Free Vibration Analysis Research Articles

Improved Fourier Series-Ritz Method for Free Vibration Analysis of Hard Coating Damping Thin-Walled Cylindrical Shells with Thickness Variation Under Arbitrary Boundary Conditions

Improved Fourier Series-Ritz Method for Free Vibration Analysis of Hard Coating Damping Thin-Walled Cylindrical Shells with Thickness Variation Under Arbitrary Boundary Conditions

Vibration Correlation Technique: Methodology Applied to Buckling of Large-Scale Sandwich Cylindrical Shell

This paper assesses the Vibration Correlation Technique's (VCT) applicability within the context of sandwich cylindrical shells through detailed numerical investigation. The study utilizes a sandwich shell from NASA's Shell Buckling Knockdown Factor project. Finite element models are implemented, incorporating initial mid-surface and thickness imperfections to replicate NASA's buckling test campaign. The numerical results are compared to the experimental data, validating the nonlinear solution with an approximate deviation of 1%. Subsequently, the VCT experimental campaign is numerically conducted through free vibration analyses at different load levels, enabling a comprehensive evaluation of VCT's applicability. The results verified the effectiveness of the VCT, demonstrating a deviation of less than 10% when estimating the buckling load for load levels below 65% of the nonlinear buckling load. Overall, the findings confirm the non-destructive nature of the VCT when employed on such structures, supporting future practical applications.

Isogeometric analysis of functionally graded panels using Bézier triangles

Isogeometric Analysis is a numerical method that integrates the concepts of geometric modeling and structural analysis. It approximates the displacement field using the same basis functions employed by CAD systems to describe the structure’s geometry. This work proposes an isogeometric formulation for analysis of functionally graded panels based on rational Bézier triangles, allowing the exact geometry representation and automatic discretization of topologically complex models. The formulation is applied to the free vibration and stability analysis of functionally graded plates and curved panels. Monotonic convergence under mesh refinement was observed in all examples. Furthermore, results show that curved functionally graded panels display a complex nonlinear behavior and can present bifurcation buckling before reaching the limit load.

Vibration Analysis of Perovskite Solar Cells Resting on Porous Nanocomposite Substrate in Thermal Environment

The free vibration analysis of a perovskite solar cell (PSC) within thermal environments is studied through a quasi-3D plate model. This model is designed to account for the stretching effects and non-uniform shear strains throughout the thickness. The PSC film is represented in the model as a thin laminated plate, comprising five distinct plies: ITO, PEDOT:PSS, perovskite, PCBM, and Au. A graphene platelets reinforced composite (GPLRC) substrate, made of Poly (methyl methacrylate), is assumed to be located under the noted five layers. The GPLRC substrate is conceptualized in the model as a porous foundation with finite depth. The foundation stiffnesses are determined using a modified Vlasov model, and the equivalent Young modulus of the foundation is evaluated using a modified Halpin–Tsai model, introducing the porosity coefficient. It is also considered that the material properties of GPLRC substrates exhibit temperature dependency. For the PSC with all edges simply supported, Navier solution method is applied to obtain the frequencies and associated mode numbers. Based on the results presented in this study, an increase in the porosity and thickness of the substrate can negatively impact the frequencies of the structure. However, natural frequencies experience almost no change if the temperature rises.

Numerical Free Vibration Analysis of Sandwich Beams with a Steel-Ceramic FGM Core and FG-CNTRC Facesheets

Numerical Free Vibration Analysis of Sandwich Beams with a Steel-Ceramic FGM Core and FG-CNTRC Facesheets

EFG meshless-ANN approach for free vibration analysis of functionally graded material plates on elastic foundation in thermal environments

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone.

Variable Stiffness and Free Vibration Analysis of Cylindrically Curved Plate with Variable Thickness Graphene Reinforced Porous Material

Variable Stiffness and Free Vibration Analysis of Cylindrically Curved Plate with Variable Thickness Graphene Reinforced Porous Material

Free Vibration Analysis of a Rotating, Dimensionally Varying Sandwich Beam Subjected to A Pulsating Axial Load

Free Vibration Analysis of a Rotating, Dimensionally Varying Sandwich Beam Subjected to A Pulsating Axial Load

Nonlocal Strain Gradient Theory for Free Vibration Analysis of FG Nano-scale Beams in Thermal Environments Using an Efficient Numerical Model

Nonlocal Strain Gradient Theory for Free Vibration Analysis of FG Nano-scale Beams in Thermal Environments Using an Efficient Numerical Model

Modal characteristics of functionally graded porous Timoshenko beams with variable cross-sections

