Eigenfrequency Analysis Research Articles

Effect of scatterer shape, opening angle and periodicity on sound attenuation by local resonating sonic crystal

Noise Control has become critical and demanding task for acoustic engineers due to continuous Technological developments in construction, transportation, and industries. These developments have raised the level of low frequency noise in densely populated areas. Unfortunately, there cannot be sufficient noise reduction with traditional acoustic materials. However, new research has shown that the manipulation of sound waves and drastic reduction in sound transmission can be possible using periodic structure known as Sonic Crystals (SnC). This study describes the eigenfrequency analysis to investigate the effect of different shapes, periodicities, and opening angles of scatterers in a Local resonating Sonic Crystal (LRSnC). The Block-Floquet boundary condition is applied to the unit cell of the LRSnC, using the Finite Element Method to study the complex acoustic wave interactions throughout the structure. An acoustic module has been applied to find the band gap and to simulate transmission loss spectra in COMSOL Multiphysics. Results show that shape, opening angle and periodicity effect the band gap and transmission loss significantly. Based on these results, it is possible to develop advanced SnC with a wider band gap and higher sound attenuation in the lower sound frequency range by carefully considering these factors.

Generalized model for eigenfrequency analysis of bolted variable-stiffness flanged-cylindrical shells

A general semi-analytical modeling method for the bolted variable stiffness composite cylindrical shell, incorporating precise modeling of the boundary and connecting flanges, is proposed in this paper. The coupling between shells and flanges is achieved through a spring-based penalty function method. A novel bolted joint model for flange connections is introduced, enabling the simulation of non-uniform pressure distributions at the joint interface. The joint model features a stiffness characterization technique that effectively improves adjustability and computational efficiency. The correctness and accuracy of the proposed modeling method are systematically validated through finite element analysis based on the ANSYS commercial software and experimental testing approaches. The series of parameter influence analyses on the bolted variable stiffness composite cylindrical shell with flanges, conducted using the proposed modeling method, accurately demonstrate the influence of geometric dimensions, fiber layup parameters, and bolt parameters on the free vibration behavior of such structures. Furthermore, these analyses aid in a deeper understanding of the dynamic characteristics of such structures, partially highlighting key design considerations and offering valuable guidance for their dynamic optimization design.

Eigenfrequency analysis using fiber optic sensors and low-cost accelerometers for structural damage detection

Structural Health Monitoring (SHM) is crucial for infrastructure safety and integrity. Arduino-based sensors are gaining popularity in low-cost SHM structures. Distributed fiber optic systems (DFOS), such as Distributed Acoustic Sensing (DAS), are employed for accurate SHM despite their high costs, computational demands, and energy consumption. The primary objectives of this work are to compare the accuracy of an accelerometer named LARA (Low-cost Adaptable Reliable Accelerometer (LARA)) that utilizes both Arduino and Raspberry Pi technologies with a DAS system in detecting structural damage and to explore the potential advantages of combining LARA and DAS to create an effective SHM tool. This study is the first to enhance the design of LARA. Subsequently, LARA and DAS were used in a laboratory setting to analyze eigenfrequency changes in a beam model with induced localized damage. Finally, this study evaluated the precision and reliability of LARA and its potential role as a trigger for DAS in detecting localized damage. The findings show that both LARA and DAS can identify changes in the eigenfrequencies of damaged structures with deviations as small as 3.68 %. Consequently, LARA demonstrated its potential as a trigger for DAS, significantly reducing the computational demands while enriching the analysis. This approach offers highly accurate eigenfrequency measurements and enhances the analytical capabilities of DAS by identifying the primary axes of the detected eigenfrequencies.

Modal spectrum analysis for an imperfect beam model with random vibration

The cross-Spectral Density (SD) is a method of analyzing the relationship between randomly-input forces and their responses in the frequency domain in spectrum analysis. It is essential for analyzing antiresonant eigenfrequencies that are difficult to understand using only direct-SD. Additionally, the mass in a beam is often analyzed in modern engineering to control the vibration characteristics of a simple beam or as a major model for error. Especially, the scalability can be expected in various fields such as nanosensors as well as macroscopic scale by studying imperfect mass. Firstly, the correlation function and SD are defined for an arbitrary vibration input in a beam. Then, the response function is established according to a harmonic input of some unit force amplitude. Moreover, the direct- and cross-SDs for the response are calculated and mathematically compared with both results. Further analysis is performed by comparing the variation of the SD with response position, the standard deviation (StDev) of the mean of maximum responses, and the bandwidth. The developed cross-SD of the imperfect beam extends the previously developed SD models of the perfect beam and can provide ideas for new types of eigenfrequency analysis, vibration isolation, etc.

