Special Topics in Structural Dynamics & Experimental Techniques, Volume 5

Future lightweight aircraft will increasingly rely on advances in lightweight, strong, highly damped, multifunctional composites. Increased damping capacity of these materials will grow in demand to ensure safe operations across adverse dynamic conditions. Traditional composite materials cannot provide this capability primarily due to a mismatch in the strength and stiffness between the fibers and hosting matrix. The purpose of this project is to design, fabricate, and test a damping material conceived as a cellular system, incorporating a periodic arrangement of tunable, non-linear, spider web-like absorbers. This novel approach proposes to produce a cellular material system incorporating an array of vibration absorbers to damp out structural-scale vibrations at the micro-scale level. The benefits include enhanced damping capacity with no weight penalty and tunability to maximize the kinetic energy transfer as required for the structure of interest. For this project, the USAFA team partnered with a team of researchers in Rome, Italy to create a macro-scale variant of a proposed carbon nanotube absorber system as a proof of concept. The team modeled, tuned, printed, and tested a structural-scale printed model of the repeating cellular system and showed an increase in damping ratio based on the tuned properties of the resonating structure.

Remote live sensor supervisory control and scenario prediction are vital aspects for asset management of deployed industrial systems. Additionally, this information can be used to schedule regular repairs and give advance warning to potentially harmful operational conditions to allow for risk mitigation procedures to be activated. This project presents some novel work in human–computer interaction via the remote sensing of a deployed structure. To demonstrate this work, modifications to DTOP-Cristallo is performed to remotely sense the acceleration of a three-storey structure. The implementation of the platform includes coding of Python, Html and Flask. With web page-based interface, the users can modify data acquisition parameters and investigate the current state of the structure. This remote sensing was performed using DTOP-Cristallo and the benchtop model of the three-storey structure deployed at the University of Sheffield.

Aerospace structures are often subjected to combined inertial acceleration and vibration environments during operation. Traditional qualification approaches independently assess a system under inertial and vibration environments but are incapable of addressing couplings in system response under combined environments. Considering combined environments throughout the design and qualification of a system requires development of both analytical and experimental capabilities. Recent ground testing efforts have improved the ability to replicate flight conditions and aid qualification by incorporating combined centrifuge acceleration and vibration environments in a “vibrafuge” test. Modeling these loading conditions involves the coupling of multiple physical phenomena to accurately capture dynamic behavior. In this work, finite element analysis and model validation of a simple research structure was conducted using Sandia’s SIERRA analysis suite. Geometric preloading effects due to an applied inertial load were modeled using SIERRA coupled analysis capability, and structural dynamics analysis was performed to evaluate the updated structural response compared to responses under vibration environments alone. Results were validated with vibrafuge testing, using a test setup of amplified piezoelectric actuators on a centrifuge arm.

Piezoelectric stack actuators can convert an electrical stimulus into a mechanical displacement, which facilitates their use as a vibration-excitation mechanism for modal and vibration testing. Due to their compact nature, they are especially suitable for applications where typical electrodynamic shakers may not be physically feasible, e.g., on small-scale centrifuge/vibration (vibrafuge) testbeds. As such, this work details an approach to extract modal parameters using a distributed set of stack actuators incorporated into a vibrafuge system to provide the mechanical inputs. A derivation that considers a lumped-parameter stack actuator model shows that the transfer functions relating the mechanical responses to the piezoelectric voltages are in a similar form to conventional transfer functions relating the mechanical responses to mechanical forces, which enables typical curve-fitting algorithms to extract the modal parameters. An experimental application consisted of extracting modal parameters from a simple research structure on the centrifuge’s arm excited by the vibrafuge’s stack actuators. A modal test that utilized a modal hammer on the same structure with the centrifuge arm stationary produced similar modal parameters as the modal parameters extracted from the combined-environments testing with low-level inertial loading.

