Nonlinear Model Updating in Structural Dynamics

Identification of nonlinear structural dynamics has received a significant attention during last decades. Yet, there are many aspects of the identification methods of nonlinear structural models to be improved. The main objective of this study is to introduce novel identification approaches for nonlinear structures. The first step in identifying nonlinear structural elements is to detect their exact location. Hence, the first section of this study focuses on the localization of nonlinear elements in structural dynamics utilizing base excitation measured data. To this end, a localization approach is used to find the location of nonlinear electromagnetic restoring force applied to the tip of a cantilever beam.Inferring the exact location of nonlinear elements, identification methods are utilized to identify and characterize the mathematical model of nonlinear structures. However, various sources of noise and error may affect the accuracy of the identified model. Therefore, in the second part of the thesis, the effect of various sources of inaccuracy on the results of nonlinear model identification is investigated. It is shown that measurement noise, expansion error, modelling error, and neglecting the effect of higher harmonics may lead to an erroneously identified model.An optimization-based framework for the identification of nonlinear systems is proposed in this work in order to avoid the bottlenecks mentioned above. The introduced method is applied to a test rig composed of a base-excited cantilever beam subjected to an electromagnetic force at the tip. According to the nonlinear response of the system, four different functions are assumed as candidate models for the unknown nonlinear electromagnetic force. The measured response is compared with the reconstructed response using various models and the most appropriate mathematical model is selected.Utilizing optimization-based identification method to characterize complex mathematical models with large number of unknown parameters would be computationally expensive. Therefore, this study introduces a harmonic-balance-based parameter estimation method for the identification of nonlinear structures in the presence of multi-harmonic response and force. For this purpose, a method with two different approaches are introduced: Analytical Harmonic-Balance-based (AHB) approach and the Alternating Frequency/Time approach using Harmonic Balance (AFTHB). The method is applied to five simulated examples of nonlinear systems to highlight different features of the method. The method can be applied to all forms of both smooth and non-smooth nonlinear functions. The computational cost is relatively low since a dictionary of candidate basis functions is avoided. The results illustrate that neglecting higher harmonics, particularly in systems with multi-harmonic response and force, may lead to an inaccurate identified model. The AFTHB approach benefits from including significant harmonics of the response and force. Applying this method leads to accurate algebraic equations for each harmonic, including the effect of higher harmonics without truncated error. In the last part of this study, the AFTHB method is applied to two experimental case studies and identifies the nonlinear mathematical model of the structures. The first case is composed of a cantilever beam with a nonlinear electromagnetic restoring force applied to the tip which is excited by a multi-harmonic external force. In the second experimental case study, a configuration of linear springs applies a geometric nonlinear restoring force to the tip of a cantilever beam resulting in internal resonance in the dynamics of the system. The good performance of the AFTHB approach in estimating the unknown parameters of the structure is illustrated by the results of identification

Bifurcation analysis and nonlinear dynamics of a capacitive energy harvester in the vicinity of the primary and secondary resonances

The objective of the present study is to examine the effect of nonlinearity on the efficiency enhancement of a capacitive energy harvester. The model consists of a cantilever microbeam underneath which there is an electret layer with a surface voltage, which is responsible for the driving energy. The packaged device is exposed to unwanted harmonic mechanical excitation. The microbeam undergoes mechanical vibration, and accordingly, the energy is harvested throughout the output electric circuit. The dynamic formulation accounts for nonlinear curvature, inertia, and nonlinear electrostatic force. The efficiency of the device in the vicinity of the primary and super-harmonic resonances is examined, and accordingly, the output power is evaluated. Bifurcation analysis is carried out on the dynamics of the system by detecting the bifurcations in the frequency domain and diagnosing their respective types. One of the challenging issues in the design and analysis of energy-harvesting devices is to broaden the bandwidth so that more frequencies are potentially accomodated within the amplification region. In this study, the effect of the nonlinearity on the bandwidth broadening, as well as efficiency improvement of the device, are examined. It is seen that as the base excitation amplitude increases, the vibration amplitude does also increase and accordingly the nonlinearity dominates. The super-harmonic resonance regions emerge and get bigger as the vibration amplitude increases, and pull-in gaps appear in the frequency response curves

Tailored twist morphing achieved using graded bend–twist metamaterials

This work develops a morphing concept that utilises a metamaterial as the passive morphing device for helicopter blades. The metamaterials are created with bend–twist coupling, which enable the blade twist under prescribed bending loads. Finite element analysis (FEA) is performed to investigate the influence of the unit cell configurations on the coupling properties of the metamaterials. The numerical models are then validated experimentally through a set of bending tests conducted with additively manufactured prototypes. Finally, the validated model is used to design a graded metamaterial, where the cell aspect ratio gradually changes along the blade span, providing unique bend–twist coupling and allowing for tailored twist to be obtained. The results suggest the graded metamaterials are capable of introducing optimised nonlinear twists to the blade during different flight conditions including both hover and forward flight

