Free Vibration Response Research Articles

An Analytical Solution on Vibration Reduction and Shear Force Mitigation of Cantilever Mindlin Plates Using Orthogonal Ribs

Vibration of aircraft wings and the dynamic stress concentration at the clamped edge are important research topics due to concerns on the safety of aircrafts. To have a better understanding of the problem, the free and forced vibration response of a ribbed rectangular cantilever plate representing a section of an aircraft wing is investigated in this study. A new analytical solution is developed for the vibration analysis of rib stiffened cantilever plates using Mindlin plate and Timoshenko beam theories alongside the finite integral transform technique. The one- and two-dimensional integral transforms are applied to the governing equations of beams and plates, respectively, where the coupling force components at the interface between the base plate and the beam(s) can be automatically defined during the integral transform. Eventually, the partial differential equations are transformed into a system of linear algebraic equations in which its derivation is rigorous and easily implemented. Good agreements are found between the results of analytical solution, finite element analysis (FEA) and related literature. The solution is then employed to study the vibration suppression of cantilever plates and the shear force at the clamped edge. It is found that the insertion of a pair of orthogonal ribs in the plate can effectively reduce its vibration. An optimum orthogonal ribbing pattern is obtained using multi-objective particle swarm optimization (MOPSO) algorithm, taking into consideration both the vibration suppression of the plate and the maximum induced shear force at the corners of the clamped edge.

Transient responses of double-curved sandwich two-layer shells resting on Kerr’s foundations with laminated three-phase polymer/GNP/fiber surface and auxetic honeycomb core subjected to the blast load

This work uses refined first-order shear theory to analyze the free vibration and transient responses of double-curved sandwich two-layer shells made of auxetic honeycomb core and laminated three-phase polymer/GNP/fiber surface subjected to the blast load. Each of the two layers that make up the double-curved shell structure is made up of an auxetic honeycomb core and two laminated sheets of three-phase polymer/GNP/fiber. The exterior is supported by a Kerr elastic foundation with three characteristics. The key innovation of the proposed theory is that the transverse shear stresses are zero at two free surfaces of each layer. In contrast to previous first-order shear deformation theories, no shear correction factor is required. Navier’s exact solution was used to treat the double-curved shell problem with a single title boundary, while the finite element technique and an eight-node quadrilateral were used to address the other boundary requirements. To ensure the accuracy of these results, a thorough comparison technique is employed in conjunction with credible statements. The problem model’s edge cases allow for this kind of analysis. The study’s findings may be used in the post-construction evaluation of military and civil works structures for their ability to sustain explosive loads. In addition, this is also an important basis for the calculation and design of shell structures made of smart materials when subjected to shock waves or explosive loads.

Vibration Analysis of Bidirectional Functionally Graded Porous Plates Using MITC3+

The article presents the vibration behavior of bidirectional functionally graded (BDFG) porous plates using the new triangular 3-node element (a cubic bubble function for the interpolation of the rotations to enrich the bending displacements) which is called the MITC3+ element. The BDFG porous plates have material properties varying in two directions with even and uneven porosity distribution. Based on Hamilton’s principle, the motion equations for BDFG plates are derived. Then, some examples are performed to verify the accuracy and reliability of the proposed method. Finally, the new numerical results on the free vibration response of BDFG porous plates are provided.

Bending and free vibration analyses of CNTRC shell structures considering agglomeration effects with through-the-thickness stretch

The present work investigates an enhanced finite element model and numerical analysis to illustrate the agglomeration effect of Carbon Nanotubes (CNTs) on static and free vibration responses of reinforced composite plate and cylindrical panel shell. The developed model is based on the kinematics of the improved first-order-shear deformation theory (FSDT), assuming a parabolic variation of the transverse shear strains and fulfilling the zero circumstance of the transverse shear stresses at the extreme structure’ surfaces omitting the use of shear correction factors. The material properties of the nanocomposite are determined using a developed micromechanical model based on the Mori–Tanaka approach. The developed finite element formulation is based on three-dimensional constitutive equations without reduction involving the addition of one parameter of thickness change combined with the Enhanced Assumed Strain (EAS) method. Four enhancement models are established and discussed. In a first attempt, the improvement of the third bending strain using one or four parameters are presented. In a second attempt, the membrane strain is enhanced with four parameters. Due to lack of investigations on structural behavior of composite structures reinforced with agglomerated CNTs, new static and free vibration results for shell structures with three level of CNT agglomeration are examined. Parametric studies are here in developed to present the influences of the characteristic parameters on the structural behavior of the CNTRC shell in a new graphic way; such as the volume fraction and agglomeration of nanofibers, geometrical parameters, and boundary conditions. Based on numerical results, it is found that the agglomeration and distributions of the reinforcing fibers are really crucial and play a significant role on the static and vibrational performances of the structure.

