Estimation of elastic bandgaps in metastructures: A comparison of physics-based and data-driven approaches

Metastructures are an emerging solution for applications in aerospace, industry, and robotics, as they inhibit the propagation of elastic waves within a specific frequency range called the “bandgap”. Accurate estimation of bandgaps is crucial for optimizing metastructures for specific purposes. Two approaches have been traditionally used: physics-based modeling, which requires precise characterization of the unit cell\u27s physical properties, and data-driven methods based on steady-state dynamic response. This study compares the effectiveness of data-driven methods (Component Mode Synthesis and FRF-Based Substructuring) with traditional physics-based methods for identifying bandgaps in multi-unit cell metastructures. We also validate the identified bandgaps using experimental reading-based methods. Our goal is to determine a more efficient and accurate approach for identifying bandgaps in metastructures, with potential implications across various fields

Band Gap Estimation of D-LEGO Meta-structures Using FRF-Based Substructuring and Bloch Wave Theory

Periodic structures are found to exhibit band gaps which are frequency bandwidths where structural vibrations are absorbed. In this paper, meta-structures are built by dynamically linking oscillators in a periodic pattern, which are referred to as dynamically linked element grade oscillators or D-LEGOs. The location of the band gaps is numerically determined for a one-dimensional D-LEGO. The unit cell for the D-LEGO structure is considered to be made up of two longitudinal bar elements of different properties. For such a structure, the frequency response functions (FRFs) of a single unit cell are used to estimate the band gaps of a periodic-lattice structure by adapting the Bloch wave theory. Alternatively, the FRF of the multi-unit cell is determined using FRF-based substructuring (FBS) approach. The band gaps resulting from these two approaches are compared and verified

A data-driven approach to the impedance matched multi-axis test method

Environmental testing is critical in certifying systems to operate and survive in harsh vibration environments. An example of this would be cargo rockets destined to deliver supplies to a low-earth orbiting space station. Aerodynamic effects would impose a distributed random excitation load onto the cargo rocket. It is imperative that test engineers perform an environmental test to replicate, as best as possible, the anticipated vibration loads on the rocket without subjecting it to the actual operational environment. Traditional in-lab environmental tests have shown to poorly reproduce the true response of a system subjected to distributed excitation loads. In recent literature, the Impedance Matched Multi-Axis Test (IMMAT) was developed to mitigate some of the current limitations of environmental tests through the use of finite element models (FEM) and multi-input multi-output (MIMO) control. As an extension of IMMAT, the present work investigates the use of a data-driven approach to supplement the creation of a numerical model used to predict optimal excitation locations and forces. The main advantage of this alternative approach to IMMAT removes the need for a FEM of the system being tested. This extends IMMAT to cases where a model of the subject being tested is not readily available and, yet, provides an opportunity for IMMAT to be deployed for certification. Additionally, a data-driven approach has the potential to capture more realistic test parameters, such as hard-to-recreate boundary conditions, material properties, and optimal excitation locations, as it is built directly from test data. There may be cases where this is advantageous, but may require better test designs. A preliminary numerical simulation is implemented to test the effectiveness and practicality of using vector fitted accelerance frequency response functions (FRF) to perform IMMAT

Expanding the teaching of single frequency vibration absorption to broadband attenuation using subordinate oscillator arrays via fettuccine pasta

Dynamic vibration absorbers (DVAs) and tuned mass-dampers (TVAs) have wide-spread applications in the aerospace industry, the automotive sector, and in civil engineering structures. There are numerous designs of active and passive vibration attenuators or absorbers that isolate structural vibrations at or around the desired frequency. All these design approaches are fundamentally different ways to modify and tune the placement of the resonant frequencies of the host structure. The current work presents a novel method to passively attenuate vibration over a broad frequency bandwidth in the presence of uncertainty. An array of linear oscillators, also referred to as subordinate oscillator arrays (SOAs), are attached to a two-degrees-of-freedom structure to produce an attenuated broadband frequency response around a target frequency. SOAs can also be interpreted as an array of DVAs and in some categories, they can be considered as an approach to meta-structures. Another objective of the current work is to develop a hands-on approach to extend classroom teaching of vibration-attenuation using SOAs made out of fettuccine strands and modeling clay. The frequencies of the oscillators in the array are tuned by varying the length of each strand and the mass of the modeling clay attached to its tip. Uncertainty in dynamic properties of such oscillators often results in mistuned SOAs with non-uniform frequency response function. Therefore, designing and testing fettuccine-based SOAs allows students to handle cases when structural uncertainties arise in engineering systems. Additionally, some of the work in the field of meta-structures can be modeled and represented by SOAs and this will provide a straight forward way to teach students some of these contemporary concepts

Estimating experimental dispersion curves from steady-state frequency response measurements

Dispersion curves characterize the frequency dependence of the phase and the group velocities of propagating elastic waves. Many analytical and numerical techniques produce dispersion curves from physics-based models. However, it is often challenging to accurately model engineering structures with intricate geometric features and inhomogeneous material properties. For such cases, this paper proposes a novel method to estimate group velocities from experimental data-driven models. Experimental frequency response functions (FRFs) are used to develop data-driven models, which are then used to estimate dispersion curves. The advantages of this approach over other traditionally used transient techniques stem from the need to conduct only steady-state experiments. In comparison, transient experiments often need a higher-sampling rate for wave-propagation applications and are more susceptible to noise. The vector-fitting (VF) algorithm is adopted to develop data-driven models from experimental in-plane and out-of-plane FRFs of a one-dimensional structure. The quality of the corresponding data-driven estimates is evaluated using an analytical Timoshenko beam as a baseline. The data-driven model (using the out-of-plane FRFs) estimates the anti-symmetric (A0) group velocity with a maximum error of 4% over a 40 kHz frequency band. In contrast, group velocities estimated from transient experiments resulted in a maximum error of 6% over the same frequency band