Vibration Of Orthotropic Plates Research Articles

Vibration of orthotropic plates with and without damping

Vibration of orthotropic plates with and without damping

Development of the Dynamic Stiffness Method for the Out-of-Plane Natural Vibration of an Orthotropic Plate

In this present paper, the dynamic stiffness method (DSM) was formulated to investigate the out-of-plane natural vibration of a thin orthotropic plate using the classical plate theory (CPT). Hamilton’s principle was implemented to derive the governing differential equation of motion for free vibration of the orthotropic plate for Levy-type boundary conditions. The Wittrick–Williams (W–W) algorithm was used as a solution technique to compute the natural frequencies of a thin orthotropic plate for different boundary conditions, aspect ratios, thickness ratios, and modulus ratios. The obtained results are compared with the results by the finite element method using commercial software (ANSYS and those available) in the published literature. The presented results by the dynamic stiffness method can be used as a benchmark solution to compare the natural frequencies of orthotropic plates.

Mathematical analogies in solving problems of strength, stability and vibrations of orthotropic plates and shells

Mathematical analogies in solving problems of strength, stability and vibrations of orthotropic plates and shells

Transverse vibration of orthotropic plate of arbitrary shape with a set of supported cutouts of arbitrary configuration taking into account distributed load on the surface

Transverse vibration of orthotropic plate of arbitrary shape with a set of supported cutouts of arbitrary configuration taking into account distributed load on the surface

К решению первой краевой задачи теории упругости о вынужденных колебаниях ортотропных пластин при наличии вязкого сопротивления.

К решению первой краевой задачи теории упругости о вынужденных колебаниях ортотропных пластин при наличии вязкого сопротивления.

Free Vibration of Orthotropic Plate on Foundation with Four Edges Free by Finite Integral Transform Method

The double finite cosine integral transform method is exploited to obtain explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate on foundation with four edges free. In the analysis procedure, the classical Kirchhohh orthotropic rectangular plate is considered and the Winkler elastic foundation is utilized to represent the elastic foundation. Because only are the basic dynamic elasticity equations of the orthotropic thin plate on elastic foundation adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by present paper is reasonable and theoretical. In order to illuminate the correction of formulations, the numerical results are also presented to comparing with that of the other references.

Method of R-function for investigation of parametric vibrations of orthotropic plates of complex shape

We propose a method for investigating parametric vibrations of orthotropic plates with complex shape for different types of boundary conditions, which is based on variational methods in combination with the R -function theory. The proposed approach is used for the solution of specific problems. In the process of numerical realization of an algorithm for a considered plate with complex shape, we construct dynamic-instability domains and dependences of deflection on the exciting frequency and time.

O собственных колебаниях ортотропных пластин при наличии вязкого сопротивления.

O собственных колебаниях ортотропных пластин при наличии вязкого сопротивления.

Parametric vibrations of orthotropic plates with complex shape

The paper proposes a method to study the parametric vibrations of orthotropic plates with complex shape. The method is based on the R-function theory and variational methods. Dynamic-instability domains and amplitude–frequency responses for plates with complex geometry and different types of boundary conditions are plotted

Nonlinear Vibration of Orthotropic Plates with Initial Stresses on a Two-parameter Elastic Foundation

Nonlinear partial differential equations for vibration of an orthotropic thick plate on a two-parameter (Pasternak type) elastic foundation subjected to a nonuniform initial stress are derived. Both rotary inertia and transverse stress are considered in the derivation. The Galerkin method is used to transform the governing nonlinear partial differential equations to ordinary nonlinear differential equations and the Runge–Kutta method is used to obtain the ratio of nonlinear to linear frequency. Numerical examples are presented for the combination of pure bending stresses and extensional stresses are taken to be the initial stresses in the plane of the plate. These equations are then applied to a simply supported orthotropic plate on a Pasternak foundation to solve its motion of nonlinear vibration. The effects of the material properties, initial stress, amplitude of vibration, and foundation stiffness on frequency ratio are discussed.

Research of nonlinear vibrations of orthotropic plates with a complex form

This paper deals with effects of large amplitude on the free and forced flexural vibrations of elastic orthotropic plates of arbitrary shape.R-function method (RFM) is applied to obtain the basis functions need for expansion of sought solution into Fourier series. The initial nonlinear system of differential equations with partial derivatives is reduced to system of ordinary nonlinear differential equations by Galerkin procedure. The solving-obtained system is carried out by Runge-Kutta or Galerkin methods. The numerical results for the plate of complex form and also rectangular form and different boundary conditions have been presented and compared with other known results.

Vibration of orthotropic plates: discussion on the completeness of the solutions used in direct methods

Fil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Bahia Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria; Argentina

Literature Review : Reduction Methods for Problems of Vibration of Orthotropic Plates: Part II: Generalized Reduction Method for Generally Orthotropic Plates with Arbitrary Shape

Literature Review : Reduction Methods for Problems of Vibration of Orthotropic Plates: Part II: Generalized Reduction Method for Generally Orthotropic Plates with Arbitrary Shape

Reduction Methods for Problems of Vibration of Orthotropic Plates

Reduction Methods for Problems of Vibration of Orthotropic Plates