Simulations and experimental investigations on the steady-state response of linear energy sinks

In recent years, a lot of new studies are focused on vibration damping mechanisms, which are significantly important due to both technical and comfort problems in industrial, commercial and residential areas. In most applications, traditional absorption mechanisms has limitations due to their limited frequency range, mechanical structures and effectivity over certain types of excitations that are causing vibration problems. Linear Energy Sinks, which are the main investigation topic of this study, provide a different way of absorption by differing from traditional damping methods which are generally based on thermal dissipation mechanisms. In these traditional methods, transferred vibratory energy is dissipated as heat and creates damping on the main structure that the damping devices are attached on. This damping methods mostly have narrow frequency range, effectivity on certain types of excitations and require noticable mechanic modifications on main structure. However, the linear energy sinks which have a particular frequency distribution absorbs the vibration energy from the main structure and preserve it, without any need for dissipative or internal damping mechanisms. Instead of heat dissipartion, the vibratory energy stays in energy sinks in a near-irreversible way. As distinct from conventional damping mechanisms, linear enegy sinks absorb vibratory energy very effectively under transient excitations. Their performance over random and harmonic excitations is also effective. Linear energy sink concept is showing similarities with dynamic vibration absorbers, which are also known as tuned mass absorbers. In both applications, oscillator(s) decrease(s) the vibration levels on the main structure on which it (they) is (are) attached to. However, the efficiency over a very narrow frequency band and functioning under harmonic excitations limit the applicability of the tuned mass absorbers. For an effective application, the natural frequency of the damper should be tuned very carefully by taking the natural frequency of the main structure and excitation frequency into account. This narrow frequency band range and possible high-amplitudes that can occur on tuned-mass absorbers create a need for additional damping mechanism in the system. Linear energy sinks, however, do not require any additional damping and able to provide damping under transient, harmonic and random excitations. The particular frequency distribution that makes attached oscillators behave as linear energy sinks is obtained by the minimization of integral kinetic energy on the main structure. The importance of that particular distribution is investigated in this study, by making several simulations. The results show that, linear distributed oscillators returns most of the vibration energy to the main structure after a certain time, where linear energy sinks efficiently retain the vibration energy and give a small part of it back. This energy recurrence behaviour is directly related to the distribution of the oscillators connected to the system. This thesis consists of two main chapters. In the first chapter, finite element simulations of a dynamic vibration absorber and linear energy sinks are made under transient, harmonic and random excitations. A lateral-vibrating fixed-free beam with tip mass is set as main structure, where small-scale beam(s) is/are used as tuned-mass absorber and linear energy sinks. The excitation frequencies in harmonic inputs are selected as from very low frequencies, passing through the natural frequency zone of main structure and going to higher frequencies. This cluster of excitation frequencies reveals the areas that both tuned-mass asbsorber and linear sinks are effective. Random excitation forces are Gaussian white noise signals. Their frequency bandwidths are located below those of attached oscillators, covering the range of attached oscillators and above those of attached oscillators. The response of tuned-mass-absorber-attached system to impulsive excitations shows no damping; vibration energy is being transferred continuously between main structure and oscillator without any damping. For harmonic excitations, the tuned-mass absorber shows no or very little efficiency below and above its tuned frequency range and leads to high amplitude vibrations when excited at frequencies that are close to new modes defined to the system by adding tuned-mass absorber. The response to random excitation points out a different disadvantage of system with tuned-mass-absorbers. Adding an absorber, i.e. a new degree of freedom, to the main structure, yields additional natural frequency. Since random signals have broadband frequency content, exciting one more mode causes large-amplitude vibrations rather decreasing them. The response of linear energy sinks to transient excitations revealed that energy sinks absorbs energy from the structure and retain it in almost irreversible way. This is the direct effect of optimal frequency distribution of linear energy sinks, which is obtained by optimization through minimization of vibration energy of the structure. The vibration energy tends to return to the main structure with linear energy sinks, as it happened in tuned-mass absorber. Nevertheless, in this case, returning energy is small amount of the total energy; which leads to expression of "nearly-irreversible". This energy recurrence behaviour is correlated to the frequency difference between oscillators. The closer the periods of the oscillators are to each other, the more energy is being transferred back to main structure. Energy transfer from oscillators to main structure starts from the low and high frequency oscillators and travels to the middle ones, which are located around main structure's natural frequency. Simulation results show that main structure with linear energy sinks function effectively under harmonic excitations, especially at higher excitation frequencies. Due to fact that the concept is studied with zero damping conditions, harmonic excitation sometimes yields resonance behaviour. In cases where harmonic excitation frequency is close to a frequency of any oscillator, the vibration gradually increases and energy sinks do not function. If this harmonic excitation frequency is slighty different than oscillator's, beating phenomena occurs. When the excitation frequency is out of optimal distribution limits, the energy sinks provides noticeable damping. The response of the system to random excitation points out that energy sink also is effective under random loads. For the excitation bands below the optimal distribution, the linear energy sinks provide small amount of damping. For the excitation band covering the optimal frequency distribution and the natural frequency of the main structure without oscillators, linear energy sinks provide high damping ratios. When the excitation band is located above the optimal frequency distribution, the energy sinks also provide damping, up to 50% decrement in amplitude. In the second chapter, experimental investigations are performed to evaluate the transient and steady-state response of linear energy sinks. The main structure is a cantilever beam vibrating laterally. The energy sinks are vibrating beams, similar to the ones that are designed for the finite element simulations. Each individual frequency of energy sinks are tuned carefully by mounting mass attachments to thin beams and measured with a laser Doppler vibrometer. A modal shaker, driven by a vibration controller, is used for transient, harmonic and random excitations to provide exactly the same excitation conditions. For the experimental studies, first two natural frequencies of the structure is concerned. For each natural frequency, two different 36-oscillator set are designed as linear energy sinks. The results indicates that, linear energy sinks performs very well under transient excitation. Nearly 75% of the vibration amplitude is decreased by the oscillators. Under harmonic excitation, the energy sinks provide damping whose level is frequency-dependant. Linear energy sinks do not provide any damping below optimal frequency distribution. However, the damping increases significantly when a harmonic excitation, that has a frequency inside optimal distribution, is applied on the structure. The damping level decreases when the excitation frequency is between two optimal sets. For the excitation frequencies inside and higher than second optimal distribution, linear energy sinks also provide remarkable damping. The experimental studies also showed that linear energy sinks function very effectively under random loads with varying frequency bandwidths. The only exception is the the area under the first optimal frequency distribution.