PROGRAMMABLE BANDGAPS IN META-STRUCTURES WITH DYNAMIC VIBRATION RESONATORS

Elastic wave propagation is controlled using metastructures with dynamic vibration resonators (DVRs). These meta-structures exhibit bandgaps whose location is determined by the attributes of the DVRs, especially their resonant frequency. However, in passive meta-structures, the bandgap location is fixed, which limits their ability to attenuate vibrations over a wide frequency range. To overcome this limitation, this study introduces a novel approach to achieve a wide programmable bandgap using a DVR with two states: high-frequency and low-frequency states. A new n-bit nomenclature for the meta-structure is introduced to absorb vibrations over a wide frequency bandwidth by switching between various n-bit configurations. The programmability of these meta-structures is assessed, and the results are validated with experiments. This novel approach allows for a wide programmable bandgap, which significantly improves the effectiveness of meta-structures in attenuating vibrations and acoustics over a broad frequency range. In conclusion, this study presents a new approach to achieving programmable bandgap meta-structures with dynamic vibration resonators, which can significantly improve their ability to mitigate vibrations and sound in various applications, including transportation, buildings, and machinery. This innovation has the potential to address several engineering challenges and contribute to the development of more efficient and effective NVH systems

ESTIMATION OF STRESS STATE IN AN AXIALLY LOADED BEAM USING MODAL DATA

Residual stresses are found to play a vital role in the dynamic behavior of the beam. These stresses are sometimes induced unintentionally due to manufacturing processes where temperate plays a role, while at other times, beams are subjected to stresses to alter their dynamic behavior for a particular application. Owing to the ubiquitous presence of the stressed beam, the estimation of its stress state becomes imperative to prevent structural failures. This study employs an approach to estimate the stress state of a beam from the natural frequencies and mode shapes. Using the modal data, the wave-numbers are calculated, and hence a dispersion relation is established. Modal analysis for a beam subjected to axial load is performed in a standard finite element software package, and the natural frequencies and the mode shapes are extracted. The analysis is performed for different values of loads, both compressive and tensile. The dispersion relation for the load cases is calculated, and the relationship between the wave-number, natural frequency, and load value is established using a curve-fitting approach. It was found that the discussed approach estimated the load value accurately. The discussed approach can be utilized to estimate the buckling of structures and stress states in a beam directly from the experimental data of the axially loaded beam

DATA-DRIVEN ESTIMATION OF BANDGAP FREQUENCIES IN METASTRUCTURES FOR ELASTIC WAVE ABSORPTION

This study investigates the elastic wave absorption behavior of metastructures in the bandgap frequency region. The bandgap region is estimated using data-driven methods based on the Frequency Response Function (FRF) of the unit cell of the metastructure. To achieve this, the unit cell is discretized using 1-D finite bar elements, and the numerical FRFs are calculated to dynamically link multiple unit cells using Component Mode Synthesis (CMS). The location of the bandgap is determined through the FRF of the multi-unit cell structure, which is referred to as Dynamically Linked Element Grade Oscillators (DLEGOs) due to the dynamic coupling between unit cells. The study also estimates the dispersion relation of the structure from the mode shapes of the finite structure. This approach is validated through the estimation of the bandgap from dispersion relations calculated using the traditional Finite Element Method. This comprehensive and validated method provides a way to estimate the edge frequencies of the bandgap in metastructures. The findings of this study contribute to the development of new metastructure designs that can inhibit elastic wave propagation in specific frequency ranges. Such designs have potential applications in various industries, including aerospace, defense, and transportation. In conclusion, this study highlights the importance of understanding the dynamic behavior of metastructures in modern engineering and their impact on various industries

Reinforcement Learning approach of switching bi-stable oscillators to adapt bandgaps of 1D-meta-structures

Meta-structures with dynamic vibrational resonators (DVRs) are programmed to control the propagation of waves and attenuate vibrations over a broadband frequency spectrum. Attributes of DVRs, such as their resonant frequency and mass, determine the location and width of the bandgap, respectively. As a result, to adaptively program bandgaps, one has to modify or tune the eigenvalues of individual DVRs, and a popular approach is to vary the stiffness of each resonator. However, the tunable range of bandgaps is often restricted to maximum change in DVRs’ stiffness. This work presents a novel approach to adaptively program bandgaps of a 1D flexural meta-structure over a broad frequency bandwidth. DVRs with two stable configurations are attached to a beam in developing the meta-structure. A numerical model is developed to illustrate the scope of the novel approach. An experimental investigation then validates the simulated results and shows the extent of the vibration absorption capabilities of the meta-structure. A reinforced learning approach is used to adaptively tune the bandgap over 220 Hz to 840 Hz

