A study on two types of rolling cylinder vibration absorbers

Mitigation of unwanted oscillations in structures induced by environmental and seismic loadings is an important problem in civil and mechanical engineering. Tuned mass dampers and dynamic vibration absorbers are widely used for mitigation of vibrations in various structures and systems. These devices usually represent a single degree of freedom mechanical oscillator connected to the main system. Vibration energy is transferred from the targeted vibration mode of the main system to the dynamic vibration absorber and dissipated in it, thereby reducing the amplitudes of motion and stresses experienced by the main system. A variety of designs for dynamic vibration absorbers and dampers have been developed over many decades. In general, they can be categorized as either employing an elastic restoring force, or gravitational pendulum types. Pendulum-based designs include hanging type and supported type. The supported type pendulum absorbers gained popularity due to their compactness, affordability, and simplicity of installation and maintenance. Examples of such devices include sliding pendulums, rocking block pendulums, track nonlinear energy sinks, unbalanced rolling spheres, and rolling ball pendulums. In this work we derive modeling equations and investigate the performance of two unidirectional devices, both of them incorporate a rolling cylinder. In one case the cylinder rolls inside a semicircular cavity, and in another case the cylinder rolls on a flat surface, while being restrained by an elastic element arranged in a vertical orientation. We present results of numerical investigations of the performance of these devices and compare them with the traditional translational spring-mass-damper type device.