Free-free Boundary Conditions Research Articles

Evaluation of inversion approaches for plates based on guided waves and modal analysis

The identification of defects in plate-like structures has been successfully treated using both local guided ultrasonic waves and global modal quantities. Although there are many papers on these techniques, a lack of comparability between the two methods persists. This makes it difficult for users to identify the most appropriate method for the defect in question. This paper examines the effect of different parameterizations of a circular defect in a square aluminum plate on the system response in a case study. The measured local ultrasound signal from a propagating guided wave makes up the initial data set. The first method uses the entire waveform for the objective function of the optimization problem, while the second considers the velocity of the A0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_0$$\\end{document} mode. In the third and fourth methods, the first and second global natural frequencies of the plate modeled with free-free boundary conditions are investigated. The numerical models are validated experimentally through measurements with a laser Doppler vibrometer. This results in the qualitative and quantitative evaluation of the objective functions for all parameter combinations of the defect. The recommendation to sequentially employ modal analysis and then the ultrasound procedure is made for the defect type used in this study. The data gathered on the objective functions suggests that potential joint employment of the natural frequency and ultrasound methods may increase computational efficiency. For a specific case, the methods could also complement each other in terms of challenges such as local minima.

Effect of magnetic field on the onset of thermal convection in a Jeffery nanofluid layer saturated by a porous medium: free-free, rigid-rigid and rigid-free boundary conditions

Effect of magnetic field on the onset of thermal convection in a Jeffery nanofluid layer saturated by a porous medium: free-free, rigid-rigid and rigid-free boundary conditions

Experimental investigation of compressive behavior and vibration properties of layered hybrid foam formed by aluminum foam/EPS-filled syntactic foam

Hybrid foams are a type of composite material created by combining two foam materials. They are preferred in many applications due to their lightweight, high strength, and ability to absorb more energy. In this research, a new hybrid foam was designed for use in sandwich cores of structural materials. The hybrid foam was formed by combining closed-cell aluminum foam and expanded polystyrene (EPS)-filled syntactic foam. The EPS-filled syntactic foams were produced with the conventional mold casting technique. Uniaxial compressive behaviors (0.5 mm/min) of layered hybrid foams consisting of EPS-filled syntactic foam with three different densities and closed-cell aluminum foam were investigated experimentally and compared with conventional single-foamed materials. These results exhibited that in general, layered hybrid foams outperform conventional single-foamed materials in terms of compressive strength. Moreover, the natural frequency and damping ratio of the layered hybrid foams were investigated by vibration tests under clamped-free and free-free boundary conditions and compared to conventional single-foamed materials. It was established that the vibration damping capacity of the layered hybrid foams improved compared to the closed-cell aluminum foam. Additionally, the microstructure of the conventional single-foamed materials was examined by SEM. In the outcome of the research, the experimental results showed that layered hybrid foam provides an opportunity to design lightweight cellular materials with effective mechanical properties.

Free vibration characteristics of integrated fluted-core composite sandwich cylinders

Due to their excellent mechanical properties and inherent design versatility, fluted-core composite sandwich structures have gained substantial attention in aerospace and rail transit applications. This study investigated the free-vibration characteristics of composite fluted-core sandwich cylinders. Theoretical models were established following the Rayleigh-Ritz method to predict the natural frequencies of sandwich cylinders under free vibration. The representative cylindrical specimens were prepared using carbon fiber-reinforced plastics (CFRP) and integrated forming co-cured method. To analyze the additional effects of cutouts on vibration performance, specimens with circular cutouts were also fabricated. The vibration tests were performed to determine the natural frequencies and modal shapes under free-free boundary conditions. Validated finite element simulations were employed to assess the accuracy of theoretical results and investigate the influences of geometric parameters on the structural vibration behavior. The results indicated that circumferential lobar modes characterized the first five mode shapes. Significant enhancements were attained by increasing the structural stiffness through adjustments in the circumferential cell number, core-ribs thickness, or size of cutouts. However, when the structural stiffness increases beyond a certain threshold, it has limited effect on the vibration frequencies. The findings provided a comprehensive understanding of the vibration characteristics and optimized design of fluted-core sandwich cylinders.

