Finite Element Free Vibration Research Articles

Finite Element Free Vibration Analysis of Clamped Functionally Graded Plate

The main objective of this research is to present analytical solutions for free vibration analysis of moderately thick plates composed of functionally graded materials. Finite element analysis using first-order shear deformation plate theory (FSDT) has been used in the research. Nine noded-isoparametric lagrangian plate bending elements are used in the analysis. Young’s modulus and density per unit volume are assumed to vary continuously through the plate thickness according to power-law distribution. The results have been validated with the existing literature available from other analytical and numerical techniques. The effect of different plate parameters such as aspect ratios, thickness to length ratios, and gradient indices on the natural frequencies of FG rectangular plates is presented. Only clamped boundary conditions have been investigated. It is found that the frequency parameter depends considerably on the said parameters.

Finite Element Free Vibration Analysis of Functionally Graded Folded Plates

Finite Element Free Vibration Analysis of Functionally Graded Folded Plates

Experimental and Finite Element Studies on Free Vibration of Areca Leaf Sheath Reinforced Polymer Composites

The present work deals with the experimental and finite element free vibration studies on areca leaf sheath reinforced polymer composites. In this study fundamental frequencies are obtained for five boundary conditions numerically (such as CFFF, CFCF, SSSS, CSCS and CCCC) and only for 2 boundary conditions (CFFF and CFCF) experimentally. The natural frequencies were determined using the CQUAD8 finite element of MSC/NASTRAN and comparison made between the experimental values and the finite element solution. The effects of age of areca palm, number of layers, type of surface modification and boundary conditions on the natural frequencies of composites were studied. The experimental values of the first, second and third natural frequencies are in good agreement with those of the finite element solution in the case of areca leaf sheath reinforced composites under CFFF and CFCF boundary conditions. The natural frequency values found increases with an increase in the number of layers, age of areca palm and alkali percentage from 5 to 15% [46, 47]. Among different boundary conditions considered, composites with the CCCC boundary condition have exhibited higher values of natural frequencies as compared to other boundary conditions under finite element solutions.

Modal Characterization of Sandwich Skew Plates

Abstract The current work focuses on the experimental and finite element free vibration studies of laminated composite sandwich skew plates. The comparison was made between the experimental values obtained by the Fast Fourier transform (FFT) analyzer and a finite element solution obtained from CQUAD8 finite element of The MacNeal-Schwendler Corporation (MSC) / NASA STRucture Analysis (NASTRAN) software. The influence of parameters such as aspect ratio (AR) (a/b), skew angle (α), edge condition, laminate stacking sequence, and fiber orientation angle (θ°) on the natural frequencies of sandwich skew plates was studied. The values obtained by both the finite element and experiment approaches are in good agreement. The natural frequencies increase with an increase in the skew angle for all given ARs.

Effect of crack location on buckling and dynamic stability in plate frame structures

It is well known that damages affect the dynamic characteristics of the structures in such a way that they may lead those structures to fail. Therefore, it is essential to construct a reliable mathematical model for estimating the effect of the damage in these structures. In this study, the effect of the straight, through-thickness crack and its location on the thin single-bay one-storey, two-bay-one-storey, and single-bay two-storey plate frames is investigated. For this purpose, a four-node quadrilateral plate bending and membrane elements are combined to perform finite element free vibration analysis of the healthy and cracked thin plate frame structures. The Classical Plate Theory is employed to satisfy the strain and stress conditions of these thin structures. A computer code is written using MATLAB to obtain the first three natural frequencies, critical buckling loads, and the first unstable regions of the healthy and cracked thin structures. To ensure the validity of the employed mathematical model, a convergence analysis is performed via ANSYS. The effect of crack location in plate frame structures is investigated by measuring the differences between the healthy and cracked structures’ first three buckling modes and the first unstable region. It is seen that the bending regions of the buckling modes are more affected by the crack than the other zones. Besides, crack occurrence within these regions has more impact on the first unstable regions. Accordingly, it has been revealed that the bending regions are the weakest locations of the frame structures. Therefore, potential cracks occurred within these regions may affect the structural integrity more than those of emerged in other regions.