The study focuses on the free vibration analysis of beams composed of functionally graded porous materials and characterized by a variable cross-section along their length. A broad range of beams is examined encompassing various tapered configurations, porosity profiles, and porosity content. The equations of motion are derived using Hamilton’s principle within the framework of Timoshenko beam theory. These equations are solved semi-analytically using the differential transform method, which has been adapted to incorporate various boundary conditions such as clamped–clamped, clamped–free, clamped–pinned, and pinned–pinned constraints within a general formulation of the beam eigenvalue problem. To validate the proposed solution technique, computed natural frequencies are compared with existing literature results for tapered inhomogeneous beams and uniform porous beams. Notably, new results are obtained for tapered porous beams. In this regard, a comprehensive parametric study explores the influence of various factors on the natural frequencies and mode shapes of functionally graded porous beams with variable cross-sections. These factors include the type of porosity profiles, a range of porosity parameters, cross-section taper ratios, and specific boundary conditions. The findings deepen our understanding of the modal characteristics of functionally graded porous beams, providing valuable guidance for engineering design and structural optimization in relevant applications. Additionally, they may serve as benchmarks for other researchers.

Theoretical and experimental transverse vibration analysis of a non-uniform composite helical tidal turbine foil

Recently, tidal energy has gained attention as an attractive renewable source of power generation. In this context, tidal turbine foils must operate in harsh conditions and extremely variable dynamic loads. Considering the expensive dynamic tests required for these large structures, developing validated dynamic models could be valuable for failure prediction and design purposes. In this paper, the free and forced vibration behaviour of the cantilevered part of a non-uniform helical tidal turbine foil made from the composite material is investigated theoretically and experimentally. In this regard, governing vibration equations of the foil with related boundary conditions are presented. The free vibration analysis of the foil is performed by solving a boundary-value problem, where a closed-form solution, based on the mode summation method, for the forced vibration of the foil is employed. Finally, the obtained numerical results (natural frequency and dynamic displacements) are compared with the corresponding results from experiments to validate the vibration equations and the employed solution. Acceptable agreement between numerical and experimental data confirms that the vibration model presented in this study can be employed to predict the dynamic response, parametric study, optimization, and design of the tidal foil without performing costly experiments.

Free vibration analysis of multi-layer perforated fibre-reinforcement damping composite beam

This paper investigates the effective elastic constants of the perforated fibre-reinforcement damping membrane, taking into account the variations in perforation array and ply orientation angle using the homogenization method and the off-axis stress-strain relation. The equations for the free vibration of the composite beam with multi-layer perforated fibre-reinforcement damping membranes are derived using the first-order shear deformation theory and the Hamilton principle. These equations are then solved using the Navier method. The novelty of this paper lies in the achievement of an effective elastic constants model and vibration analysis for the multi-layer composite beam under simply supported boundary conditions. The calculated results are then compared with experimental values and finite element results to validate the theoretical model and method. Furthermore, the paper explores the graphical variation of mechanical performance with system parameters, providing a theoretical foundation for future researchers in the composite field.

Transfer matrix modeling for asymmetrically-nonuniform curved beams by beam-discrete strategies

Nonuniform and curved beams can be found in extensive engineering scenarios, ranging from big-scale structures of buildings, bridges to small mechanical systems of aerofoils, blades, micromachines, robotics and sensors. However, variable curvature and transverse asymmetry often lead to a complicated dynamic modeling. In this paper, two beam-discrete strategies are comparatively presented for the free vibration analysis of transversely asymmetric and curved beams and even their combinations. The proposed methodology involves discretizing a general nonuniform and curved beams into a sequence of constant beam segments with non-coaxial nodes or inclination angles, which enables a modular transfer matrix modeling process and hence offers a new way to divide the complex modeling into easier steps. A unified transfer matrix is derived for constant beam elements with non-coaxial nodes and inclination angles accounting for the shear deformation, rotary inertia and axial load in any combinations. The proposed beam-discrete strategies with a unified transfer matrix provide a new perspective in contrast to previous investigations. The advantages of easy programming and small degrees of freedom in the traditional transfer matrix method is extended to transversely asymmetric nonuniform and curved beams. Comparative validation with several engineering beams confirms these advantages.