Study on free vibration response of a liquid retaining composite structure considering fluid-wall interaction

Study on free vibration response of a liquid retaining composite structure considering fluid-wall interaction

A new higher-order beam theory for buckling and free vibration responses of laminated composite and functionally graded porous beams

The present study introduces a novel higher-order shear deformation theory for assessing buckling and free vibration characteristics in laminated composite and functionally graded porous beams. The proposed theoretical framework effectively considers three variables and eliminates the need for a shear correction factor. The governing equations are derived from the Lagrange principle, while Legendre-Ritz functions are utilised to solve the resulting problem. Various types of laminated composite beams with arbitrary lay-ups and functionally graded porous beams with symmetric or unsymmetric configurations are analysed. To validate the accuracy and efficiency of the proposed theory, several numerical examples are conducted and compared against the results of existing research endeavours.

Vibration and thermomechanical transient response of doubly curved FGM panels with porosities and elastically restrained edges

The present paper aims to analyze the influences of porosities, elevated temperature and elasticity of in-plane boundary conditions on the free vibration and nonlinear transient response of functionally graded material (FGM) doubly curved panels subjected to uniform lateral pressure. Porosities are assumed to exist in the FGM according to even and uneven distributions. Effective properties of porous FGM are determined using a modified rule of mixture. Basic equations in terms of deflection and stress function are derived basing on the classical shell theory taking into account von Kármán–Donnell nonlinearity and initial geometrical imperfection. Analytical solutions for simply supported panels are assumed and Galerkin method along with Runge–Kutta scheme are applied to obtain the deflection–time response for nonlinear dynamic analysis. Numerical results demonstrate that tangential constraints of edges have extremely significant influences on the vibration and transient response of porous FGM panels exposed to an elevated temperature. The analysis also reveals that porosities have negative and positive effects on the dynamic response of FGM panels at reference and elevated temperatures, respectively. Furthermore, when the edges are restrained, initial imperfection importantly influence the behavior tendency of porous FGM panels exposed to preexist thermal environment.

Vibration Analysis of a Carbon Nanotube Reinforced Uniform and Tapered Composite Beams

In this study, free and forced vibration responses of carbon nanotube reinforced uniform and tapered composite beams are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced uniform and tapered composite beams are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available in literature. Various parametric studies are also performed to investigate the effect of aspect ratio, percentage of CNT content, ply orientation, and boundary conditions on natural frequencies and mode shapes of a CNT reinforced composite beam. It was observed that the addition of carbon nanotube in fiber reinforced polymer composite (FRP) beam enhance the stiffness of the structure which consequently increase the natural frequencies and alter the mode shapes.

Electromechanical coupling enriched finite element method for dynamic characteristic of piezoelectric materials structures

To improve the application depth and breadth of intelligent unit devices made from piezoelectric structures, their kinetic properties shall be urgently studied. Herein, based on the basic equations and boundary conditions of piezoelectric materials, an interpolation coverage function of node displacement was introduced into the displacement shape function and potential shape function of coupling electromechanical finite element method (FEM), forming an electromechanical coupling enriched FEM generalized shape function. Together with the variation principle, an electromechanical coupling enriched FEM was put forward, and its motion equations were deduced. Next, the free vibration and transient response of the piezoelectric structure were analyzed, and the accuracy and validity of the new method were validated with numerical cases. Results show this method has high application prospects for analyzing the dynamic properties of piezoelectric material structures.

Model-assisted clustering for automated operational modal analysis of partially continuous multi-span bridges

Long multi-span bridges represent a broad section of the civil roadway infrastructure. Despite being so common, their condition-based maintenance through vibration-based Structural Health Monitoring (SHM) has been scarcely investigated in the literature. The dynamic identification of such structures through Operational Modal Analysis (OMA) is especially challenging due to of their quasi-periodic nature and the common existence of weak inter-span coupling. Even when designed following an isostatic scheme, there always exists a certain degree of coupling between spans due to the continuity of the deck, the pavement and imperfect expansion joints. Hence, the modal poles of the spans typically appear as dense clusters with closely spaced frequencies and mode shapes with similar wavelengths, which significantly hinders the identification of physical poles through stabilization diagrams. In this light, this paper proposes a model-based machine learning approach to conduct and interpret the OMA results of partially continuous multi-span bridges. The proposed method is a hierarchical clustering approach that leverages on the analytical solution of the vertical free vibration response of multi-span girders with weak inter-span rotational coupling, allowing the estimation of the modal features of any bridge configuration ranging from simply supported to perfectly continuous conditions. Detailed parametric analyses and discussions are presented to appraise the correlation between the inter-span rotational coupling and the clustering of the modal poles of multi-span bridges, as well as the influence of damage conditions of varying severity and extension. On this basis, a model-based cut-off distance threshold for hierarchical clustering of stable poles is proposed to assist the automation of the global OMA of multi-span bridges. The developed formulation is tested in a real-world in-operation seven-spans reinforced concrete girder bridge, the Trigno V Bridge in Italy.