Finite Element Free Vibration Analysis of Marine Composite Laminates with Variable Stiffness

Ouyang, X., 2020. Finite element free vibration analysis of marine composite laminates with variable stiffness. In: Yang, D.F. and Wang, H. (eds.), Recent Advances in Marine Geology and Environmental Oceanography. Journal of Coastal Research, Special Issue No. 108, pp. 270–273. Coconut Creek (Florida), ISSN 0749-0208.Reinforced variable stiffness composites are commonly used in marine engineering and marine engineering structures. The free vibration behavior of composite laminates varies with varying stiffness. Classical layering theory and first-order shear deformation theory are used to model the structure. On the basis of the virtual work principle and the finite element method, the vibration equation is established. The curved fiber can improve the design performance of composite laminates, and the free vibration behavior of composite laminates with variable stiffness can be changed by changing the orientation of the fiber.

“Traveling-wave tube mechanics simulator suite” a CAD/CAE integrated rapid redesign system of vibration analysis for traveling-wave tubes

Traveling-wave tubes (TWTs) are popularly used as the microwave power amplifier in civil and military applications and have a high mechanical sensitivity. It is necessary to understand their vibration characteristics under all operating conditions. To address this issue, a CAD/CAE integrated rapid redesign system of vibration analysis with unified data architecture (UDA) has been developed and presented in this paper. The UDA is presented to make CAD and CAE be an organic entity. This system is composed of the following four layers: (i) CAD/CAE integrated design environment, (ii) parametric modeling and fast modeling platform with custom-built tools, (iii) accurate and fast finite element free vibration analysis solver based on rapid solving techniques of equation, and (iv) fast finite element random vibration analysis solver. The CAD/CAE integrated system concept is typically applied in loop design-analysis-redesign procedures. In this CAD/CAE integrated design system, the designers can freely and rapidly complete component design and performance analysis simultaneously instead of using two different software or two interface environment. To improve the accuracy and efficiency of large-scale finite element vibration analysis, especially for free vibration analysis, an improved Lanczos iteration method with a new three-level preconditioner is developed and pseudo excitation method is introduced to perform random vibration analysis. The new three-level preconditioner is composed of a multifrontal block incomplete cholesky preconditioner, a p-type multigrid preconditioner, and a block Jacobi preconditioner. The developed system has been applied to the design of TWTs and been found to shorten the design cycle significantly compared with ANSYS.

Free vibration studies on plates with central cut-out

The present work deals with the experimental and finite element free vibration studies on isotropic and laminated anti-symmetric angle-ply composite plates with central cut-out under clamped-free–clamped-free boundary condition. The natural frequencies were determined using the CQUAD8 finite element of MSC/NASTRAN and comparison made between the experimental values and the finite element solution. The effects of aspect ratio, cut-out size and cut-out shape on the natural frequencies of plates were studied. The experimental values of the first, second and third natural frequencies are in good agreement with those of the finite element solution in the case of both isotropic and laminated composite plates with and without cut-outs. The non-dimensional frequency coefficient Kf are found increases with increase in length-to-cut-out size ratio (d/a) irrespective of the cut-out shape. In case of laminated composite plates, the non-dimensional frequency coefficient Kf increases monotonically with an increase in the aspect ratio irrespective of hole size and shapes for all the three modes of vibration.

