Vibration Characteristics Of Plates Research Articles

Vibration characteristics of eccentric annular plates

An effective theoretical method for investigating the vibration characteristics of eccentric annular plates is developed. The vibration equation of eccentric annular plates is solved by utilizing the Bessel function as the vibration mode function and combining it with the translational addition theorem for cylindrical vector wave functions. Substituting the boundary conditions into the vibration mode function yields the frequency equation. The natural frequencies and corresponding vibration modes of the plate are obtained by determining the natural frequency coefficients. Compared with the results obtained from the finite element method (FEM) and vibration experiment, the correctness of the mode shapes and natural frequencies of the plate obtained by the present method are validated. The influences of several parameters such as the eccentric distance, the structural parameters, and various boundary conditions on the vibration characteristics of the plates are discussed. An analysis on the mode composition of the eccentric annular plates is also presented. The research results are useful for the practical engineering applications of the eccentric annular plates.

Influence of Carbon Nanotubes on Stability and Vibration Characteristics of Plates and Panels in Thermal Environment: A Review

Influence of Carbon Nanotubes on Stability and Vibration Characteristics of Plates and Panels in Thermal Environment: A Review

Free vibration of in-plane bi-directional functionally graded materials rectangular plates with geometric imperfections and general elastic restraints

This research addresses the free vibration performance of bi-directional functionally graded materials (BDFGMs) rectangular plate with general boundary restraints and geometrical imperfections. The symmetric/asymmetric material distributions subject to power-law along in-plane two directions are considered. Two types of geometric imperfections are formulated employing transcendental functions, including the sine-type imperfection which is global eccentric/symmetrical and depicted by sine and exponential functions, and the cosine-type global/localized imperfections which is simulated by hyperbolic and cosine functions. The general boundary restraints are imitated by artificial virtual springs. The Lagrangian energy function is formulated, and then vibration characteristics of plates are acquired with the Ritz method and improved Fourier series. Verifications are carried out for accuracy of theoretical model and reliability of solution method. A comprehensive numerical investigation are exhibited to explore the influencing mechanism of material distribution patterns, geometrical imperfection modal and elastic boundary restraints on vibration performance of rectangular plates. The results show that the in-plane material gradient can function as regulatory measures for dynamic characteristic of plates. In addition, geometric imperfections may cause singularity in vibration performance of plate. These innovative results may serve as a benchmark for future studies on design or analysis of plates.

A Unified Solution Method for Free Vibration of Arbitrarily Shaped Plates without or with Cracks

This paper presents a new approach for analyzing the free vibration of thin plates with arbitrary piecewise smooth curvilinear contour under various boundary conditions. It can also be applied to plates with cracks. This approach is based on the transformation of energy integral expressions and the domain decomposition technique. Furthermore, boundary conditions are modeled by using linear springs to restrain the plate edges. For obtaining the expressions of energy integral, the arbitrarily shaped domain of integration is divided into several trapezoid domains with curved sides by a set of parallel lines passing through the intersection points of contour curve segments. Then, Jacobi orthogonal polynomials are introduced as the admissible functions, so that the repeated integrals in the energy expressions are reduced to definite integrals analytically. At this point, the calculation method of the energy functional is determined by the equation forms of the curve segments of the plate contour. When the equations of the curve segments allow the integrands to have analytic primitive functions, the energy functional has an analytical solution. Otherwise, the Gauss–Legendre method is used to obtain the numerical solution. Accordingly, the arbitrarily shaped plate with cracks is decomposed into several arbitrarily shaped subdomains based on the cracks. Each subdomain is handled according to the above procedure. The continuity conditions at the interconnecting interfaces of the subdomains are realized by linear springs. The plate without or with crack is modeled by setting the spring stiffness to infinity or 0. The accuracy of the proposed method is verified by comparing the obtained results with the published results. Furthermore, the vibration characteristics of plates with various shapes, such as astroid-shaped plates and cracked elliptical plates, are investigated. These new results can serve as benchmarks for further studies on the vibration of plates.

Vibration and stability analysis on the water entry process of a thin plate

In this study, the stability and vibration characteristics of a thin plate in the water entry process are investigated. In the water entry process, the mass, damping and stiffness of the system change continuously with time to make the stability of the fluid-structure system exhibit the time-varying characteristics. Based on the nonlinear plate theory and the linear potential flow theory, the equation of motion of the plate interacting with external airflow and water flow is established. For the linear equation, the changes of the natural frequencies of the plate entering the water are researched by applying the generalized eigenvalue method, from which the stability of the system is analyzed. For the nonlinear equation, the displacement time responses and phase portraits of the plate subjected to harmonic excitation are discussed by numerical simulations. When the plate enters the water, the stability of the plate becomes worse. The range of the external excitation frequency makes significant effects on the vibration characteristics of the plate. The plate falls into instability with the entry velocity increasing. Finally, the effects of the fluid density, the aspect ratios and the length-to-thickness ratios of the plate on the stability and vibration characteristics of the plate are discussed.

