Free Vibration Research Articles

Analysis of laminated shells using pseudospectrals and the Reissner-Mixed Variational Theorem

In this paper, we combine the Carrera’s Unified Formulation CUF and a pseudospectral technique for predicting the static deformations and free vibrations behaviour of thin and thick cross-ply laminated shells. For the first time, the Reissner-Mixed Variational Theorem is used together with pseudospectrals to achieve a highly accurate technique. The accuracy and efficiency of this numerical technique for static and vibration problems are demonstrated through numerical examples.

Nonlinear free vibration analysis of multi-directional functionally graded porous sandwich plates

Multi-directional functionally graded materials (MFGMs) have attracted significant research attention due to their advantages over one-directional FGMs. In MFGM structures, material properties can be tailored to grade in the required direction, overcoming practical problems like excessive temperature gradients or extreme deflections. This paper aims to investigate the nonlinear free vibration of MFG porous sandwich plates to improve their application in sandwich structures. The two outer layers of the plates are composed of three-directional functionally graded material (3D-FGM), with a bi-directional functionally graded material (2D-FGM) core layer. Additionally, the porosity distribution within the material matrix is assumed to be either even or uneven across the plate thickness. A higher-order finite element model based on Shi's plate theory and the von Kármán assumption is developed. The nonlinear free vibration frequencies are determined through the maximum vibrational amplitude using an iterative algorithm with a displacement control strategy. The accuracy and effectiveness of the proposed model are demonstrated through a comparison with published data. The results show that the vibration response is significantly influenced by various parameters. Specifically, increasing the material gradient indexes in the thickness direction enhances the frequency ratio, while increasing the gradient indexes in the length and width directions reduces it. Higher porosity coefficients in the core layer decrease the frequency ratio, whereas higher pore coefficients in the outer layers increase it. The additional knowledge gained from this study can help with future analysis and design procedures related to the nonlinear responses of these complex structures.

Effects of Graphene Reinforcement on Static Bending, Free Vibration, and Torsion of Wind Turbine Blades.

Renewable energy markets, particularly wind energy, have experienced remarkable growth, predominantly driven by the urgent need for decarbonization in the face of accelerating global warming. As the wind energy sector expands and turbines increase in size, there is a growing demand for advanced composite materials that offer both high strength and low density. Among these materials, graphene stands out for its excellent mechanical properties and low density. Incorporating graphene reinforcement into wind turbine blades has the potential to enhance generation efficiency and reduce the construction costs of foundation structures. As a pilot study of graphene reinforcement on wind turbine blades, this study aims to investigate the variations of mechanical characteristics and weights between traditional fiberglass-based blades and those reinforced with graphene platelets (GPLs). A finite element model of the SNL 61.5 m horizontal wind turbine blade is used and validated by comparing the analysis results with those presented in the existing literature. Case studies are conducted to explore the effects of graphene reinforcement on wind turbine blades in terms of mechanical characteristics, such as free vibration, bending, and torsional deformation. Furthermore, the masses and fabrication costs are compared among fiberglass, CNTRC, and GPLRC-based wind turbine blades. Finally, the results obtained from this study demonstrate the effectiveness of graphene reinforcement on wind turbine blades in terms of both their mechanical performance and weight reduction.

Free and forced vibration analysis of uniform and stepped conical shell based on Jacobi-Ritz time domain semi-analytical method

Free and forced vibration analysis of uniform and stepped conical shell based on Jacobi-Ritz time domain semi-analytical method

Free vibration of functionally-graded piezoelectric semiconductor rectangular beam under thermal load

In this paper, the free vibration of a functionally-graded piezoelectric semiconductor (FGPS) rectangular beam under thermal load is studied within the framework of the theory of Timoshenko beam and the theory of piezoelectric semiconductor. It is assumed that the material properties in the functional gradient layer change smoothly. The multi-field coupling in the beam is deduced by introducing the first-order shear deformation theory in this paper, and the governing equations including motion equation, Gauss law and current continuity condition are obtained. The vibration of a simply supported FGPS rectangular beam is realized by solving the governing equations. In numerical examples, the natural frequencies of the FGPS rectangular beam under thermal load are analyzed through different perspectives. The results show that for different length scales, the natural frequency of the FGPS beam under thermal load is reduced by increasing the initial electron concentration in a certain range. The damping characteristics are insensitive to temperature change, and the damping characteristics are decreased by increasing length to thickness ratio and the thickness of the FGPS layer.