As Structural Health Monitoring (SHM) being implemented more over the years, the use of operational modal analysis of civil structures has become more significant for the assessment and evaluation of engineering structures. Machine Learning (ML) and Deep Learning (DL) algorithms have been in use for structural damage diagnostics of civil structures in the last couple of decades. While collecting vibration data from civil structures is a challenging and expensive task for both undamaged and damaged cases, in this paper, the authors are introducing Generative Adversarial Networks (GAN) that is built on the Deep Convolutional Neural Network (DCNN) and using Wasserstein Distance for generating artificial labelled data to be used for structural damage diagnostic purposes. The authors named the developed model “1D W-DCGAN” and successfully generated vibration data which is very similar to the input. The methodology presented in this paper will pave the way for vibration data generation for numerous future applications in the SHM domain.

Like many mechanical systems hammer drills are subject to high-frequency external loading. For a proper design it is key to get a good grasp on the commonly encountered loads during operation. However, due to the strongly varying boundary conditions in which they are operated, e.g., hand-held, and the high-frequency range of interest model-based input estimation methods such as Kalman filtering are difficult to exploit for these applications. In this study, an impulse response matrix deconvolution approach has been adopted to estimate the impact forces applied to an existing hammer driller system. This approach relies purely on affordable sensor data for its setup, avoiding the need of calibration of complex numerical models. The impulse response procedure was validated against an experiment with complex boundary conditions with the objective of demonstrating the effectiveness of the method to retrieve accurate estimates in difficult-to-model configurations. The experiments result in high frequency excitations of the hammer and system responses with a high modal density, thus requiring a filter implementation with a high resolution to capture all the system dynamics and prevent numerical instabilities. The experimental responses used in the validation were time history data of strain and hammer impact force. The validation showed that the impulse response filter is superior to model-based estimation techniques and is quite robust to the system intrinsic non-linearities arising from complex damping mechanisms, wave propagation phenomena and boundary conditions.

Identification and modeling of joint dynamics is an important issue in the dynamic modeling of structures with joints. Moreover, structures connected by joints may show nonlinear behavior due to the existence of dry friction between the connected elements, especially at higher levels of vibration. Therefore, nonlinear identification of joints and parameterization of them is a necessary step in the dynamic analysis of structures. In this study, a new method is proposed for the identification of nonlinear joint forces as functions of relative responses in the frequency domain, which are used to model joint dynamics. In the proposed method, nonlinear joint forces are calculated by using both the measured nonlinear frequency responses of the system, and the calculated or measured linear frequency response functions (FRFs) of the substructures or calculated linear FRFs of the coupled structure at certain points by using estimated values for linear joint parameters. It is important to note that the proposed method does not require measurements at the connection DOFs, which is an advantage since it is generally not practical to make measurements at joints. To demonstrate the performance of the identification method proposed, as well as its sensitivity to measurement errors, two lumped parameter systems connected to each other by nonlinear elements are considered. In these case studies, simulated results representing experimental measurements are used. It is observed that the proposed method is robust to measurement noise, and nonlinear parameters of the connection can be identified accurately.

The non-destructive determination of internal forces in bars for existing building structures is a forward-looking challenge for the construction industry. The application of validated techniques would not only allow the detection of overloads or structural changes according to the load-bearing behavior, it would also allow the verification of the original structural analysis. Based on an experimental modal analysis, tried and tested methods to determine the tensile forces of cables in the operating condition have existed for many years. Due to the slenderness of the cables, even normal forces have a large influence on their natural frequencies: The higher the tensile forces, the higher the geometrical system stiffness, which increases natural frequencies. An equivalent effect occurs when considering load-bearing elements subjected to compression, whereby larger compressive forces lead to a reduction in the geometrical system stiffness and thereby to a reduction in natural frequencies. While various methods have been experimentally investigated for tension cables and tension rods, only a few elaborations are known with respect to structural compression rods. This research presents a system identification method based on the experimental determination of the modal parameters of a compression steel bar. Using an iterative optimization procedure, the design parameters of a basic model including the compressive force are iteratively adjusted until the best possible agreement between the experimental measurements and a theoretical analysis is found. For this purpose, a deviation function is formulated and an evolutional algorithm — in this case facilitating a Particle Swarm Optimization — is used to solve the optimization problem. The Particle Swarm Optimization is an innovative metaheuristic algorithm that allows searching for the global minimum even for complicated nonlinear functions. The method is experimentally validated on slender steel beams with varying compressive forces. Laboratory results from three different steel profiles combined with two different bearing conditions each are presented. Therefore, six specimens were constructed and tested with four different force levels each. The average deviation over all 24 tests between the optimized force and the actual force directly measured by a load cell was determined as 7.4%.

