Chapter 12 Free-Pendulum Vibration Absorber Experiment Using Digital Image Processing Richard Landis, Atila Ertas, Emrah Gumus, and Faruk Gungor Abstract Using image processing and analysis, the dynamic behavior of the beam-free-pendulum system under low and high sinusoidal excitation was investigated. The system responses were investigated experimentally in the neighborhood of primary resonance condition. The results exhibited autoparametric interaction between the beam and the free pendulum when the primary resonance condition was satisfied. Experiments were conducted for two different pendulum weights under two different shaker forcing amplitudes, and the results were compared. Experimental data were obtained by sweeping between the frequencies that contain the resonance condition under investigation. The results of experiments for different beam-tip mass and pendulum mass ratios indicate that more powerful absorption action can be achieved when the smaller mass ratios are used. Keywords Nonlinear vibration • Autoparametric vibration absorber • Internal resonance • Free pendulum absorber 12.1 Introduction There is widespread interest in pendulum modeling and the use of the pendulum as a vibration absorber. This interest ranges from the dynamics of Josephson’s Junction in solid state physics [1] to the rolling motion of ships [2] and the rocking motion of buildings and structures under earthquakes [3]. Vibration mitigation has found extensive usage in aerospace structures, civil engineering structures, and mechanical machinery. A comprehensive survey on vibration suppression devices was given by Sun et al. [4]. They reviewed the current developments in passive absorbers, adaptive absorbers, and active absorbers. Passive tuned vibration absorbers are also referred to as dynamic vibration absorbers [5] or tuned mass dampers. Much of the analytical work done on the inverted spherical pendulum for undamped systems was done by Lowenstern [6], Hemp and Sethna [7] and by Moran [8] for damped systems. These three papers dealt with the stability criteria of the inverted spherical pendulum. Recently, Ertas and Garza investigated the dynamics and bifurcations of an impacting spherical pendulum with large angle and parametric forcing. The pendulum system was studied with nine different bobs and two different base configurations with an external frequency of 24.6–24.9 Hz. Comparative analysis was performed at low and high Coulomb damping values for the inverted, impacting pendulum [9]. Passive and active vibration absorbers were used by many researchers to reduce the vibration level of flexible structures. Miwa et al. reported the case involving an active mass damper (AMD) system installed on the roof of a building to investigate the vibration characteristics of multi-story houses built on soft ground near vibration sources such as railways and expressways [10]. Muller et al. studied the modeling and control techniques of an active vibration isolation system. They compared experimental findings with simulated data and discussed the results [11]. Holt and Singh investigated the active/passive vibration control of continuous systems by zero assignment. They reported that the results of their study would lead to the developments in the control strategies for complex structures and implementation of piezoelectric actuators and sensors for vibration control [12]. Viguie ´ and Kerschen, used the concept of nonlinear energy sink (NES) to reduce the vibration level of multi-degree-of-freedom linear structures. They reported that this approach requires the development of an efficient NES design procedure. Their research presented such a procedure based upon bifurcation analysis using the software MatCont [13]. R. Landis • A. Ertas (*) • E. Gumus • F. Gungor Mechanical Engineering Department, Texas Tech University, Lubbock, TX 79409, USA e-mail: aertas@coe.ttu.edu D. Adams et al. (eds.), Topics in Nonlinear Dynamics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series 28, DOI 10.1007/978-1-4614-2416-1_12, # The Society for Experimental Mechanics, Inc. 2012 167