Vibration characteristics of plates and shells with functionally graded pores imperfections using an enhanced finite shell element

The novelty of the current study is the development of an enhanced finite shell model using the first order shear deformation theory (FSDT) to study the vibration characteristics of imperfect functionally graded (FGM) plates and shells including porosities. Unlike standard (FSDT) theory, the proposed model presents an improvement of the FSDT via the introduction of a quadratic shear function allowing the exact representation of the parabolic distribution of the shear strains and avoiding the utilization of shear correction factors which are computationally costs. The finite element method is used for the discretization of the equations of motion and the assumed natural transverse shear strain (ANS) method is employed to avoid shear locking problems. The effect of porosity parameter and its distributions, namely even and uneven forms, is investigated through different numerical illustrative examples. The present finite shell element model provides better agreement with exact solutions in comparison by other theories. Finally, effects of different factors on vibrational behavior of imperfect FGM porous plates and shells are examined in detail.

Self-loosening effects on vibration characteristics of plates with bolted joints: An experimental and finite element analysis

Vibration characteristics of a plate with six-bolt single-lap joint are investigated in both experimental tests and finite element (FE) method. The FE results are obtained using nonlinear steady-state dynamic analysis via ABAQUS software. The interaction surface is simulated by a nonlinear elasto-plastic thin interface layer. Natural frequencies are measured using experimental modal tests for various bolt tightening torques. The FE model is updated using the direct method and the effectiveness parameters are evaluated by experimental data. Finally, the effect of self-loosening of bolted joints on vibration characteristics of the response signal, including natural frequencies, energy parameters, kurtosis, and standard deviation are investigated. The results obtained from the FE model show good agreement with ones from the experimental modal test. Additionally, it can be concluded that for the bolt loosening defects identification, time-domain processes, and energy-based signal parameters, standard deviation, and kurtosis of the vibration signals are more appropriate rather than natural frequencies analysis.

Study of plate vibrating in fluids having part-through crack at random angles and locations

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Hygrothermal effect on vibration of magnetostrictive viscoelastic sandwich plates supported by Pasternak's foundations

In hygrothermal environment, vibration study of a simply supported smart sandwich plate embedded in an elastic substrate medium is presented in the present article. The sandwich plate contains layers of fiber-reinforced and magnetostrictive materials and core of viscoelastic material. The kinematic equations system is derived via employing Hamilton's principle with considering the transverse shear strains with and without the normal strains effect. Various numerical examples are carried out to study the effects of temperature rise, degree of moisture concentration, elastic foundations parameters, thickness ratio, aspect ratio, thickness ratio of magnetostrictive layer to viscoelastic layer, modes, lamination schemes, magnitude of the feedback coefficient, position of the magnetostrictive layers and viscoelastic structural damping coefficient on controlled motion and vibration characteristics of plate. Some observation about influences of the temperature and humidity concentrations on vibration characteristics of studied plate are presented in detail. The outcomes indicate that the hygrothermal environments have negative effects on vibration suppression of advanced composite structures especially the uniform hygrothermal distribution. The frequencies increase with increasing the viscoelastic structural damping coefficient and the foundation constants.

Study on Fluid-Solid Coupling for Vibration Characteristics of Stiffened Plate

In this paper, the vibration characteristics of plate and stiffened plate in the flow field are calculated by employing fluid-solid coupling method. The wet-frequency and wet-mode numerical computing results are analyzed. The influence of boundary condition, edge length ratio and depth of water on wet mode and wet frequency are studied. A mixed finite element-boundary element method is adopted in the numerical calculation, which makes the added water mass matrix calculation be limited to the liquid-solid interface. Thereby, the calculated amount is significantly reduced and the calculation efficiency is increased.

Vibration of plates immersed in hot fluids

The vibration of structures immersed in water has been studied by Lamb and others. The influence of thermal stresses on the vibration characteristics of plates has been investigated and reported by several researchers. The work reported here deals with the determination of natural frequencies of plates immersed in water and subjected to six types of temperature distributions. The analysis is based on finite element method. A comment on thermal buckling of plates immersed in water is also reported.

Vibration Characteristics of Aluminum Plates Reinforced with Boron-Epoxy Composite Material

Vibration characteristics of aluminum plates reinforced with boron epoxy composite material were investigated experimentally and analyt ically. Variations in the natural frequencies, mode shapes, and damping with filament angle were studied. Vibration characteristics of the re inforced plates were also compared with all-aluminum plates. Results of this study demonstrate the merit of using directional com posite materials in design for controlling vibration characteristics of plates. For example, experimental results show that the frequency of the first mode can be changed 77 percent by adjusting the fiber orientation with no change in the plate mass. Results also showed that the damping coefficients could be controlled with filament orientation and that the maximum damping occurred for modes having maximum straining of the matrix and minimum straining of the filaments. Regardless of the filament orientation, all the reinforced plates had more damping than the all-aluminum plates. However, these damping values tend to be less than those normally associated with conventional built-up aerospace structures. Analytical results used in this report were in qualitative agreement with experimental trends for nodal pattern and frequency variations with filament orientation. However, in some cases, quantitative frequency corre lation was poor. To obtain better correlation, a more sophisticated finite element, including effects such as interlaminar shear, matrix viscoelasticity, and metal-epoxy interface properties, might be necessary.