Resonant passive energy balancing of morphing helicopter blades with bend–twist coupling

With increasing demand for rotor blades in engineering applications, improving the performance of such structures using morphing blades has received considerable attention. Resonant passive energy balancing (RPEB) is a relatively new concept introduced to minimize the required actuation energy. This study investigates RPEB in morphing helicopter blades with lag–twist coupling. The structure of a rotating blade with a moving mass at the tip is considered under aerodynamic loading. To this end, a three-degree-of-freedom (3DOF) reduced-order model is used to analyse and understand the complicated nonlinear aeroelastic behaviour of the structure. This model includes the pitch angle and lagging of the blade, along with the motion of the moving mass. First, the 3DOF model is simplified to a single-degree-of-freedom model for the pitch angle dynamics of the blade to examine the effect of important parameters on the pitch response. The results demonstrate that the coefficient of lag–twist coupling and the direction of aerodynamic moment on the blade are two parameters that play important roles in controlling the pitch angle, particularly the phase. Then, neglecting the aerodynamic forces, the 3DOF system is studied to investigate the sensitivity of its dynamics to changes in the parameters of the system. The results of the structural analysis can be used to tune the parameters of the blade in order to use the resonant energy of the structure and to reduce the required actuation force. A sensitivity analysis is then performed on the dynamics of the 3DOF model in the presence of aerodynamic forces to investigate the controllability of the amplitude and phase of the pitch angle. The results show that the bend–twist coupling and the distance between the aerodynamic centre and the rotation centre (representing the direction and magnitude of aerodynamic moments) play significant roles in determining the pitch dynamics

An Optimization-Based Framework for Nonlinear Model Selection and Identification

This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses at the measured coordinates of the nonlinear structure. The application of the method is demonstrated on a clamped beam subjected to a nonlinear electromagnetic force. In the proposed method, the assumption is that the form of nonlinear force is not known. For this reason, one may assume that any nonlinear force can be described using a Taylor series expansion. In this paper, four different possible nonlinear forms are assumed to model the electromagnetic force. The parameters of these four nonlinear models are identified from experimental data obtained from a series of stepped-sine vibration tests with constant acceleration base excitation. It is found that a nonlinear model consisting of linear damping and linear, quadratic, cubic, and fifth order stiffness provides excellent agreement between the predicted responses and the corresponding measured responses. It is also shown that adding a quadratic nonlinear damping does not lead to a significant improvement in the results

Comparison of Three Commonly Used Genetic Markers for Detection of Leishmania Major: An Experimental Study

BACKGROUND፡ Leishmaniasis is a vector-borne disease caused by an intracellular protozoan parasite called Leishmania spp. Different species produce different clinical outcomes; the majority of cases are cutaneous forms. Leishmania major is one of the main causative agents of cutaneous leishmaniasis (CL). Various methods are being using to diagnose CL, including microscopic examination, culture, and molecular detection of the parasite genome.METHOD: In the current study, we tried to compare three common molecular markers, including Kinetoplast DNA (kDNA), Cytochrome b (Cyt b), and Internal transcribed space 1 (ITS1), for the detection of Leishmania major. After cultivation of standard strain of L. major MHOM/IR/75/ER in RPMI 1640, certain number of promastigotes was subjected to DNA extraction and different PCR reactions.RESULTS: The lowest number of the parasite (5 promastigotes) can be detected by kDNA-PCR, followed by Cyt b-PCR (10 promastigotes), and ITS1-PCR (50 promastigotes).CONCLUSION: In conclusion, kDNA-PCR was the most sensitive marker and may provide more reliable data in the initial screening, especially in false-negative results provided by parasitological methods due to the low number of parasites

Harmonic-Balance-Based parameter estimation of nonlinear structures in the presence of Multi-Harmonic response and force