Instability analysis of vibrated thermo-convection in Casson nanofluid suspension

This work is motivated by the importance of vertical vibration in nanofluids suspension, because of its wide applications in heat exchangers from one fluid to another, controlling the mixing in microvolumes, pharmaceutical industry, and engineering. The current study analyzes the effects of high-frequency vertical vibration on a horizontal Casson nanofluid layer heated from below saturated between rigid-rigid, rigid-free, and free-free boundary conditions. Field equations are derived by using time-average method, which describes the vibrational thermo-convection. These field equations are solved by utilizing linear stability analysis and Galerkin technique to obtain the thermal stability curve. By using this curve, the impacts of vertical vibration and physical governing factors on temperature profile are discussed. High-frequency vertical vibration is observed to have a stabilizing effect on Casson nanofluid suspension, thereby reducing thermo-convective heat transfer from one fluid to another. Stability threshold of vibrated suspension is increased approximately as [Formula: see text] and [Formula: see text] when [Formula: see text] and [Formula: see text], respectively. The significance of Brownian motion and thermophoretic force on convective heat transfer with vertical vibration is discussed. The resisting nature of Casson nanofluid on vibrational convective heat transfer is also tabulated.

Flügge shell theory and solution for the vibration analysis of a thin elastic cylindrical panel of varying curvature

In this paper, the free vibration behavior of isotropic and orthotropic cylindrical shell panels with variable curvature subjected to certain ends boundary conditions is analyzed by the transfer matrix technique and solved by the Romberg integration approach. Flügge’s shell theory is employed to model the governing three-dimensional equations of vibration and Fourier’s approach is used to deform the displacement fields as trigonometric functions in the longitudinal direction. As a result of a semi-analytical procedure is conducted, the coupled governing equations of panel problem can be written in a matrix partial differential equation of first order with variable coefficients and reduced from the two-dimensional problem to one-dimensional one which is solved numerically as an initial-value problem. The proposed model is applied to get the natural frequencies and mode shapes for the vibration behavior of two-side simply-supported cylindrical panels with simply-supported, free-free, clamped-free and clamped-clamped ends boundary conditions lying at their curved edges. The sensitivity of the vibration behavior to the variety of curvature, panel parameters and material orthotropy of shell is studied.

Sandwich designs for high levels of noise and vibrations

Lightweight materials with high structural damping and reasonably well flexural performance are demanded in some components of aerial vehicles such as interior part of helicopters where high levels of noise and vibrations exist. One of the best choices for this is through the use of a polymer matrix composite with suitable fiber orientations and a structural foam core. In this study, face sheets from a woven carbon fiber reinforced polymer plies and a foam core with three different thicknesses (10.7 mm, 25.4 mm, and 49.8 mm) have been used to manufacture sandwich structures to yield high dynamic values (damping and flexural rigidity). To measure these values, the sandwich beams with free-free boundary conditions were subjected to free vibration tests using a non-contact response measuring system. The measurements were made for the first, second and third natural frequencies, and compared to numerical modal analysis via the ANSYS package program. The results from experimental and numerical methods are found to be reasonably good in agreement and show that the sandwich structures are able to give high damping values, in general. It seems the specimens with relatively low thickness give relatively high damping values compared to the others, whereas the thicker ones are useful for high frequency domains and flexural rigidity. The behaviors of the beams have been found frequency dependent, due to the viscoelastic behavior of the foam cores at high frequency levels.

ONSET OF DARCY-BRINKMAN CONVECTION IN A ROTATING BIDISPERSIVE POROUS MEDIUM

The onset of Darcy-Brinkman convection in a rotating bidispersive porous layer is studied for different boundary configurations. Rotating bidispersive porous layer manifests in many applications such as food and chemical processes, rotating machinery, the petroleum industry, solidification and centrifugal casting of metals, biomechanics, and geophysical problems. Three types of boundary configurations are considered, namely rigid-rigid, rigid-free, and free-free boundaries. The fluid motion is characterized using the Brinkman-Darcy equation with a single temperature in macro and micro phases. The linear stability theory is used, and the obtained eigenvalue problem is addressed analytically for the free-free boundary conditions. The eigenvalue problems for the rigid-rigid and rigid-free boundaries are solved numerically. The effects of the Taylor number, momentum transfer coefficient, permeability ratio, Darcy number, and porosity ratio on the system's stability are graphically explored. The Darcy number, permeability ratio, and Taylor number are found to have a stabilizing influence on the system. Further, it is found that the momentum transfer coefficient shows destabilizing effect. The porosity ratio is found to have a stabilizing impact on the system.