Multiple Input Multiple Output (MIMO) vibration testing provides the capability to expose a system to a field environment in a laboratory setting, saving both time and money by mitigating the need to perform multiple and costly large-scale field tests. However, MIMO vibration test design is not straightforward oftentimes relying on engineering judgment and multiple test iterations to determine the proper selection of response Degree of Freedom (DOF) and input locations that yield a successful test. This work investigates two DOF selection techniques for MIMO vibration testing to assist with test design, an iterative algorithm introduced in previous work and an Optimal Experiment Design (OED) approach. The iterative-based approach downselects the control set by removing DOF that have the smallest impact on overall error given a target Cross Power Spectral Density matrix and laboratory Frequency Response Function (FRF) matrix. The Optimal Experiment Design (OED) approach is formulated with the laboratory FRF matrix as a convex optimization problem and solved with a gradient-based optimization algorithm that seeks a set of weighted measurement DOF that minimize a measure of model prediction uncertainty. The DOF selection approaches are used to design MIMO vibration tests using candidate finite element models and simulated target environments. The results are generalized and compared to exemplify the quality of the MIMO test using the selected DOF.

This work presents a novel vibration damping approach for bladed structures. Piezoelectric transducers bonded to a structure can be used simultaneously as actuators and sensors to mitigate the vibrations of their host. This can be achieved by connecting a transducer to a digital vibration absorber composed of a voltage sensor, a digital processing unit and a current injector. The digital vibration absorber thereby emulates a piezoelectric shunt. In this study, this technique is applied to bladed structures featuring small modal damping and closely spaced resonance frequencies grouped in mode families. A strategy exploiting the high modal density is presented. Effective vibration mitigation is experimentally demonstrated on multiple mode families simultaneously.

Although automatic impact hammers are often used in dynamics and vibration research, they are seldom if ever used in resource-constrained environments such as undergraduate labs or in emerging nations. The cost of a commercially available automatic modal hammer, which typically costs more than USD 10,000, is the primary reason for the technology’s limited adoption. An inexpensive, automatic modal hammer could thus be useful in educational labs for studying dynamical systems. The goal of this research is to develop a low-cost, repeatable, and scalable automatic modal hammer. The study’s primary goal is to develop and test an open-source modal hammer for studying dynamical systems, including the ones which are strongly nonlinear. A standard modal hammer is mounted on the shaft of a stepper motor, with an encoder controlled by a hybrid servo drive and a microcontroller. The combination of the motor, servo drive, and encoder allows for micro-stepping and precise control of the motor shaft, and thus the motion of the modal hammer. The stepper motors used in this hammer are similar to those found in small 3D printers and CNC machines and are thus widely available and inexpensive. An airplane wing model with a non-smooth nonlinear vibration absorber is used to demonstrate the automatic hammer’s functionality.

This paper proposes a hybrid crack estimation technique that utilizes digital images from cameras and physics-based simulations to perform online diagnosis and prognosis of miter gate. To fully capture the localized effect of the crack, a global-local coupled finite element (FE) model is first created. An iterative global-local (IGL) algorithm is then developed to provide increased accuracy over sub-modelling at the expense of increased computational cost. To replace the process of solving the complex local FE, a Gaussian process (GP) surrogate model is further constructed to increase the computational efficiency. By interpolating the nodal displacement values collected from the surface around the crack, another GP surrogate model is developed to generate synthetic images similar to that obtained from cameras. The results demonstrate that the proposed method can efficiently predict the parameters of the crack growth model as well as to estimate the true crack length.