Thermomechanical Response of Functionally Graded Ti-6Al-4V and Zirconia Biomaterial Plates

This article studies the free vibration responses of functionally graded material (FGM) porous nanoplates exposed to thermal load. The developed mathematical model includes a shear deformation, size-scale, and microstructure influence by a high-order shear deformation (HSDT) and nonlocal strain gradient (NGST) theories. The study considers four different porosity patterns across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The equation of motion of the FGM porous nanoplate, including the effects of thermal load, is derived with Hamilton's principle, and then solved analytically by employing the Navier method. For the free vibration responses of the nanoplate, the effects of nonlocal and strain gradient elasticities, temperature rise, porosity volume fraction and its distribution are analyzed.

Static bending, free and forced vibration responses of organic nanobeams in a temperature environment

Static bending, free and forced vibration responses of organic nanobeams in a temperature environment

PENGARUH INTERAKSI TANAH-STRUKTUR PADA TANAH LUNAK TERHADAP DILATASI DARI DUA BANGUNAN TINGGI AKIBAT GEMPA

Earthquakes that occur in buildings can lead to collision force with the next building if the initial gap between the two buildings is not sufficient for its free vibration responses. Collisions can cause amplification of the internal forces in the structural elements and the collision force on the contact zone is usually not considered in the initial design so that it can lead to damage and collapse of buildings. This study aime to determine the effect of Soil-Structure Interaction in the dilatation of two structures in soft soil with consideration of the collision to the next building. The structure is modeled as a structural system with multi degree of freedom (MDOF). The upper structure is considered linear elastic model and does not have damping as well as the lower structure (foundation). The collision can only occur on the floor level of the two buildings in which the contact zone is modeled as an elastic element. The rheological model for Soil-Structure Interaction are taken as a horizontal spring and a rotational spring. Structural dynamic equations was solved by using the Houbolt integration method. The resolution of numerical program was solved by the Matlab software. The results of study showed that soil-strucutre interaction increases the relative displacement under the condition of initial distance (gap) between the two buildings was reduced.

Free and forced vibration response of a laminated composite sandwich beam with dual honeycomb core: Numerical and experimental study

AbstractFree and forced vibration characteristics of composite sandwich beams with single‐core (SC) and dual‐core (DC) are investigated in this study. The wet hand‐layup technique is followed to make the composite face sheet, and honeycomb cores are 3D printed using the fused filament fabrication method. The natural frequencies of SC and DC sandwich beams were measured using experimental modal tests and validated through a three‐dimensional finite‐element model. Also, parametric studies on the geometry of composite structures are performed to scrutinize the effect of DC sandwich beams with different ply orientations, length‐to‐breadth ratios, core thickness, and core cell wall thickness. In addition, the transverse vibration responses of SC and DC sandwich beams are examined under harmonic force excitations at different end conditions. The study result shows that the sandwich beam's vibration behavior is enhanced by the inclusion of a core.

Static and free vibration response of a box-girder bridge using the finite element technique

PurposeIn this study, a finite element model of a box-girder bridge along with the railway sub-track system is developed to predict the static behavior due to different combinations of the Indian railway system and free vibration responses resulting in different natural frequencies and their corresponding mode shapes.Design/methodology/approachThe modeling and evaluation of the bridge and sub-track system were performed using non-closed form finite element method (FEM)-based ANSYS software.FindingsFrom the analysis, the worst possible cases of deformation and stress due to different static load combinations were determined in the static analysis, while different natural frequencies were determined in the free vibrational analysis that can be used for further analysis because of the dynamic effect of the train vehicle.Research limitations/implicationsThe scope of the current investigation is confined to the structure's static and free vibration analysis. However, this study will help the designers obtain relevant information for further analysis of the dynamic behavior of the bridge model.Originality/valueIn static analysis, the maximum deformation of the bridge deck was found to be 10.70E-03m due to load combination 5, whereas the maximum natural frequency for free vibration analysis is found to be 4.7626 Hz.

Free Vibration Response of a Steel Liquid Storage Tank with Porous and Perforated Columns via an Exact Continuum Method

The presence of predictable cavities inside a structure is often preferable as it will reduce the vibration amplitude. In this article, inspired by the traditional mass attached to the beam system, in order to solve the problem of free vibration of the steel liquid storage tank with a column made of porous and perforated materials using an exact analytical continuum model is formed. The free vibration response of the mass attached column made of porous materials and holes is established by using a new analytical method known as the Fourier series with Stokes’ transform. The free vibration frequencies are obtained by using an eigen-value approximation, and the influences of the number of holes, filling ratio, porosity and other parameters on the free vibration response are explored. It is shown that an increase in the mass parameter, filling ratio and porosity parameter of the column with an attached mass system could significantly affect the free vibration response of the system.