Tunable elastic wave transmission and resonance in a periodically aligned tube-block structure

A tube-block structure is proposed to realize tunable elastic wave transmission and resonance, consisting of periodically aligned circular tubes sandwiched and joined by two blocks. Finite element simulations for a unit structure are carried out to reveal the frequency dependence of the transmission behavior for the normal incidence of longitudinal and transverse waves in the tube-block structure. As a result, the transmission ratios are found to take multiple local maxima at different peak frequencies. Eigenfrequency analysis shows that the local resonances of the tube and the block surfaces occur at the peak frequencies in the transmission ratios. The peak frequencies originating from the local resonance of the tube depend on its radius and thickness, while those from the resonance on the block surfaces are in good agreement with the theoretical relation between the interval of the periodically aligned tubes and the wavelength of the Rayleigh wave. Furthermore, when the tube-block structure is subjected to compressive loading, the deformation shifts the peak frequencies of the transmission ratio corresponding to the local resonance of the tube. This result implies that the proposed structure has the potential to serve as a tunable meta-interface between solid blocks.

A novel multi-step superposition model for the dispersion analysis of multiaxial prestressed plate-like structures

Understanding the dispersion characteristics of multi-axial prestressed plate-like structures is crucial for the engineering application of guided wave non-destructive testing. However, existing analytical and semi-analytical models neglect both constitutive and geometric nonlinearities induced by the prestress and require tedious theoretical derivation and coding, which may not achieve accurate predictions. To address these issues, a convenient model based on the multi-step superposition analysis was proposed to investigate the effects of an arbitrary multiaxial prestress on the dispersion characteristics of plate-like structures. The core idea of this model involves introducing an initial configuration to describe the static pre-deformation between undeformed and final states; then, the dynamic wave motion was superimposed on the initial pre-deformation for the eigenfrequency analysis. Additionally, the strain energy density of the hyperelastic material was implanted and set as the relevant variable between the two steps by the inheritance of the solution. This model significantly improved the accuracy compared to the conventional method, as validated through biaxial acoustoelastic experiments. Subsequently, the acoustoelastic responses of the multiaxial prestressed 6061-T6 aluminum plate were investigated. The results reveal that the non-uniform in-plane prestress leads to the coupling of guided wave modes propagating along non-principal directions. Furthermore, the effects induced by multiaxial prestress in the frequency bands with low dispersion could be decomposed into the sum of the effects induced by three uniaxial prestresses with a very small deviation. This work provides new insights into the acoustoelastic behavior and a theoretical basis to optimize the guided wave mode and frequency.

Simulation-based approach to estimate influencing factors on acoustic resonance spectra of additively manufactured mechanical metamaterials

Acoustic Resonance Testing is a nondestructive testing method based on the analysis of eigenfrequencies of structures. While it is a well-established technique for conventionally manufactured parts, more research is needed to use the technique to quantify the properties of complex, filigree structures like additively manufactured parts. Therefore, this work examines simulation-based generation of synthetic data to estimate influencing factors caused by additive manufacturing. Using numerical eigenfrequency analysis, a systematic study of the vibration modes of a Ti6Al4V metamaterial unit cell with multistable mechanical behaviour reveals the interplay between the material properties, geometrical parameters and manufacturing-induced defects. The simulations enable the identification of specific eigenfrequencies for which the highest influence of manufacturing variations on the vibration modes are to be expected in experiments, for example, with regards to the Young’s modulus, spring width, or deflection-induced change in geometry. Frequency shift plots visualize the predicted effects of different parameters and form the basis for future guided experimental design and analysis for complex structures. The simulation-based approach allows a screening of multiple influencing factors, which is not possible experimentally. The simulation-based generation of synthetic data will contribute to the improvement of the interpretation of acoustic spectra and will extend the acoustic resonance testing for more complex structures.

All‐Polarized Elastic Wave Attenuation and Harvesting via Chiral Mechanical Metamaterials

AbstractManipulating elastic waves of all polarizations is highly challenging due to the complex behavior of elastic waves. To achieve simultaneous broadband vibration attenuation and energy harvesting across all polarizations of elastic waves at low‐frequency ranges, a chiral mechanical metamaterial‐based energy harvester is proposed in this study. The systematic development of a complete bandgap and defect structure is achieved through theoretical eigenfrequency analysis and numerical simulations. The defect structure is incorporated to induce defect modes for all wave polarizations within the complete bandgap region, ensuring their compatibility with the overall shape of the structure. The proposed chiral mechanical metamaterial with defect (CMMD) demonstrated significant performance improvements, achieving electrical output power enhancements that are 20.5 times for flexural waves and 511.4 times for longitudinal‐torsional waves compared to the defectless chiral mechanical metamaterial. This study accentuates the thoughtful design and multifaceted utility of chiral mechanical metamaterials, paving the way for their application not only in energy harvesting but also in wave attenuation for various polarizations.