Free vibration and stationary stochastic response analyses of heated composite laminated plate with varying thickness and curvilinear fiber using a meshfree method

Free vibration and stationary stochastic response analyses of heated composite laminated plate with varying thickness and curvilinear fiber using a meshfree method

Dynamic examination of closed cylindrical shells utilizing the differential transform method

This article presents an innovative approach using the Differential Transform Method (DTM) to analyze the vibration characteristics of cylindrical shells, integrating Taylor's series with Sander's classical theory. It demonstrates DTM's efficiency, accuracy, and potential as an alternative method. The study introduces a novel application of the DTM in exploring the free vibration of cylindrical shells, detailing a technique to address challenges such as normalization, linear solution methodologies, and parameter derivative modifications. A dimensionless parameter analysis evaluates the impact of length, radius, thickness, and modulus of elasticity. Comparative analysis with Hybrid Finite Element Method (FEM) data and validation against existing literature highlights DTM's precision and reliability. In conclusion, DTM offers a robust solution for the eigenvalue problem in coupled differential equations, providing accurate vibration parameters. Additionally, an important relationship between the modulus of elasticity and frequency in the dimensionless state was obtained.

Additional Natural Frequency of the Beam Carrying a Spring-Mass System: Lost and Found

Abstract This study revisits the free vibration of a cantilever beam with a mass-spring system attached at the tip of the beam. We recover the natural frequencies that were reported in some special case, and establish that there could be an additional, “lost” frequency that was somehow not uncovered in previous investigations. This frequency is found hereinafter.

Free Vibrations of Open Cylindrical Shells with Various Elliptic Cross Sections

Free Vibrations of Open Cylindrical Shells with Various Elliptic Cross Sections

Free vibration analysis of composite aircraft wing

Free vibration analysis of composite aircraft wing

Application of bilateral iterative displacement control method to nonlinear free vibration analysis of dual-FG nanocomposite circular plates

This paper studies the geometrically nonlinear free vibration of a novel nanocomposite circular plate. The matrix of the nanocomposite structure is made of functionally graded (FG) polymer, and the distribution of graphene platelets (GPLs) as the reinforcement is assumed based on the five various linear FG models. Therefore, this novel nanocomposite is called dual-FG. The Voigt rule of mixture and Halpin-Tsai method are employed to homogenize FG polymer, and distribution of the GPLs within the matrix, respectively. Moreover, the whole structure is fixed on a nonlinear Kerr elastic foundation. The displacements of the plate are estimated by means of the first-order shear deformation theory (FSDT). Von-Kármán type of geometrically nonlinear relations expresses the plate's strains. The generalized differential quadrature (GDQ) technique, bilateral iterative displacement control method (BIDCM), and the weighted residual Galerkin procedure are implemented to extract the free vibration characteristics of the structure. The developed structure is validated with those reported in the open literature. A comprehensive parametric study is conducted to illustrate the effect of various parameters on the dynamic response of the dual-FG nanocomposite circular plate. It will be observed that the influence of the volume fraction and distribution model of GPL is more pronounced on the vibration frequency in the FG matrix. It was noted that the volume fraction of graphene platelets (GPL) and the power-law index of the matrix exhibit a direct and inverse relationship, respectively, with the natural frequency of the structure. Furthermore, the V-GPL model exhibits the highest percentage growth in nonlinear frequencies, while the Λ-GPL model shows the least growth. This observation is particularly pronounced for plates with hinged boundary conditions.

Free vibration response of micromorphic Timoshenko beams

In this paper the authors investigate the free vibration of a two-length-scale nonlocal micromorphic Timoshenko beam, which is shown to overlap with the nonlocal strain gradient Timoshenko beam under certain conditions. Hamilton’s principle is utilized to obtain a system of two coupled fourth-order equations of motion governing the eigen-deflection and the eigen-rotation of the beam. Uncoupling both equations leads to two eight-order differential equations. Using Ferrari’s method, exact solutions are derived for the eigenfrequencies for various boundary conditions, including simply supported, clamped-clamped, clamped-free, and clamped-hinged boundary conditions. The obtained results are compared with those published in the literature using similar nonlocal strain gradient cases. A detailed parametric study is then performed to emphasize the role of the variationally-derived higher-order boundary conditions (natural higher-order boundary conditions or mixed higher-order boundary conditions). It is noted that when the difference in length-scales is large, the effect of the slenderness of the beam on the frequencies is amplified. Finally, the hardening or the softening effect of the beam model can be achieved through a choice of the ratio between the two length-scales.