Vibro-acoustic Analysis Inside Cross Ply Laminated Composite Cavity

In this vibro-acoustic problem, an acoustic domain is confined within a partly flexible laminated composite rectangular enclosure, subjected to harmonic excitement. A mobility relation is derived from the finite element free vibration analysis, to relate acoustic pressure and structural velocity normal to the containing structure. A boundary element solver for the Helmholtz equation with 8 noded quadratic isoparametric elements is developed from pressure-velocity formulation. Velocity is specified over the rigid part of the boundary. In the interactive boundary the mobility relation correlates nodal pressures and velocities, neither being explicitly known. The pressure boundary values are solved from the boundary element equations coupled with the mobility relations, while the velocity at flexible boundary is computed from mobility relationship. New results presented here reveal the effects of the symmetric and anti-symmetric cross ply laminated composite cavity with the variation in wall thickness and increase in number of layers.

On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through-width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature.

Foundation damping and the dynamics of offshore wind turbine monopiles

The contribution of foundation damping to offshore wind turbines (OWTs) is not well known, though researchers have back-calculated foundation damping from “rotor-stop” tests after estimating aerodynamic, hydrodynamic, and structural damping with numerical models. Because design guidelines do not currently recommend methods for determining foundation damping, it is typically neglected. This paper investigates the significance of foundation damping on monopile-supported OWTs subjected to extreme storm loading using a linear elastic two-dimensional finite element model. The effect of foundation damping primarily on the first natural frequency of the OWT was considered as OWT behavior is dominated by the first mode under storm loading. A simplified foundation model based on the soil-pile mudline stiffness matrix was used to represent the monopile, hydrodynamic effects were modeled via added hydrodynamic mass, and 1.00% Rayleigh structural damping was assumed. Hysteretic energy loss in the foundation was converted into a viscous, rotational dashpot at the mudline to represent foundation damping. Using the logarithmic decrement method on a finite element free vibration time history, 0.17%-0.28% of critical damping was attributed to foundation damping. Stochastic time history analysis of extreme storm conditions indicated that mudline OWT foundation damping decreases the maximum and standard deviation of mudline moment by 7–9%.

Experimental and numerical identification of structural modes for engineering education

Development of simple classroom demonstration device and software for visualization of structural normal modes is presented. Device is made of parts of old speaker, controlled with personal computer, where the harmonic motion of solenoid is used as an excitation for beam and plate models. Simple code for finite element free vibration analysis of plates is written in Wolfram Mathematica. Good agreement of results and attractive visual patterns of normal modes attracted attention of students. Results are confirmed using modern modal testing methods. Presented approach is complementary to standard teaching of structural dynamics.

Free vibration and buckling response of hat-stiffened composite panels under general loading

The paper presents finite element free vibration and buckling analysis of laminated hat-stiffened shallow and deep shells using arbitrarily oriented stiffener formulation. Modified approach for modelling the curved stiffener is implemented using necessary transformations. A simplified stiffener formulation is presented to accommodate various shapes of stiffener shapes in developing the rigidity matrix for the finite element formulation. Investigation has been carried out on free vibration and buckling analyses of laminated composite stiffened shell structures with laminated open section (rectangular or ‘T’ shaped) and closed section (‘hat’ shaped) stiffeners. Parametric study on the hat-stiffened panels for the free vibration and buckling analyses confirms that the closed section stiffener being torsionally rigid is found to show better performance over open section stiffeners.

A mixed differential quadrature and finite element free vibration and buckling analysis of thick beams on two-parameter elastic foundations

As a first endeavor, a mixed differential quadrature (DQ) and finite element (FE) method for boundary value structural problems in the context of free vibration and buckling analysis of thick beams supported on two-parameter elastic foundations is presented. The formulations are based on the two-dimensional theory of elasticity. The problem domain along axial direction is discretized using finite elements. The resulting system of equations and the related boundary conditions are discretized in the thickness direction and in strong-form using DQM. The method benefits from low computational efforts of the DQ in conjunction with the effectiveness of the FE method in general geometry and systematic boundary treatment resulting in highly accurate and fast convergence behavior solution. The boundary conditions at the top and bottom surface of the beams are implemented accurately. The presented formulations provide an effective analysis tool for beams free of shear locking. Comparisons are made with results from elasticity solutions as well as higher-order beam theory.