Modal properties investigation of a carbon/glass fiber-reinforced polymer composite sandwich structure with lozenge-like core: An experimental and finite element simulation

The vibration properties of a carbon fiber-reinforced polymer (CFRP) and glass fiber-reinforced polymer (GFRP) composite sandwich panels with lozenge-like core and free-free boundary conditions are experimentally determined in this research. The sandwich panels manufactured for this study are composed of CFRP, GFRP, and epoxy resin. A modal experiment is performed using a modal hammer with an acceleration sensor to obtain modal properties of the structure, including natural frequencies, damping ratio, mode shapes, and frequency responses. Eventually, the comparison of vibration characteristics of the CFRP sandwich panel with the GFRP sandwich panel with almost identical geometry is discussed in detail. Furthermore, a finite element simulation is developed to validate the precision of the experimental data. It is recognized that the finite element results are in remarkably good agreement with those obtained by modal experiments. Hence, the finite element analysis and experiment method could be utilized to predict the modal properties of the CFRP and GFRP composite sandwich panels.

Influence of the Experimental Setup on the Damping Properties of SLM Lattice Structures

BackgroundMetal lattice structures obtained through Selective Laser Melting may increase the strength-to-weight ratio of advanced 3D printed parts, as well as their damping properties. Recent experimental results showed that AlSi10Mg and AISI 316L lattices are characterized by higher Rayleigh damping coefficients with respect to the fully dense material. However, some unclear or contradictory results were found, depending on the experimental setup adopted for modal analysis.ObjectiveIn this work the influence of the experimental setup when performing modal analysis on different SLM AISI 316L lattice structures was deeply investigated. The study provides a critical comparison of various experimental modal analysis approaches, allowing to evaluate the influence of external damping sources and material internal damping phenomena.MethodsThe dynamic behaviour of SLM AISI 316L specimens incorporating lattice structures was estimated by means of pulse testing and sinusoidal excitation through an electromagnetic shaker. The validity of the viscous damping model was assessed by means of sinusoidal excitation with different levels of vibration velocity. Moreover, the influence of experimental setup on modal analysis results was critically evaluated, by considering different actuators, contact and non-contact sensors and boundary/clamping conditions.ResultsThe classical viscous damping model describes with good approximation the damping properties of SLM lattice structures. When exciting single specimens in free-free conditions, those embedding lattice structure and unmelted metal powder filler were characterized by superior internal damping properties with respect to the specimens incorporating the lattice structure without any filler, which was however more effective than the full density equivalent material. Most of the other experimental setups introduced additional external damping sources, that could alter this important outcome.ConclusionsSLM lattice structures embedded into 3D printed components provide superior damping properties against mechanical and acoustic vibrations and the metal powder filler does significantly enhance such damping capacity. A correct estimation of material internal damping was achieved by applying non-contact sensors and free-free boundary conditions, whereas other experimental setups were partly inadequate.

Study on linear and nonlinear stability analysis of double diffusive electro-convection in couple stress anisotropic fluid-saturated rotating porous layer

The influence of rotation and electric field on the onset of double-diffusive convection in rotating anisotropic couple stress fluid embedded porous media, which is caused by the combined action of external AC electric field and heating from below, has been investigated in this study. The associated equations were solved using the normal mode technique in conjunction with the modified Brinkman model, with free-free and rigid-rigid boundary conditions. Solute concentration and temperature are treated as independent parameters for the two diffusive components. Finally, neutral stability curves have been sketched to show how various flow parameters affect neutral stability. It is noticed that electric field has destabilizing effect on thermodynamic convection while rotation couple stress parameters have a tendency to stabilize the physical system under consideration. Furthermore, heat and mass transport have been studied using non-linear analysis in unsteady case. It is found that rotation, couple stress, porous parameters has influence of declining heat and mass transport while electric and anisotropic parameters have effect of boosting up heat and mass transport.