A study on graphene-reinforced magneto-electro-elastic laminated nanoplate's thermomechanical vibration behaviour based on a higher-order plate theory

Sandwich nanostructures incorporating piezoelectric and magneto-electro-elastic properties have emerged as promising candidates for next-generation smart devices and composites. Due to their exceptional design, fabrication, and energy conversion capabilities, these structures are extensively utilised as sensors and actuators in nano-electromechanical systems. Accordingly, in this article, the free vibration behaviour of a multifunctional laminated (MFL) nanoplate with piezoelectric PZT5-H and magnetostrictive CoFe2O4 (cobalt-ferrite) face layers and a graphene-reinforced core layer is investigated by applying a higher-order sinusoidal shear deformation theory (HSDT). In addition, two different material cases consisting of Ti6Al4V and ZrO2 materials and two foam models, uniform and symmetric, are considered for the foam core layer. Hamilton's principle is used to obtain the plate's governing equations. Navier's solution approach is utilised to get the natural frequencies of the laminated nanoplate under thermal load and electric and magnetic fields. A parametric study is performed to determine the effects of volumetric graphene content, the foam model and its pore ratio, face/core material content, external electric and magnetic potential, and thermal load on the free vibration response of the MFL nanoplate. The obtained numerical results can be a reference point for future research on layered porous MEE structures, especially for micro/nano-sized systems.

Accurate Free Vibration Analysis of Stepped Orthotropic Rectangular Cantilevered Plates Under the Framework of Symplectic Mechanics

Accurate Free Vibration Analysis of Stepped Orthotropic Rectangular Cantilevered Plates Under the Framework of Symplectic Mechanics

Vibration of bolted composite cylindrical-cylindrical flanged shells considering contact characteristics

A semi-analytical model for bolted composite cylindrical-cylindrical flanged shells (BCCFS) considering the influence of the flange and the connection characteristics of the bolted flange joint is established. In the model, flanges are treated as annular plate structures and modeled using Kirchhoff plate theory. To simulate the connectivity performance of the bolted flange joint, a surface-spring model considering the pressure distribution characteristics is developed and applied to the model of the bolted structure. A method based on fractal contact theory is proposed to identify stiffness-related parameters of the surface-spring model, which avoids additional tensile experiments of the bolted joint. Sufficient modal tests are performed to validate the accuracy of the model. Furthermore, the effects of flange thickness, length ratio of two shells, and quantity of bolts on the free vibration characteristics of the structure are studied. The frequency veering phenomenon with the variation of size parameters is found and analyzed in depth.

Frequency analysis of open/closed polygonal channel aerostructures made of hybrid nanocomposite materials and supported by piecewise elastic foundation using GDQE technique

This research delves into the theoretical exploration of the generalized differential quadrature element (GDQE) method for analyzing the dynamic response and natural frequency of aerospace structures, specifically polygonal channels found in aircraft, satellites, and space vehicle components. These structures are critical in aerospace engineering, serving in various capacities such as airframe components and fluid conveyance systems. Emphasizing the practical significance of these structures, the study incorporates the influence of ground or support conditions, employing a two-parameter piecewise elastic foundation model. The investigated open or closed channels are characterized as laminated functionally graded hybrid nanocomposites, specifically denoted as FG-HNC, reinforced with Carbon nanotubes (CNTs) and Clay nanoparticles (CNP). Each composite layer is reinforced with randomly oriented and uniformly distributed tubes and particles. The homogenization of the hybrid composite domain is performed using the hierarchy Halpin-Tsai micromechanical rule. Utilizing the GDQE technique, the channels are discretized into plate elements, and motion equations for each plate element are calculated based on first-order shear deformation theory and Hamilton's principle. The resulting equations are then solved using the standard GDQ method, with subsequent application of appropriate continuity conditions at shared element boundaries. In this comprehensive study, the research scrutinizes the effects of structure dimensions, channel sides crank angles, composite characteristics, and boundary conditions on the free vibration behavior of the polygonal channels. By offering detailed insights into the vibrational characteristics of FG-HNC structures, this study contributes to the advancement of aerospace engineering design and analysis.

Aerodynamic force correlation of a foundational streamlined box girder under vortex-induced vibration in turbulent flow fields

Study on the vortex-induced vibration (VIV) performance of structures under vibration states in turbulent flow fields is closer to the essence of bridge VIV in real service environments, which has been lacking in existing research. The key parameter used in the VIV performance evaluation, vortex-induced force (VIF) correlation, was focused on in this paper. A foundational streamlined box girder was selected, and free vibration sectional model tests were conducted in turbulent flow fields using synchronous pressure-vibration measurement. The results indicate that turbulence have an impact on the VIV performance of streamlined box girder. The presence of turbulence is likely to decrease the VIV amplitude, but sometimes it may also increase it. The phase difference between the leading and trailing edges of the structural upper surface is approximately 100°, and the vortices on the upper surface do not drift continuously. The streamwise correlation of VIFs decreases to varying degrees with the increase in turbulence intensity. The aerodynamic force spanwise correlation when the structure is stationary is significantly weaker than when it is in a vibrational state. When the structure experiences sustained VIV, the spanwise correlation of VIFs decreases with increasing turbulence intensity, increases with increasing amplitude, and decreases with increasing spanwise distance and tends to be constant at a certain distance. Finally, an extended model based on Ricciardelli's correlation function was proposed, which can better describe the VIF spanwise correlation of streamlined box girders under different amplitudes.