3-D digital photogrammetric measurement of the structure and 3-D finite element free vibration analysis

3-D digital photogrammetric measurement of the structure and 3-D finite element free vibration analysis

A coupled FE‐BE analysis of acoustic cavities confined inside laminated composite enclosures

The structural acoustic problem, wherein an acoustic domain is confined within a partly flexible laminated composite enclosure is presented. From the finite element free vibration analysis of the laminated folded plate structure a mobility relation is derived between the normal velocity of the structure and normal pressure on the structure. A boundary element solver for the Helmholtz equation with quadratic isoparametric elements is developed using pressure‐velocity formulation. Velocity is known over certain parts of the boundary, the rest being the interactive boundary, where the mobility relation correlates nodal pressures and velocities, neither explicitly known. The pressure boundary values are solved from the boundary element and the mobility relations, while the nodal particle velocities and domain pressures are computed at desired points thereafter. New results presented here reveal the effects of the variation in magnitude of structural damping, fiber angles and the thickness of walls.

Finite Element Free Vibration Analysis of Smart Laminated Composite Beams and Plates

The present paper deals with the development of a finite element method for the free vibration analysis of smart laminated composite beams and plates. The structure consists of a laminated composite substrate to which are surface bonded or embedded a set of piezoelectric layers, one of which is a sensor while the others are actuators. The analysis considers the linear piezoelectric constitutive relations and the first order shear deformation behaviour. An eight noded quadratic isoparametric piezoelectric element is developed to discretize the analysis domain, and the same shape functions are used to describe the electrical field, the charge density, the structural geometry as well as the structural displacements. Numerical results are obtained to study the effects of (1) stacking sequences of the composite laminae and piezoelectric layers, (2) geometric boundary conditions and (3) application of electrical voltages on the free vibration frequencies.

A finite element free vibration analysis of a thermally stressed spinning plate

A Lagrangian quadratic finite element formulation is used to analyse the free vibration problem in spinning isotropic plates exposed to a thermal environment. The plate is oriented arbitrarily with respect to the spinning hub. The inplane component of the distributed centrifugal force produces inplane tensile stresses that add to the bending strain energy. The normal component is added to the inertia force. A finite element steady-state heat conduction analysis of the plate yields the two-dimensional temperature field (convection terms due to spinning inertia are accounted for). In the thermo-structural interface, the inplane thermal forces, and subsequently the inplane thermal stresses, are evaluated. These stresses further affect the bending strain energy. The formulation includes the effects of transverse shear deformation and rotary inertia of the plate. In the numerical examples considered, the effects of the speed of rotation, the hub radius and the high temperature gradients on the non-dimensional frequency parameter, are clearly brought out.

Finite element free vibration analysis of eccentrically stiffened plates

A new finite element model is proposed for free vibration analysis of eccentrically stiffened plates. The formulation allows the placement of any number of arbitrarily oriented stiffeners within a plate element without disturbing their individual properties. A plate-bending element consistent with the Reissner-Mindlin thick plate theory is employed to model the behaviour of the plating. A stiffener element, consistent with the plate element, is introduced to model the contributions of the stiffeners. The applied plate-bending and stiffener elements are based on mixed interpolation of tensorial components (MITC), to avoid spurious shear locking and to guarantee good convergence behaviour. Several numerical examples using both uniform and distorted meshes are given to demonstrate the excellent predictive capability of this approach.

Finite element free vibration analysis of point supported laminated composite cylindrical shells

A finite element analysis for the free vibration behaviour of point supported laminated composite cylindrical shells is presented. Eight-noded curved quadrilateral isoparametric elements are used. The formulation is based on the assumptions of the first order shear deformation theory for thin, shallow shells. Some of the results obtained in the analysis are compared with those present in the existing literature. Several numerical results are also presented for selected material parameters, shell geometry and support spacing to study the free vibration characteristics of various point supported laminated composite cylindrical shells.