Vibration Control in Meta-Structures Using Reinforcement Learning

This chapter considers using reinforcement learning (RL) to adaptively tune frequency response functions of meta-structures. RL algorithm tunes the stiffness of the spring of the lumped multi-DOF system, as the lumped mass is varied. As some of the lumped masses are modified by 10%, the spring’s stiffness is tuned to maintain the original bandgap. A Q-Learning algorithm is used for RL, wherein the Q-value is updated based on Bellman’s equation. The results compare the frequency response functions of the terminal masses of the baseline and varied mass structure

Estimation of Elastic Band Gaps Using Data-Driven Modeling

The paper discusses estimation of elastic band gaps of a one-dimensional periodic structure using the frequency response functions (FRFs) of a unit cell. A unit cell considered in this paper consists of two masses with a spring between them. Such unit cells are connected with a coupled spring to design a periodic lattice structure. The paper establishes the FRF for a different number of unit cells using FRF-based sub-structuring (FBS). The wave-equation method is then used to estimate the dispersion curves and eventually band gaps. The paper follows a data-driven modeling approach to develop state-space models for estimating dispersion curves from FRFs. The vector fitting algorithm creates a data-driven model of the unit cell from noisy FRFs. A multi-unit cell lattice is simulated from data-driven models using FBS. Additionally, the paper investigates tuning of elastic band gaps by changing the mass and the stiffness of the unit cells

Vibration Isolation in 3D Printer Using Meta-Structures

Reducing vibrations in a 3D printer is crucial in improving the quality of printed prototypes. Ideally, the noise from the actuators in 3D printers should not hinder the print quality. However, isolating the printer surface from vibrations is challenging. Therefore, in this paper, a novel vibration-isolating frame is designed for building a novel 3D printer. Such a structure would absorb external vibrations and isolate the print-plate, thereby improving the print quality. The proposed frame is a meta-structure that absorbs vibrations over a frequency bandwidth. The structure is built with assembling multiple identical unit cells. Each unit cell is an assembly of 1D beams of varying cross-sections. The current paper’s objective is to design a fame that produces in-plane and out-of-plane bandgaps. Finite element models iterate over multiple designs, which are validated in the lab through robust experimentation. The paper discusses the design methodology and the corresponding results

Modeling of Hysteresis Effect of SMA using Neuro Fuzzy Inference System

Hysteresis is the dependence of a physical property, not only on the present controlled parameters, but also on the path travelled. Although Shape Memory Alloys (SMAs) exhibit a myriad of nonlinearities, SMAs show two major types of nonlinear hysteresis. During cyclic loading of the SMAs, it is observed that one type of hysteretic behavior depends on the rate of heating the SMAs, whilst the variation of maximum temperature of SMA in each cycle results in the other hysteretic behavior. This hysteretic behavior gives rise to major and minor nonlinear loops of SMAs. The present work analyzes the nonlinearities of hysteretic envelopes, given the different maximum temperature reached for each hysteretic cycle on the strain of the SMA. This work then models this behavior using Adaptive Neuro Fuzzy Inference System (ANFIS) and compares it to experimental results. The nonlinear learning and adaptation of ANFIS architecture makes it suitable to model the temperature path hysteresis of SMAs

PARAMETRIC-FEEL ALGORITHM: DEVELOPING A PARAMETRIC VECTORFITTING MODEL FOR EVENT LOCALIZATION IN CALIBRATED STRUCTURES

For smart structures, especially in the context of human activity, the force exerted and the location it happened is of significant relevance. This paper revisits and improves the performance in localizing and characterizing an input force with precalibrated structures through vibration measurement. The Force Estimation and Event Localization (FEEL) Algorithm have been discussed as a means of calculating the force of an impact and pinpointing its location. Unlike other time-of-flight approaches, FEEL does not require time synchronization, instead using transfer functions between possible impact locations and sensor locations to estimate force and localize impact. However, this approach is limited to locations where transfer functions are available. To overcome this limitation, a rowing hammer test was used to determine Frequency Response Functions (FRFs) at various points on a beam with a uniform rectangular cross-section. The Vector-Fitting algorithm was then used to improve the FRF approximation by moving poles to more advantageous locations, enhancing convergence, and lowering noise. Using the curve fitting approach, residues and FRFs were interpolated for additional locations. The extended FEEL algorithm was then used to localize impacts and estimate forces at these additional locations. This method can be used in applications such as tracking customer movement in retail establishments, detecting falls, tracking rehabilitation progress, and estimating building occupancy