Static and free vibration analyses of a bike using finite element method

Abstract A successfully designed bike should possess safety and comfort for the riders. A safe bike means that its structure must be strong enough to prevent from damage due to various external loads and a comfortable bike means that its suspension systems must be excellent enough to reduce the transmissibility of disturbance coming from the uneven roads to the rider. In order to achieve the above goals, various methods have been presented; however, most of them assumed that each part of a bike is a “rigid body” except the helical (coil) springs. For the last reason, this paper tries to use more versatile finite element method (FEM) to perform the static and free vibration analysis of a bike. It is believed that a finite element model with all parts of a bike replaced by the “elastic” elements or lumped masses should be more realistic. In this paper, the entire bike structure is modeled by using three kinds of beam elements: pinned-pinned (P-P), pinned-clamped (P-C) and clamped-clamped (C-C) beam elements. Among the main parts of a bike structure, the main frame and rim are modeled by the C-C elements, the elastic effect of each tire is modeled by using a P-C element, and each spoke or each “spring-damper unit” is modeled by a P-P element. The key point of this paper is to study the influence of some pertinent parameters on the lowest several natural frequencies and mode shapes of the bike. It is found that the radius of the hub (disks), the pretension of each spoke, the mass of various attachments or rider, and the riding gesture of a rider have significant influence on the free vibration characteristics, the static deformations and internal forces (and moments) of the pertinent structural members of a bike. Because the mass of a rider is much greater than that of the bike structure itself, the static and dynamic characteristics of a bike with and without a rider on it must be studied, separately.

Keywords Rider, Bike, Suspension System, Finite Element Method, Elastic Element, Lumped Mass, Main Frame, Rim, Tire, Spoke, Natural Frequency, Mode Shape

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Static and free vibration analyses of a bike using finite element method

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