STODOLA-VIANELLO ITERATION METHOD FOR FREE TORSIONAL VIBRATION ANALYSIS OF MONOSYMMETRIC BOX-BEAM BRIDGES

Box-beam bridges are used in large spans and wider decks due to their high strength and greater torsional and flexural stiffness. They are usually prone to vibration due to moving vehicular traffic. Their eigenfrequency analysis is a crucial aspect of their design in order to ensure that the natural frequency is not close to the excitation frequency to avert resonance failures. The free torsional vibration equation is a fourth order partial differential equation (PDE) with variable parameters. For prismatic cross-sections, homogeneous and isotropic materials the governing PDE have constant parameters. This paper explores the Stodola-Vianello iteration method (SVIM) for solving the PDE for isotropic, homogeneous prismatic box-beams. Harmonic response is assumed, decoupling the PDE to two equations, one in terms of time and the second an ordinary differential equation (ODE) in terms of space coordinates. The Stodola-Vianello method is used by the method of four successive integrations to express the ODE as an algebraic iteration problem with four constants of integration. The four boundary conditions are used to solve for the four constants of integration, thus making the problem determinate. Application of the boundary conditions results in the full determination of the iteration equations. For simply supported boundaries studied in the work, a trigonometric buckling shape function that satisfies all the boundary conditions is employed in the SVIM formula to obtain the next bucking modal shape function. The requirement for convergence is then used to establish the characteristic buckling equation from which the eigenvalues are obtained. The solution to the characteristic buckling equation gave the exact mathematical expression for the natural torsional frequency at the nth vibration mode. The frequencies are determined for the first eight vibration modes and compared with previously obtained values. It was found that the natural frequencies are identical with previously found values of the exact natural frequencies. The natural frequency obtained is exact because it satisfies the PDE and the boundary conditions at all points in the domain.

A reduced-order-model-based equivalent circuit for piezoelectric micro-electro-mechanical-system loudspeakers modeling.

Piezoelectric micro-electro-mechanical-system (MEMS) speakers are emerging as promising implementations of loudspeakers at the microscale, as they are able to meet the ever-increasing requirements for modern audio devices to become smaller, lighter, and integrable into digital systems. In this work, we propose a finite element model (FEM)-assisted lumped-parameters equivalent circuit for a fast and accurate modeling of these types of devices. The electro-mechanical parameters are derived from a pre-stressed FEM eigenfrequency analysis, to account for arbitrarily complex geometries and for the shift of the speaker resonance frequency due to an initial non-null pre-deflected configuration. The parameters of the acoustical circuit are instead computed through analytical formulas. The acoustic short-circuit between the speaker front and rear sides is taken into account through a proper air-gaps modeling. The very good matching in terms of radiated sound pressure level among the equivalent circuit predictions, FEM simulations, and experimental data proves the ability of the proposed method to accurately simulate the speaker performance. Moreover, due to its generality, it represents a versatile tool for designing piezoelectric MEMS speakers.

Eigenfrequency analysis of bridges using a smartphone and a novel low-cost accelerometer prototype

Eigenfrequency analysis of bridges using a smartphone and a novel low-cost accelerometer prototype

Unlocking Efficiency in Radio-Frequency Heating: Eigenfrequency Analysis for Resonance Identification and Propagation Enhancement in Nigerian Tar Sands.

Nigerian bituminous tar sands are among the world's largest deposits of bitumen and heavy oil. They are estimated to contain 38-40 billion barrels of heavy oil and bitumen, spanning approximately 120 km in length and 4-6 km in breadth. With global commitments to net zero emissions and various energy transition plans, improvements in the recovery methods for heavy oil and bitumen are being sought. To address this, renewable energy electrothermal enhanced oil recovery is considered an eco-friendly alternative. In our study, we introduce a novel Reservoir-Waveguide-Debye model. This model explores the enhancement of penetration for radio-frequency electromagnetic (EM) waves, which can be generated from renewable energy sources. These waves facilitate the viscosity reduction of heavy oil and bitumen. Through a comprehensive 2D numerical simulation employing the bulk properties of bituminous tar sands, we assess the propagation of EM fields within porous media. We utilize the industrial heating radio-frequency bandwidth of 1-60 MHz to conduct frequency domain investigations. Our analysis delves into propagation modes using eigenfrequency analysis, pinpointing the EM resonance of the tar sands. Furthermore, we investigate the impact of mesh refinement on the EM eigenfrequencies of porous media at both the microscale (400 μm) and macroscale (100 m in radial distance). Our results demonstrate the occurrence of resonance phenomena at complex eigenfrequencies around 27.12 and 54.24 MHz in both the microscale and macroscale models of the bituminous sands. This breakthrough research offers promising insights into harnessing renewable energy-driven EM waves for efficient thermal recovery processes in the Nigerian bituminous tar sands, thus fostering sustainable and eco-friendly energy solutions.

