NES-BASED VIBRATION ABSORBERS FOR MECHANICALSTRUCTURAL ELEMENTS IN A BROAD FREQUENCY AND ENERGY RANGE

Abstract

Vibration is a common phenomenon found in mechanical-structural systems, arising from diverse sources such as the system’s unbalanced forces as well as external loads such as harmonic and shock loads, moving loads, and fluid-induced forces. Excessive vibration causes structural damage or potential collapse due to fatigue, especially when vibration takes place frequently near the resonating frequency. As the change in temperature and moisture content also affects the natural frequency of an engineering system, the passive linear vibration absorption and isolation techniques are not very useful as these are effective only within a narrow range of excitation frequencies. Consequently, linear designs are enhanced by introducing non-linearity into the system. Over the past two decades, significant attention has been directed towards non-linear oscillators with non-linear stiffness, known as non-linear energy sinks (NESs). An NES is typically characterized as a system with 'intrinsic nonlinearity,' making it 'non-linearizable.' A key feature of NES is its ability, as an essentially nonlinear system, to respond across a relatively broad frequency and energy range. This study delves into the passive dissipation of unwanted vibration energy from primary structures/systems to a locally situated essentially non-linear attachment or NES, leveraging phenomena like targeted energy transfer (TET) or non-linear energy pumping. Therefore, the thesis deals with some of the important issues related to the reduction of vibration amplitude of mechanical/structural systems employing an NES to (i) a beam carrying an unbalanced rotor; (ii) a beam subjected to large amplitude excitations; (iii) a sandwich plate in the thermal environment; (iv) a composite plate in the hygrothermal environment; and (v) a pipe-in-pipe (PIP) system exposed to the vortex-induced vibration (VIV). The study entails mathematical modeling using the Euler-Bernoulli beam theory for the beam and the PIP system, the Kirchhoff thin plate theory for the sandwich plate, and the classical laminate plate theory for the laminated composite plate. Further, the partial differential equations are derived using the Euler-Lagrange equation, followed by Galerkin's mode discretization method to obtain second-order ordinary differential equations. These equations are then solved numerically in MATLAB using a Runge-Kutta-based ODE solver. For analytical solutions, the complexification averaging (CX-A) method is employed, which transforms the second-order differential equation into a set of first-order equations, solved in MATCONT for equilibrium points using an arc-length continuation method. Additionally,standard optimization techniques like particle swarm optimization (PSO) and multi-objective genetic algorithms (GA) are used to optimize NES parameters for better performance. Sensitivity analysis is also conducted to verify values of the optimum parameters. Moreover, various techniques like post-transient phase portraits, Poincaré maps, bifurcation diagrams, and the largest Lyapunov exponent curve are employed to analyze dynamic responses of the proposed systems, including periodic, multi-periodic, quasiperiodic, phase lock, and chaotic responses. The research work starts with the application of NES for vibration attenuation of a beam supporting an unbalanced rotor. The amplitude of force exerted by rotating components on the supporting structure varies quadratically with rotor speed, potentially exciting multiple modal frequencies of the support beam as the machine accelerates. Hence, an effective vibration mitigation system is crucial to address resonance across a range of operating speeds. Therefore, an NES attached beneath the beam carrying the unbalanced rotor, thus forming a beam-unbalanced rotor-absorber (BUA) system, is numerically and analytically explored. Results demonstrate the NES's efficacy in reducing vibration amplitude across various rotor speeds, corresponding to resonant modes. The phenomenon of targeted energy transfer from the beam to the NES, characterized by a nonlinear beat, 1:1 resonance capture, and subsequent escape, occurs for the optimum NES parameter. And therefore, the corresponding NES significantly reduces vibration amplitudes for the first resonant mode by 95%, and for the third and fifth modes by 70% and 90%, respectively. The NES also performs effectively over a range of rotor unbalance levels. The stability of the BUA system is reduced when the NES stiffness and mass increase, however, an increase in NES damping reduces the unstable band of the steady-state response. Subsequently, the performance of a two-degree-of-freedom (TDOF) NES is investigated for a beam under large amplitude harmonic excitations and compared with that of a single-degree-of-freedom (SDOF) NES. The TDOF NES demonstrates effective attenuation of resonant peaks, reducing the first peak amplitude by approximately 95% and dissipating 90-98.98% of vibration energy. It outperforms the SDOF NES, particularly for large amplitude excitations. Chaotic responses of the beam are examined using the largest Lyapunov exponents with varying parameters. Higher NES stiffness, mass, and excitation amplitude contribute to system chaos, while higher NES damping reduces instability, providing a stable response. Moreover, the investigation extends to a sandwich plate in a thermal environment, particularly on sandwich plates with thin face sheets, as temperature changes affect their natural frequencies more significantly. Results indicate a reduction of dominant resonant peaks by approximately 70.55% to 95.47%, with the NES dissipating vibration energy in the range of 90% to 98.61% at different temperature variations. Stability and bifurcation analyses suggest that optimal NES parameters yield a simple periodic response near the resonance frequency. Furthermore, nonlinear vibration control and stability analysis of a cantilever composite laminated plate exposed to a hygrothermal environment using NES is also investigated. This study reveals variations in the first two assumed natural frequencies due to changes in temperature, moisture and fiber angle orientation. The optimal NES configuration reduces the peak amplitude of the first mode by approximately 70% and dissipates around 68% of the plate's vibration energy in a hygrothermal environment. Additionally, stability and bifurcation analyses indicate that higher NES damping values lead to a simple periodic response near the resonance frequency. Moreover, in both the study, some nonlinear responses such as periodic, multi-periodic, quasiperiodic and chaotic are observed for different values of excitation frequencies. In these studies, the NES damping is found to reduce the unstable band of the amplitude-frequency curves. Additionally, a fluid-structure interaction model examines the effect of NES on flow-induced vibration in a non-compliant viscoelastic PIP system subjected to VIV. Preliminary findings indicate that for some range of values of centralizer stiffness and fluid velocities, the oscillation amplitude of the PIP system is significant. Therefore, NES is used. About 98.95% reduction in amplitude is achieved using the NES for the inner fluid velocity range 𝑉2 ∈ (0.0, 2.5) where large oscillations persist. The findings also reveal a significant reduction in amplitude oscillations with NES utilization, attributed to out-of-phase oscillations between the PIP system and the wake oscillator. In addition to this, the NES reduces the lock-in regime in amplitudevortex velocity curves by approximately 25.04%. Nonlinear response analyses detect periodic, multi-periodic, and quasi-periodic responses at various points along the amplitude-VSF curve of the system. In summary, this comprehensive study investigates the application of NES in various engineering scenarios, demonstrating its effectiveness in mitigating vibration and enhancing structural stability across a wide range of conditions and excitation types. Some work in this study could be carried forward and can be useful to explore the capacity of NES for effective vibration attenuation in other engineering systems.