An Assessment of a New Hyperbolic Shear Deformation Theory for the Free Vibration Analysis of Cosine Functionally Graded Doubly Curved Shells under Various Boundary Conditions

An Assessment of a New Hyperbolic Shear Deformation Theory for the Free Vibration Analysis of Cosine Functionally Graded Doubly Curved Shells under Various Boundary Conditions

Size-dependent free vibration analysis of multidirectional functionally graded nanobeams via a nonlocal strain gradient theory

Size-dependent free vibration analysis of multidirectional functionally graded nanobeams via a nonlocal strain gradient theory

A refined shell theory considering the effects of transverse normal strain for the analysis of functionally graded porous shallow shells with double curvature

In this paper, a static and free vibration analysis of functionally graded porous shallow shells with double curvature containing an even distribution of porosity is investigated using a trigonometric shear and normal deformation theory. Both the effects of transverse shear and normal strains are included in the present theory to investigate their effects on the responses of FGM porous shells. The theory satisfies zero transverse shear stress conditions at the top and bottom surfaces of the shell. Hamilton’s principle is used for obtaining governing equations and boundary conditions of the present theory for functionally graded porous shallow shells. The FGM porous shell is assumed isotropic at any point within the shell domain, with its elastic properties varying across its thickness by a power law in terms of the volume fractions of the shell constituents. The simply-supported FG porous shell is analyzed in the present study using the Navier method. The numerical results of FGM porous plates are obtained and compared with other higher-order theories available in the literature to verify the present theory. Further, the numerical results are presented for the FGM porous shells with double curvature. The effects of a/h ratios, porosity distribution factor, and radii of curvature on deflections, stresses, and fundamental frequencies are presented. The solution of hyperbolic and elliptical FGM porous shells is presented for the first time in this paper.

Nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells: Theoretical and experimental investigations

In this study, the nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells (FHSCSs) are investigated theoretically and experimentally. Initially, a time-domain minimum residual (TDMR) method is first adopted for the analysis of nonlinear free and forced vibrations of the FHSCSs, which is based on a dynamical model developed, with the effective material parameters of the foam-filled honeycomb core being obtained by employing the Gibson method and the Hamilton equivalence technique. Based on the high-order shear deformation shell principle and von Karman's theory, the nonlinear natural frequencies and resonant responses are solved using the Broyden iterative approach and TDMR method. Furthermore, several literature results are utilized for the rough verification of such a method. Meanwhile, the FHSCS specimens are made manually and comprehensive tests with various base excitation energies are undertaken to provide a thorough validation of the current method. It can be found that the largest calculation errors of natural frequencies and resonant responses are 4.9 and 12.3%, respectively. Finally, the influences of the core form and base excitation amplitudes on the nonlinear vibration behaviours of the FHSCSs are examined. It can be noticed that the foam-filled FHSCS structure exhibits a more excellent anti-vibration capability compared to the non-foam-filled structure. The solving method, fabrication technique, and valuable findings in the current study highlight the path for the design and implementation of such advanced shells.

Free Vibration Analysis of Toroidal Shell Segments Reinforced by Graded Graphene in Elastic Medium

Free Vibration Analysis of Toroidal Shell Segments Reinforced by Graded Graphene in Elastic Medium

Free vibration analysis of bio-inspired double- and cross-helicoidal laminated composite plates

Nature-built structures effectively sustain higher loads without failing, even though they are made of weak organic materials. The laminated construction mode in various fish scales provides them toughness and flexibility. The present manuscript aims to carry out the free vibration analysis of double- and cross-helicoidal laminated composite plates inspired by the scales of fish. The study has been carried out using the recently proposed finite element-based higher-order zigzag theory. The influence of aspect ratio, side-to-thickness ratio, skew angle, and end conditions on the free vibration behavior of double- and cross-helicoidal plates is depicted. The mode shapes of the plates are studied in detail. The free vibration behavior of skew plates is also studied for the first time. An improved performance of the helicoidal plate compared to the conventional lamination scheme has been obtained.

Free vibration Analysis of Beams with Functional Gradient Materials with Cracks

The article presents the development of a dynamic model for a functionally graded material (FGM) beam incorporating cracks. Initially, it assumes an exponential distribution of material properties along the thickness direction of the beam and simulates the opening crack using a zero-mass rotational spring model. This approach enables the calculation of bending stiffness and local flexibility at the cracked section. Subsequently, drawing upon Timoshenko beam theory and von Kármán geometric nonlinear theory, the study formulates the energy equation of the beam and establishes the partial differential control equations for the cracked FGM using Hamilton's principle. The method of separation of variables is employed to discretize the partial differential motion equations into ordinary differential motion equations. Beam functions serve as mode functions, whose unknown coefficients are determined according to the boundary and continuity conditions, thereby yielding the natural frequencies and mode shapes of the cracked FGM beam. Numerical analysis is conducted to evaluate the impact of boundary conditions, the relative position of cracks, and the length-to-thickness ratio on the natural frequencies of the cracked FGM beam.