Experimental and Numerical Modal Analysis of a Bladed Rotor

The behavior of an asymmetric bladed rotor was investigated in this study. The bladed rotor which performs solid-solid, liquid-liquid, liquid-solid separation processes is part of the decanter machine and named as screw conveyor. The purpose of this study is to determine the dynamics of the rotor on the free conditions for future development of the asymmetric and blade assembled rotors. It is important for the designer to determine the natural frequencies of the bladed asymmetric rotor so that some precautions can be taken during the design of the machine and in the operating conditions of the machine. This study consisted of two parts. In the experimental one, the modal test of the bladed rotor was performed and in the numerical part, the modal analysis of the rotor was carried out under free-free boundary conditions using a simulation program based on the finite-element method. The natural frequencies of the blades and the rotor were obtained experimentally and numerically. It was found that the experimental results and numerical results were in good agreement. Besides, it was concluded that the two mode shape was equal to the transverse mode frequency of the rotor and blades and the following mode shapes correspond to the bending and torsion mode frequencies of the blades. Since the shape properties of the rotor and blades are different, it has been observed experimentally and numerically that their natural frequencies also differ.

Linear and Non-Linear Stability Analysis for Thermal Convection in A Bidispersive Porous Medium with Thermal Non-Equilibrium Effects

The linear instability and nonlinear stability analyses are performed for the model of bidispersive local thermal non-equilibrium flow. The effect of local thermal non-equilibrium on the onset of convection in a bidispersive porous medium of Darcy type is investigated. The temperatures in the macropores and micropores are allowed to be different. The effects of various interaction parameters on the stability of the system are discussed. In particular, the effects of the porosity modified conductivity ratio parameters, and , with the inter-phase momentum transfer parameters and, on the onset of thermal Convection are also considered. Furthermore, the nonlinear stability boundary is found to be below the linear instability threshold. The numerical results are presented for free-free boundary conditions.

Closed-form existence conditions for bandgap resonances in a finite periodic chain under general boundary conditions.

Bragg scattering in periodic media generates bandgaps, frequency bands where waves attenuate rather than propagate. Yet, a finite periodic structure may exhibit resonance frequencies within these bandgaps. This is caused by boundary effects introduced by the truncation of the nominal infinite medium. Previous studies of discrete systems determined existence conditions for bandgap resonances, although the focus has been limited to mainly periodic chains with free-free boundaries. In this paper, we present closed-form existence conditions for bandgap resonances in discrete diatomic chains with general boundary conditions (free-free, free-fixed, fixed-free, or fixed-fixed), odd or even chain parity (contrasting or identical masses at the ends), and the possibility of attaching a unique component (mass and/or spring) at one or both ends. The derived conditions are consistent with those theoretically presented or experimentally observed in prior studies of structures that can be modeled as linear discrete diatomic chains with free-free boundary conditions. An intriguing case is a free-free chain with even parity and an arbitrary additional mass at one end of the chain. Introducing such an arbitrary mass underscores a transition among a set of distinct existence conditions, depending on the type of chain boundaries and parity. The proposed analysis is applicable to linear periodic chains in the form of lumped-parameter models, examined across the frequency spectrum, as well as continuous granular media models, or similar configurations, examined in the low-frequency regime.

Mechanical and dynamic responses of unidirectional/woven carbon fiber reinforced thermoset and thermoplastic composites after low velocity impact

It is highly important to determine how mechanical and dynamic properties of composite materials will change after impact loads considering the coupled effects of composite design parameters. For these reasons, three-point bending and vibration tests have been carried out for the carbon fiber reinforced thermoset and thermoplastic composites with various stacking sequences before and after low velocity impact, and it is expected that these results achieved from the current study will be beneficial for applications where high damping and impact resistance are demanded together. In this context, vibration tests were carried out under free-free boundary conditions, and their natural frequencies, flexural moduli and structural damping were obtained. Furthermore, three-point tests were conducted in the elastic region with 1 mm/min crosshead speed using a universal test machine, and thus flexural moduli of the composite specimens were obtained. The results were validated by comparing the flexural moduli obtained from the both vibration and three-point bending tests, found to be reliable and comparable. As a result of the current study, it was concluded that woven fabric reinforced composite specimens exhibited 50% higher specific damping capacity (SDC) but 70% lower flexural modulus than unidirectional specimens thanks to biaxially fiber alignment. On the other hand, specific damping capacities of the thermoset and thermoplastic composites with different stacking sequences have been examined, and it was observed that thermoset specimens exhibited unexpectedly 192% higher SDC compared to the thermoplastics. This was interpreted as even though thermoplastics are normally expected to exhibit more damping than thermosets, stacking sequence being more effective on damping responses. Apart from that, although there were slight changes in material properties due to degradation in structural integrity after 2 m/s and 3 m/s low-velocity impacts, it was not found to be significantly effective due to the limited damage areas.