Hybrid isogeometric-based analysis and experimental investigation on the dynamic response characteristics of a clamped circular plate partially in contact with fluid

The aim of this study was to analyze the effect of fluid presence on the dynamic response characteristics of the thin circular plate and the distortions associated with the wet mode shapes. To this end, series of numerical calculations and experimental measurements were performed to investigate the free vibration characteristics of clamped circular plate under in-vacuo conditions and when it is partially in contact with fluid. In the experimental studies, the clamped boundary conditions are imposed on the circular end plate of the horizontal rigid cylindrical tank by closely-spaced bolts, and measurements were performed based on roving hammer impact technique. The proposed numerical approach was divided into two parts based on linear hydroelasticity theory. In the first stage, the thin circular plate is considered to be under in-vacuo conditions, and the mathematical model for this problem is developed based on the isogeometric finite element method (IGAFEM). The fluid environment is introduced in the second stage of the study in which the generalized in-vacuo modal displacements constitute the boundary conditions of the potential flow problem. The influence of fluid medium is incorporated in the system of equations in the form of fluid added mass, and the corresponding fluid forces are calculated by the isogeometric boundary element method (IGABEM). It is observed that the fluid presence has significant effects on the dynamic response characteristics of the test structure, and the specifically, the distortions of wet mode shapes were noticeable due to presence of free surface of the water. Overall, it is found that the natural frequencies and corresponding mode shapes obtained by conducted experiments and adapted numerical framework are in favorable agreement.

Sound transmission loss analysis of novel sandwich plate with star-shaped auxetic cellular cores

A star-shaped auxetic cellular metamaterial with a negative Poisson’s ratio (NPR) was employed in this study to model lightweight sandwich panels, and an analysis of its sound transmission characteristics was conducted. Utilizing the first-order shear deformation theory (FSDT) and the Hamiltonian principle, the free vibration equation for the sandwich plate is derived. Subsequently, leveraging the fluid-structure coupling condition and incorporating the Navier method, the sound transmission loss (STL) is analytically described. The efficacy of the proposed method is validated through numerical analysis and an acoustic insulation experiment using an impedance tube. Based on the theoretical modeling, it is calculated that the sound insulation effect of the star-shaped cellular core exceeds that of the traditional reentrant cellular with NPR. A systematic analysis is subsequently conducted to explore the impact of star-shaped cellular structure parameters on the STL of the sandwich panel. It can be obtained that the increase in core layer thickness leads to a reduction in the first-order resonance frequency of the sandwich panel, but concurrently diminishing its sound insulation performance. The change of the connecting rib length exerts a more considerable influence on the structure’s STL compared to the side rib length. While as the cell wall thickness reduces from 2.0 to 1.0 mm, the average STL of the sandwich plate across the analysis band decreases by 8.43%, from 46.3 to 42.7 dB.

Damping characteristics of High-Temperature superconducting pinning maglev levitation system

High-temperature superconducting (HTS) pinning maglev has achieved rapid development in recent decades. The levitation system of the HTS pinning maglev is mainly composed of Dewar with built-in HTS bulks and permanent magnet guideway (PMG). For a maglev transportation system, damping is important for vibration attenuation, and the inherent damping characteristics of the HTS pinning maglev system have not been evaluated clearly. In this paper, the damping characteristics of the HTS pinning maglev system are analyzed through experiments and simulations. Experiments are conducted to measure the dynamic responses of the system under free and forced vibrations. The logarithmic envelope method is used to evaluate the system damping under free vibration. The cross-correlation function is utilized to obtain the phase difference between the system vibration signal and excitation signal, and then calculate the system damping under forced vibration conditions. In addition, a two-dimensional finite element model including HTS bulks, PMG, and Dewar conductive shells is established to evaluate the damping force generated by each component during system vibrations. The additional eddy current damping of the conductive Dewar shell is considered and analyzed. Finally, from the perspective of system damping and thermal stability of HTS bulks, suggestions for selecting Dewar shell materials are proposed.