Failure mechanisms of anisotropic pentamode-based bridge bearings: A dynamic analysis

Pentamodes are known for their almost zero shear modulus while providing high compression stiffness; a characteristic, which renders pentamodes suitable for application in seismic isolation. The current study focuses on bearings composed of alternating layers of pentamode crystals of an elastoplastic material with rigid steel plates. Pushover analyses are conducted, and plastic inges are gradually created. The failure mechanisms of the bearing are discussed and compared to those without stiffening plates. The influence of the directionality of an induced earthquake is also investigated. Since pentamode unit cells and pentamode modules are only symmetrical with respect to a vertical level, their structural response is anisotropic. Consequently, a bearing symmetric with respect to its diagonal is not expected to have an isotropic response. Depending on the formulation the ability to withstand the induced shear loading can be increased up to 30–50%. The cells, modules and bearings are proven to feature a weak direction defined by their lowest nodes, which specify how they are connected to the ground. It is proposed that a bearing composed of rotated instead of justified layers would be more isotropic. Positive and negative aspects of such a structure are discussed. The dynamic behavior of layered pentamode bearings is also discussed. Eigenfrequency and dynamic analyses of real-life bridge bearings under harmonic and real time histories showed that stiffening plates may improve a bearing’s response up to 115%.

Design, analysis and comparison of piezoelectric geometric arrangements

In smart materials, piezoelectric materials are ever-increasing attention because the combination of two ferroic orders such as mechanical and electrical fields. These piezoelectric materials can be used as both sensor and actuator in energy harvesting, medical instruments, automobile and aerospace applications. Even in the research field, piezoelectric material is one of the highlited areas to enhance the output and sensitivity by optimizing the structure, shape, load and material. The present work focuses on the geometrical arrangements of a cantilever beam model to enhance the output voltages in short circuit and open circuit conditions with two piezoelectric materials. The design and simulation of seven different geometrical arrangements (Structure 1,2,3,4,5,6,7) are done using FEA-based COMSOL Multiphysics. PZT-5H Structure 2 (1 Substrate with 1 piezoelectric segment) gives a high output voltage of 181 V and 469 V in both short circuit and open circuit conditions respectively compared to BaTiO3. Also, a comparative study of eigenfrequency analysis and frequency domain analysis is carried out and comparatively structure 4 is giving high voltage at lower frequency 546.95 Hz. It is also observed that these structures are using less material and are cost-efficient.

Patch sticking for efficient mode-converting transmission of elastic waves

The concept of patch sticking, which can be widely seen in daily life, such as medical care and houseware repair, is introduced in this work for wave manipulation. Specifically, we stick an array of patches on an aluminum plate for efficient mode conversion between in-plane longitudinal and transverse waves. The patches have a carefully designed dimension, and are stuck with specific distances and angles. The working mechanism is revealed through eigen-frequency analysis, and experimental validation is carried out. Our work offers a simple and convenient solution for elastic wave manipulation, and could inspire the design of novel meta-devices.

Analysis of the interaction between torsion wave and phononic crystal in pipes

This article presents an analysis of torsional wave propagation in phononic crystal-based metamaterials. Such structures hold great promise as tools for wave manipulation. The unit cell of the presented structure was meticulously examined to obtain dispersion curves, revealing the presence of bandgaps and negative group velocities. The calculations of effective material parameters, based on eigenfrequencies, are presented to substantiate the existence of the bandgap and the negative value of group velocity. Time-domain simulations were conducted at various frequencies to analyze the wave behavior. In the case of negative group velocity, the wave inside the metamaterial propagates in the same direction as the incident wave. To verify the existence of negative velocity, a 2D Fast Fourier Transform (FFT) was performed, and the results from the 2D FFT data analysis align perfectly with the eigenfrequency analysis.

