Vibration absorbers are provided which utilize a torsional spring and a dynamic mass to control vibrations that occur within the structure to which they are attached. Additionally, pipeline systems are provided which utilize such vibration absorbers including a mass and a torsional spring to control the vibrations that occur within the pipeline system. In various embodiments of the present invention, the torsional spring is one or more elastomer elements coupled between the dynamic mass and a support frame to produce a spring force responsive to pivotal rotation of the dynamic mass relative to the support frame. In various embodiments, one or more elastomer elements arranged in series or in parallel may be used as the torsional spring to provide a desired vibratory dampening characteristic for applications, such as pipelines. Use of such torsional springs may provide a more simplified design with less mechanical joints which may be less susceptible to failure in harsh environments.