This chapter presents a hierarchical Bayesian framework for the system parameter identification of vibrating systems using spatially incomplete and noisy output-only response measurements. The parameters to be identified are treated as random variables, whose distributions are approximated by a finite number of evolving particles. For each realization of the parameters, an output-only Bayesian filter is employed for the unknown input and state estimation, creating thus a bank of filters that are recursively weighted, upon assimilation of the measurement information, and subsequently updated in order to narrow down the range of system parameters and converge to the target values.

pyFBS is an open-source Python package for frequency-based substructuring. The package implements an object-oriented approach for dynamic substructuring. This tutorial is intended to introduce structural dynamics and NVH engineers to the research toolbox in order to overcome vibration challenges in the future. The focus will be on experimental modeling and post-processing of datasets in the context of dynamic substructuring applications. The state-of-the-art methods of frequency-based substructuring, such as the virtual point transformation, the singular vector transformation, and system-equivalent model mixing, are available in pyFBS and will be presented. Furthermore, basic and application examples, as well as numerical and experimental datasets that are provided, are intended to familiarize users with the workflow of the package. pyFBS is demonstrated with two example structures. First, a simple beam-like structure is used to demonstrate how to start with the experimental modeling, FRF synthesis, virtual point transformation, and mixing of system equivalence models. Second, an automotive test structure is used to demonstrate the use of the pyFBS on a complex structure where in-situ transfer path analysis is used to characterize the blocked forces. This tutorial is intended to provide an informal overview of how research can be powered by open-source tools.

One of the easiest to observe conditions where waves occur in nature is the undulatory motion of aquatic animals and micro-organisms. In these bio-mechanisms, there is oscillatory locomotion which results in propulsion as the motion is accompanied by energy transfer from one end of the specimen or structure to the other end. Recent years have also seen a rise in the replication of the propulsive capabilities of these animals into aquatic robots. The use of smart materials to actuate and mimic the fin and tail characteristics of a fish has been attempted in various ways. Miniature robots actuated by piezoelectric materials have been effectively used for propulsion due to their simplicity and innovative actuating mechanism. These miniature robots find their application in the regime of underwater propulsion because of their size, flexibility, and ability to mimic fish locomotion. In most of these studies, the undulatory motion of these aquatic robots is achieved by discretizing the fin of the robot into multiple segments and synchronizing the oscillatory motion of individual segments to replicate continuous traveling waves. As a part of such endeavors, the present work attempts to use smart materials to actuate and mimic the fin motion characteristics of a fish. The bio-inspired design of the miniature robots consists of two brass shims supported by four piezoelectric bimorphs. The undulatory motion displayed by aquatic animals is mimicked by generating anechoic traveling waves in these brass fins. Anechoic traveling waves propagate in a structure without undergoing reflections at the structural boundaries. Such waves are generated by taking advantage of the structural dynamics of the fin under multi-input excitation.

Visualization of mode shapes is a crucial step in modal analysis. However, the methods to create the test geometry, which typically require arduous hand measurements and approximations of rotation matrices, are crude. This leads to a lengthy test set-up process and a test geometry with potentially high measurement errors. Test and analysis delays can also be experienced if the orientation of an accelerometer is documented incorrectly, which happens more often than engineers would like to admit. To mitigate these issues, a methodology has been created to generate the test geometry (coordinates and rotation matrices) with probe data from a portable coordinate measurement machine (PCMM). This methodology has led to significant reductions in the test geometry measurement time, reductions in test geometry measurement errors, and even reduced test times. Simultaneously, a methodology has also been created to use the PCMM to easily identify desired measurement locations, as specified by a model. This paper will discuss the general framework of these methods and the realized benefits, using examples from actual tests.