Dynamic Analysis Of Rectangular Plate Research Articles

Dynamic Analysis of Rectangular Plate Stiffened by Any Number of Beams with Different Lengths and Orientations

The present work is concerned with dynamic characteristics of beam‐stiffened rectangular plate by an improved Fourier series method (IFSM), including mobility characteristics, structural intensity, and transient response. The artificial coupling spring technology is introduced to establish the clamped or elastic connections at the interface between the plate and beams. According to IFSM, the displacement field of the plate and the stiffening beams are expressed as a combination of the Fourier cosine series and its auxiliary functions. Then, the Rayleigh–Ritz method is applied to solve the unknown Fourier coefficients, which determines the dynamic characteristics of the coupled structure. The Newmark method is adopted to obtain the transient response of the coupled structure, where the Rayleigh damping is taken into consideration. The rapid convergence of the current method is shown, and good agreement between the predicted results and FEM results is also revealed. On this basis, the effects of the factors related to the stiffening beam (including the length, orientations, and arrangement spacing of beams) and elastic parameters, as well as damping coefficients on the dynamic characteristics of the stiffened plate are investigated.

Dynamic analysis of rectangular plates crossed by distributed moving loads

This study investigates the dynamic behaviour of plates crossed by distributed moving gravitational and inertial loads, in the case in which the relative magnitude of the moving mass introduces a coupling effect with the structure, with possible applications to the vibration analysis of railway bridges. A rectangular Kirchhoff plate is considered, simply supported on two opposite edges and free on the other two edges, loaded by a partially distributed mass travelling in the parallel direction with respect to the free edges. The formulation includes damping, and it is accomplished by the Rayleigh–Ritz method, expressing the solution in semi-analytical form. The shape functions for describing the transverse displacement field of the plate are selected as tensor products of linearly independent eigenfunctions of homogeneous uniform beams in flexural vibration, yielding a low-order model with time-dependent coefficients. Numerical examples are then presented and discussed, aimed at investigating the effects of each of the model governing parameters.

Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

Natural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular, elliptic, circular as well as oval openings with various plate thicknesses and different combinations of boundary conditions. The results are compared with those obtained by the finite element method (FEM) as well as those available in the relevant literature, and very good agreement is achieved.

Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

Natural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular, elliptic, circular as well as oval openings with various plate thicknesses and different combinations of boundary conditions. The results are compared with those obtained by the finite element method (FEM) as well as those available in the relevant literature, and very good agreement is achieved.

Dynamic analysis of rectangular plates with a single side crack and in contact with water on one side based on the Rayleigh–Ritz method

A computational method is proposed based on the Rayleigh–Ritz method for the analysis of dynamic characteristics of a baffled rectangular plate with an arbitrary side crack and in contact with an infinite water domain on one side. Based on the hypothesis that the water is incompressible, inviscid and the motion is irrotational, the added mass density expressed by the displacement trial functions is obtained by means of Green function method. The behavior of crack is described by the corner functions, and the natural frequencies and the corresponding modes are calculated through the Rayleigh–Ritz technique. The validity and the accuracy of the proposed method are demonstrated based on the comparison with the results obtained by ANSYS and those published in other literature, and the influences of water on the natural frequencies and mode shapes of the rectangular plates with side cracks are investigated. It is illustrated that the differences between dry and wet mode shapes increase with increasing mode order on the whole, except for the completely free plates, and the differences are evident for some higher modes.

Dynamic Analysis of Sandwich Plates with a Constraining Layer and a Magnetorheological Fluid Core

The dynamic analysis of rectangular plate with a magnetorheological fluid core and a constraining layer is investigated. The dynamic equations of the sandwich plate are derived using finite element method. The natural frequencies and loss factors of the sandwich plate with different varying parameters are studied in this paper. When the magnetic field intensities increase, the frequencies will increase and the loss factors will reduce. With the thickness of MR layer increasing the frequency will get down at first and then go up rapidly. Furthermore the effects of MR core layer thickness on modal loss factors and thickness of constraining layer are discussed in this paper.

Hybrid method for vibration analysis of rectangular plates

This paper presents a semi-analytical approach for the dynamic analysis of rectangular plates. The mathematical model is developed using a hybrid combination of the finite element method and Sanders’ shell theory. The in-plane, membrane displacement components are modelled by bilinear polynomials and the out-of-plane, normal to mid-surface displacement component is modelled by an exponential function that represents a general form of the exact solution of the equations of motion. The displacement functions are obtained by exact solution of the equilibrium equations of the rectangular plates. The mass and stiffness matrices are then determined by exact analytical integration to establish the plate's dynamic equations. The effect of various geometrical parameters and boundary conditions on the dynamic responses of the rectangular plates has been explored in this work. The results are in satisfactory agreement with those of experiments and other theories.

Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation

The geometrically nonlinear static and dynamic analysis of thin rectangular plates resting on elastic foundation has been studied. Winkler–Pasternak foundation model is considered. Dynamic analogues Von Karman equations are used. The governing nonlinear partial differential equations of the plate are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The analysis provides for both clamped and simply supported plates with immovable inplane boundary conditions at the edges. Various types of dynamic loading, namely a step function, a sinusoidal pulse and an N-wave, are investigated and the results are presented graphically. The accuracy of the proposed HDQ–FD coupled methodology is demonstrated by the numerical examples.

DYNAMIC ANALYSIS OF RECTANGULAR PLATES WITH STEPPED THICKNESS SUBJECTED TO MOVING LOADS INCLUDING ADDITIONAL MASS

This paper presents a simplified analytical method for rectangular plates with arbitrarily- and eccentrically-stepped thickness, such as building slabs, subjected to moving loads, including the effect of the additional mass. The discontinuous variation of the bending stiffness and mass of the plate due to the variation of the thickness can be expressed continuously by means of a characteristic function, which is defined as a Dirac function existing continuously in a prescribed region, as proposed by the author's previous work. Since the bending stiffness used here is given exactly by the actual bending stiffness at each point, a modification of the bending stiffness used in an equivalent plate analogy is unnecessary. It is clarified from numerical computations that the effect of the additional mass due to moving loads is significant for heavy-weight additional mass but is negligible for usual additional mass with 65 kg. Then, approximate but accurate solutions for a current plate subjected to stationary and moving loads are proposed by excluding the effect of additional mass. The numerical results obtained from the proposed theory for simply-supported and clamped plates with stepped thickness, excluding the effect of additional mass, show good agreement with results obtained from the finite element method using FEM code NASTRAN.

Total Lagrangian formulation for the large displacement analysis of rectangular plates

AbstractIn this paper, a method for the non‐linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co‐ordinate system using the assumptions of the classical theories of plates. Non‐linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time‐invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two‐parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non‐linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non‐linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected structural elements.

Free vibration analysis of rectangular plates with cutouts allowing for transverse shear deformation and rotary inertia

AbstractThe energy approach using the variational procedure in conjunction with the finite difference technique has been applied for the Mindlin theory dynamic analysis of rectangular plates with cutouts in which account is taken of the effects of both transverse shear deformation and rotary inertia. This study has clearly demonstrated that the discrepancy with the thin plate theory solutions increases with increasing values of thickness ratio β and the error due to the thin plate assumptions increases particularly for the higher modes. It is also concluded that the effect of a cutout becomes more pronounced as the thickness of the plate approaches the size of cutout.