dampers are utilised to control vibration in a wide range of industries, including automotive, aerospace, machine tool and civil engineering applications, where their robustness, tolerance of harsh environments and freedom from maintenance make them attractive where conventional damping treatments cannot be used. The energy dissipation of a granular damper is governed by the collective motion of the particles, which is normally predicted using discrete element simulations that are computationally demanding. This paper examines how far this collective motion can be described by a simple kinematic model in which the granular medium is treated as a single rigid body that detaches from the enclosure, travels freely under gravity, and collides inelastically with the enclosure ends. Conditions are obtained for the detachment and re-contact instants and for the excitation amplitudes at which the collective collisions are most effective. The predictions are compared with previously reported discrete element simulations and measurements of the dissipated power of a cylindrical damper excited at different frequencies. The model reproduces the simulated collective velocity histories and locates both optimum amplitudes with acceptable accuracy. The simple models fail in the intermediate amplitude range, where the collective motion extends over several excitation periods, and at high frequencies, where the compliance of the medium becomes important. Within these limits, the model can support the early sizing of dampers for practical applications at a small fraction of the computational cost of the simulations.

Anahtar Kelimeler

• granular damping
• particle damping
• kinematic modelling
• bouncing bed

Düşey titreşim altındaki granüler sönümleyicilerin kinematik model yaklaşımı üzerine

Öz

Granüler sönümleyiciler; otomotiv, havacılık ve uzay, takım tezgâhları ve inşaat mühendisliği uygulamaları dahil olmak üzere pek çok sektörde titreşim kontrolü amacıyla kullanılmaktadır. Sağlamlıkları, zorlu çevre koşullarına dayanımları ve bakım gerektirmemeleri, onları geleneksel sönümleme uygulamalarının kullanılamadığı durumlarda uygun kılmaktadır. Bir granüler sönümleyicinin enerji sönümlemesi parçacıkların toplu hareketi tarafından belirlenmektedir. Bu hareket genellikle hesaplama maliyeti yüksek ayrık elemanlar yöntemi benzetimleri ile tahmin edilmektedir. Bu çalışmada, granüler ortamın tek bir rijit cisim olarak ele alındığı basit bir kinematik modelin bu toplu hareketi ne ölçüde tanımlayabildiği incelenmektedir. Bu rijit cisim hazneden ayrılmakta, yerçekimi etkisi altında serbestçe hareket etmekte ve hazne uçlarıyla elastik olmayan çarpışmalar yapmaktadır. Ayrılma ve yeniden temas anları ile toplu çarpışmaların en etkin olduğu tahrik genlikleri için koşullar elde edilmiştir. Model tahminleri, farklı frekanslarda tahrik edilen silindirik bir sönümleyicinin sönümlenen gücüne ilişkin daha önce yayımlanmış ayrık elemanlar benzetimleri ve ölçüm sonuçları ile karşılaştırılmıştır. Model, benzetimlerden elde edilen toplu hız-zaman değişimlerini yeniden üretmekte ve her iki optimum genliği kabul edilebilir bir doğrulukla belirlemektedir. Bu tür basit modeller iki durumda başarısız olmaktadır: toplu hareketin birkaç tahrik periyoduna yayıldığı ara genlik aralığında ve granüler ortamın esnekliğinin önem kazandığı yüksek frekanslarda. Bu sınırlar dahilinde model, pratik uygulamalara yönelik sönümleyicilerin ön boyutlandırılmasına benzetimlerin hesaplama maliyetinin çok küçük bir kısmıyla destek sağlayabilmektedir.

Anahtar Kelimeler

• Enerji yutumu
• granüler sönümleme
• kinematik modelleme
• tanecikli sönümleme

Kaynakça

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