Testing nonlinear structures to characterise their internal nonlinear forces is challenging. Often nonlinear structures are excited by harmonic forces and yield a multi-harmonic response. In many systems, particularly ones with strong nonlinearities, the effect of higher harmonics in the force and responses cannot be ignored. Even if the intended excitation is a single frequency sinusoidal force, the interaction of the shaker and the nonlinear structure can lead to harmonics in the applied force. The effects of these higher harmonics of the input force on nonlinear model identification in structural dynamics are often neglected. The objective of this study is to introduce an identification method, motivated by the alternating frequency/time approach using harmonic balance (AFTHB), which is able to consider both multi-harmonic forces and multi-harmonic responses of the system. The proposed AFTHB method can include all significant harmonics by selecting an appropriate time step and sampling frequency to guarantee the accuracy of the results. An analytical harmonic-balance-based (AHB) approach is also considered for comparison. However, the inclusion of all significant harmonics of the response in the analytical expansion of the nonlinear functions is often cumbersome. Furthermore, the AFTHB method can easily cope with complex nonlinearities such as Coulomb friction and with multi-degree of freedom nonlinear systems. Including the effect of higher harmonics in the identification process reduces the approximation error due to truncation and very accurate approximation of the balanced equations of each harmonic is obtained. The proposed identification method requires prior knowledge or an appropriate estimation of the type of system nonlinearities. However, the method of model selection may be used for a set of candidate models, and avoiding a dictionary of arbitrary candidate basis functions significantly reduces the computational costs. This paper highlights the important features of the AFTHB method to ensure accurate estimation using four simulated and two experimental examples. The effects of the number of harmonics considered, the modelling error, measurement noise and the frequency range on the quality of the estimated model are demonstrated

A novel pathogenic variant in the MARVELD2 gene causes autosomal recessive non-syndromic hearing loss in an Iranian family

BACKGROUND AND AIMS: Hearing loss (HL) is the most common sensorineural disorder and one of the most common human defects. HL can be classified according to main criteria, including: the site (conductive, sensorineural and mixed), onset (pre-lingual and post-lingual), accompanying signs and symptoms (syndromic and non-syndromic), severity (mild, moderate, severe and profound) and mode of inheritance (Autosomal recessive, autosomal dominant, X-linked and mitochondrial). Autosomal recessive non-syndromic HL (ARNSHL) forms constitute a major share of the HL cases. In the present study, next-generation sequencing (NGS) was applied to investigate the underlying etiology of HL in a multiplex ARNSHL family from Khuzestan province, southwest Iran. METHODS: In this descriptive study, 20 multiplex ARNSHL families from Khuzestan province, southwest of Iran were recruited. After DNA extraction, genetic linkage analysis (GLA) was applied to screen for a panel of more prevalent loci. One family, which was not linked to these loci, was subjected to Otogenetics deafness Next Generation Sequencing (NGS) panel. RESULTS: NGS results showed a novel deletion-insertion variant (c.1555delinsAA) in the MARVELD2 gene. The variant which is a frameshift in the seventh exon of the MARVELD2 gene fulfills the criteria of being categorized as pathogenic according to the American College of Medical Genetics and Genomics (ACMG) guideline. CONCLUSION: NGS is very promising to identify the molecular etiology of highly heterogeneous diseases such as HL. MARVELD2 might be important in the etiology of HL in this region of Iran

On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error

The objective of this study is to investigate the sensitivity of the Equivalent Dynamic Stiffness Mapping (EDSM) identification method to typical types of inaccuracy that are often present during the identification process. These sources of inaccuracy may include the presence of noise in the simulated/measured data, expansion error in the estimation of unmeasured coordinates, modelling error in the updated underlying linear model, and the error due to neglecting the higher harmonics in the nonlinear response of the system. An analytical study is performed to identify the structural nonlinearities of two nonlinear systems, a discrete three-DOF Duffing system and a cantilever beam with a nonlinear restoring force applied to the tip of the beam, considering the presence of all the aforementioned sources of inaccuracy. First, the EDSM technique is utilized to identify the nonlinear elements of two example systems to verify the accuracy of the EDSM technique. Finite Element modelling, the Modified Complex Averaging Technique (MCXA), and arc-length continuation are exploited in this study to obtain the steady state dynamics of the nonlinear systems. Numerical models of the two systems are then simulated in MATLAB and the numerical results of the simulation are used to identify the unknown nonlinear elements using the EDSM technique and investigate the effect of different sources of error on the outcome of the identification process. The nonlinear response of the system has been regenerated using the identified parameters with the sources of error present and the generated response has been compared to the simulated response in the absence of any noise or error. The EDSM technique is capable of identifying accurately the nonlinear elements in the absence of any source of inaccuracy although, based on the results, this method is highly sensitive to the aforementioned sources of inaccuracy that results in significant error in the identified model of the nonlinear system. Finally, an optimization-based framework, developed by the authors, is utilized to identify the nonlinear cantilever beam and the results are compared with the results of the EDSM technique. It is shown that by using the optimization method, the inaccuracy due to different sources of noise and error is significantly reduced. Indeed, by using the optimization method, the necessity to use an expansion method and consider the higher harmonics of the response is eliminated