Influence of geometric parameters on free vibration behavior of an aluminum honeycomb core sandwich beam using experimentally validated finite element models

The hexagonal honeycomb core sandwich panels used in the satellite structure are subjected to severe vibration during launch. Therefore, the amounts of natural frequencies of these panels are of great importance for design engineers. Three-dimensional finite element modeling of the core considering all geometric parameters (i.e., a high-fidelity model) to achieve accurate results is not cost-effective. The honeycomb core is traditionally equivalent to a homogenized continuum core (i.e., a low-fidelity model) using simple analytical relations with ignoring the adhesive layer at the double cell-walls and radius of inclined cell-wall curvature. In this study, analytical formulations are first presented for the prediction of the equivalent elastic properties of a hexagonal aluminum honeycomb with considering all geometric parameters including adhesive layer thickness, cell-wall thickness, inclined cell-wall length, radius of inclined cell-wall curvature at the intersection, internal cell-wall angle, and honeycomb height. Then, two aluminum honeycomb core sandwich beams with free-free boundary conditions are modeled and analyzed in Abaqus finite element software, one with 3D high-fidelity core and the other with 3D low-fidelity core. In order to validate the results of the equivalent model, the modal analysis test was performed and the experimental natural frequencies were compared. The obtained results show a good agreement between the 3D low-fidelity and high-fidelity finite element models and experimental results. In addition, the influence of the above-mentioned geometric parameters has been investigated on the natural frequencies of a sandwich beam. [Formula: see text]

Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

Estimation of the Frequency Response Function of the Rotational Degree of Freedom

One of the factors that influence the dynamic characteristics of machining systems is the cutting tool. Cutting tools are very diverse, and receptance coupling substructure analysis (RCSA) is essential for analyzing the dynamic characteristics of each tool. For RCSA, a full receptance matrix of the equipment and tools is essential. In this study, rotational degree-of-freedom receptance was estimated and analyzed using translational receptance. Displacement/moment receptance was analyzed according to the distance of the response point using the first-and second-order finite difference methods. The rotation/moment receptance was estimated according to the distance of the response point. Rotation/moment receptance was analyzed using Schmitz’s method and compensation strategies. The limitations of these strategies were analyzed, and the rotation/moment receptance for the beam under free-free boundary conditions was predicted using the second compensation strategy.

Design philosophy for ultrasonic motors using the bending hybrid modes

Due to the merits of simple structure, large output force and high speed, a lot of ultrasonic motors based on the hybrid of bending modes have been presented in recent years, but the principle of selecting different bending modes has not been studied. A design philosophy for bending hybrid ultrasonic motors is proposed and studied in this work. The length-height ratio is introduced to evaluate the geometrical sizes of ultrasonic stator based on the resonance frequency, while the width-height ratio is used for the hybrid of different bending modes. Based on the mode shapes of different bending modes under the free-free and free-fixed boundary conditions, the practicable combination modes of bending modes are finally discussed and summarized including the layouts of piezoceramics and driving feet, the positions of clamping points, and the motion types of motors. The first three order bending modes are selected as test objects, some prototypes are designed and fabricated to validate the mode shapes of bending modes. With the proposed design philosophy, the combination modes of bending modes can be determined and the geometrical sizes of ultrasonic stator can be evaluated according to the practical application requirements.

Model order reduction and dynamic characteristic analysis of the bolted flange structure with free-free boundaries

The problem of model order reduction and dynamic characteristic analysis of the bolted flange structure with free-free boundary conditions is studied by proposing a novel simplified modeling method. The proposed simplified modeling method is able to reduce the finite element model of the linear components through free-interface mode synthesis method and condense the number of degree-of-freedom of the joint interface through coordinate condensation, which can fix the model size not to increase with the number of bolts and greatly reduce the computational cost. Rigid-body mode elimination is also considered to further reduce the order of the integrated dynamic equation and avoid the problem of computational instability in the proposed simplified modeling method. An experimental bolted flange structure with free-free boundary conditions is built and the corresponding modal testing is carried out to verify the accuracy of the proposed simplified modeling method. Comparative results of modal testing and simulation indicate that gravity leads to unequal bending frequencies of the same order in X and Y directions, which also proves that the proposed simplified modeling method is able to analyze the dynamic characteristic of the bolted flange structure with free-free boundary conditions.