Analysis of CNT-based SAW sensor for the detection of volatile organic compounds

This paper presents a multi-layer one-port surface acoustic wave (SAW) sensing device and its response based on the adsorption of different volatile organic compounds (VOCs). The finite element method was used to model and simulate a multi-layered SAW device. A piezoelectric substrate 128ᵒ YX-cut Lithium Niobate (LiNbO3), polyisobutylene (PIB) polymer, and carbon nanotube (CNT) multilayer SAW resonating sensor was modeled and used for generating Rayleigh waves. Electromechanical coupling coefficient (K2), admittance (Y11), S-parameter (S11), and metallization ratio (MR) were computed for the proposed heterostructured device. The sensing properties of proposed SAW sensor was investigated for several organic compounds such as trichloroethylene (C2HCl3), trichloromethane (CHCl₃), acetone (C3H6O), acetonitrile (C2H3N), cyclohexane (C6H12), dichloromethane (CH2Cl2) and diethyl ether (C4H10O). Eigenfrequency analysis of the SAW sensor was evaluated from 100 ppm to 500 ppm gas concentration at room temperature. The observed results were compared with the existing research and found to be more effective in terms of sensitivity.

Bending and eigenfrequency analysis of glass fiber reinforced honeycomb sandwich shell panels containing graphene-decorated with graphene quantum dots

The present study employs a finite element (FE) formulation to examine the free vibration and bending analyses of sandwich shells made of a glass fiber reinforced polymer (GFRP) composite honeycomb core and graphene decorated with graphene quantum dots (GDGQD) reinforced by GFRP composite face layers. The mechanical characteristics of the GFRP composites with GDGQD reinforcement were evaluated using experimental tests. The FE formulation was developed to compute the vibration and bending responses of the sandwich shells via MATLAB software. The Lagrange method is used for dynamic analysis, whereas the principle of potential energy is used for static analysis. The FE model's validity is compared to numerical data reported in the literature in terms of frequencies and deflection, and the results demonstrate excellent agreement. The impacts of the end conditions, core-to-facesheet thickness ratio, curvature ratios, and weight percent of GDGQD are studied further in relation to the bending and dynamic properties of GFRP sandwich shells.

Machine learning discovery of optimal quadrature rules for isogeometric analysis

We propose the use of machine learning techniques to find optimal quadrature rules for the construction of stiffness and mass matrices in isogeometric analysis (IGA). We initially consider 1D spline spaces of arbitrary degree spanned over uniform and non-uniform knot sequences, and then the generated optimal rules are used for integration over higher-dimensional spaces using tensor products. The quadrature rule search is posed as an optimization problem and solved by a machine learning strategy based on adaptive gradient-descent. However, since the optimization space is highly non-convex, the success of the search strongly depends on the number of quadrature points and the parameter initialization. Thus, we use a dynamic programming strategy that initializes the parameters from the optimal solution over the spline space with a lower number of knots. With this method, we found optimal quadrature rules for spline spaces when using IGA discretizations with up to 50 uniform elements and polynomial degrees up to 8, showing the generality of the approach in this scenario. For non-uniform partitions, the method also finds an optimal rule in a reasonable number of test cases. We also assess the generated optimal rules in two practical case studies, namely, the eigenvalue problem of the Laplace operator and the eigenfrequency analysis of freeform curved beams, where the latter problem shows the applicability of the method to curved geometries. In particular, the proposed method results in savings with respect to traditional Gaussian integration of up to 44% in 1D, 68% in 2D, and 82% in 3D spaces.

Deep learning algorithms for design of periodic structures and dispersion curves calculation

Periodic structure is useful and powerful tool for the wave manipulation. The development of design and analysis of periodic structures using traditional methods (analysis of eigenfrequencies by the finite element method) takes quite a lot of time. Machine learning and deep learning algorithms can speed up the development and subsequent analysis of periodic structures. In this work, we consider a particular case of the propagation of torsional waves in cylindrical objects, the calculation of their dispersion curves, and methods for generating the design of a unit cell of periodic structure by a given bandgap configuration. To achieve this goal, autoencoders and diffusion models were used. A dataset of unit cell shapes and their dispersion curves were used as training data. First, the dispersion curves were analysed to form a bandgap configuration, which was then fed to the input of the neural network. The neural network generates unit cell shape as the output data. Information about dispersion curves is also very important for the analysis of periodic structures. To calculate the dispersion curves, the possibility of using deep learning methods is considered - the problem is the opposite of the previous one. According to the given form, the neural network should calculate dispersion curves. The paper presents the results of applying this method for calculating dispersion curves.