Analytical modeling on the vibration response of a beam‐stiffened Mindlin thick plate with free boundary conditions

AbstractThis paper presents a new analytical solution for the vibration response of a beam‐stiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform. In the solution, the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions. It provides an easily implemented tool for exploring complex edge value problems for a class of higher‐order partial differential equations represented by fully free‐stiffened Mindlin thick plates. The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam‐stiffened plate with those calculated using a beam‐stiffened thin plate and those from finite element analysis.

A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to investigate the free vibration response incorporating the porosities and microstructure-dependent effects. Two types of tri-coated FG shells are investigated, hardcore and softcore FG shells, and five distribution patterns are proposed. A novel modified field of displacement is proposed by reducing the number of variables from five to four by considering the shear deformation effect. The shell is rested on a viscoelastic Winkler/Pasternak foundation. An analytical solution based on the Galerkin approach is developed to solve the equations of motion derived by applying the principle of Hamilton. The proposed solution is addressed to study different boundary conditions. The current study conducts an extensive parametric analysis to investigate the influence of several factors, including coated FG nanoshell types and distribution patterns, gradient material distribution, porosities, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and elastic foundation variation on the fundamental frequencies. The provided results show the accuracy of the developed technique using different boundary conditions.

Structural damage severity classification from time-frequency acceleration data using convolutional neural networks

Structural damage identification involves interpretation of vibration measurements to identify patterns that are indicative of changes in structural characteristics. Identification of such patterns using machine learning (ML) algorithms is a primary task in data-driven structural health monitoring. However, providing ML algorithms with features that are sensitive to damage has always been a challenge for accurate damage detection. In recent years, deep Convolutional Neural Networks (CNNs) proved to be versatile and powerful tools to identify the underlying patterns directly from low-level raw data. This study explores the applicability of CNNs to damage severity classification. A new format of input data for CNN damage identifiers is proposed based on time–frequency representations of acceleration data from multiple sensors. First, Continuous Wavelet Transformation (CWT) of acceleration response is employed to derive the time–frequency data, then, the results of transformations from multiple accelerometers are stored in separate channels creating a three-dimensional block of data. Such input data provide a CNN with structural information that expands into time, frequency, and spatial domains. To evaluate the accuracy of such a CNN-based classifier, a dataset comprised of free vibration response of a concrete beam under impact hammer tests is utilized. It is shown that a CNN trained with CWT data can successfully classify various severity of the damage, from minor to severe, with 100% accuracy. Also, this study examines the sensitivity of the CNN classifier to the number of training samples. It is demonstrated that the accuracy of such a network has a relatively lower sensitivity to the number of training samples and/or the number of measurement points to the degree that it maintains an F1-score above 0.813 when trained with data from one impact point and one sensor. On the other hand, for the case of a CNN classifier trained directly with time-series acceleration data the value of the F1-score drops to 0.590. Moreover, when compared with a multilayer perceptron trained with the extracted modal properties, it is illustrated that CNN classifiers have a better capability in capturing key features from the measurement, and thus produce more accurate predictions. Therefore, the combination of CNN classifiers with time–frequency data from multiple sensors results in damage identifiers that are less sensitive to sample size and more robust to changes in excitations and measurement points.

Uncertainty quantification in free vibration and aeroelastic response of variable angle tow laminated composite plate

The influence of uncertainty in material properties on free vibration and aeroelastic response of variable angle tow (VAT) laminated plates is presented in this work. Free vibration analysis is conducted by a finite element model based on third-order shear deformation theory. The FE model is further coupled with MSC. Nastran to carry out aeroelastic analysis of VAT laminates in the subsonic regime. MSC. Nastran helps to extract the aerodynamic influence coefficient matrix at discrete values of reduced frequencies using Doublet Lattice Method. The accuracy and adaptability of the highly efficient radial basis neural network (RBFN) based surrogate model developed for uncertainty analysis are checked by comparing the result with that of the Monte Carlo simulation. Stochastic analysis of natural frequencies and flutter characteristics of VAT laminates are conducted through various parametric studies. Variance-based sensitivity analysis is used to calculate the contribution of individual material properties to the free vibration and aeroelastic response of VAT laminates. Further, the influence of the highly sensitive properties on the structural failure probability is estimated. This research can be leveraged to predict the probability of failure of the structure at different levels of material uncertainty present in it.