Large amplitude flexural vibration of eccentrically stiffened plates
TL;DR: In this article, the large amplitude free flexural vibrations of thin, orthotropic, eccentrically and lightly stiffened elastic rectangular plates are investigated, and the modal equations for the nonlinear free vibration of stiffened plates are obtained for the cases when the stiffeners are assumed to be smeared out over the entire surface of the plate, and when the stiffnesseners are located at finite intervals.
About: This article is published in Journal of Sound and Vibration.The article was published on 1979-12-08. It has received 9 citations till now. The article focuses on the topics: Stiffening & Orthotropic material.
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TL;DR: In this paper, the spline finite strip method has been used for the analysis of stiffened plates of arbitrary shapes, and the results have been compared with those of other investigators.
Abstract: Large amplitude, free flexural vibration of stiffened plates has been investigated by the spline finite strip method. This is the first attempt to get a satisfactory solution of this problem by spline finite strip method in the form of an eigenvalue problem. The effects of large amplitude have been taken into account by adopting von Karman's large deflection plate theory and the formulation has been done in the total Lagrangian coordinate system. The resulting nonlinear equations have been solved by the newly developed method, a linearized updated mode with nonlinear time function approximation. The generalized form of spline finite strip method has been used for the analysis of plates of arbitrary shapes. The stiffener has been elegantly modeled so that it can be placed anywhere within the plate strip and it need not follow the nodal lines. The arbitrary orientation and eccentricity of the stiffener have been incorporated in the formulation. Plates and stiffened plated have been analyzed, and the results have been presented and compared with those of other investigators.
19 citations
TL;DR: In this paper, a free vibration analysis of initially deflected stiffened plates subjected to uniformly distributed loading with different flexural boundary conditions involving simply supported and clamped ends and zero displacement in-plane boundary conditions has been presented.
Abstract: Free vibration analysis of initially deflected stiffened plates subjected to uniformly distributed loading with different flexural boundary conditions involving simply supported and clamped ends and zero displacement in-plane boundary conditions has been presented. A domain decomposition technique depending on the number, orientation and location of the stiffeners is employed to ensure sufficient number of computation points around the stiffeners. Geometric non-linearity arising out of large deflection is accounted for by consideration of non-linear strain-displacement relations. Mathematical formulation is based on a variational form of energy principle, and a solution technique, where static analysis serves as the basis for the subsequent dynamic study, is followed. The results are validated with the published results of other researchers. The dynamic behavior has been presented in the form of backbone curves in a dimensionless frequency-amplitude plane. Vibration mode shapes along with contour plots ar...
10 citations
TL;DR: In this article, a general solution to the geometrically nonlinear analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section, subjected to arbitrary loading is presented.
9 citations
TL;DR: In this article, the influence of the discrete ribs on the wavenumbers of harmonic waves propagating along the ribs is investigated, and the effect of the stiffness parameters of the ribs on natural frequencies and modes of a cross-ribbed plate is studied.
Abstract: A rectangular plate reinforced with longitudinal ribs is considered. The influence of the discrete ribs on the wavenumbers of harmonic waves propagating along the ribs is investigated. The effect of the stiffness parameters of the ribs on the natural frequencies and modes of a cross-ribbed plate is studied
8 citations
TL;DR: In this article, a large amplitude forced vibration analysis of stiffened plates with free edges under harmonic excitation through a numerical method is carried out, in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude.
Abstract: This paper undertakes a large amplitude forced vibration analysis of stiffened plates with free edges under harmonic excitation through a numerical method. The methodology adopted is an indirect one in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Free vibration analysis at the deflected configuration of the same system is also carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the governing equations in both forced and free vibration cases are derived using Hamilton’s principle. The set of nonlinear governing equations is solved by employing an iterative direct substitution method with an appropriate relaxation technique. A multidimensional quasi-Newton method, known as Broyden’s method, is separately used when the system becomes computationally stiff. The results for a reduced system are validated with the published results of other researchers. For different combinations o...
6 citations
Cites background from "Large amplitude flexural vibration ..."
...Varadan and Pandalai (1979) investigated eccentrically stiffened rectangular plates with clamped boundaries and movable in-plane edge conditions using Lagrange’s equation....
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References
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58 citations
TL;DR: In this paper, an analytical analysis of free flexural large amplitude vibrations of orthotropic rectangular plates with all-clamped and all-simply supported stress-free edges is presented.
43 citations
33 citations
TL;DR: In this article, the Von Karman field equations for flexible oblique plates with an initial curvature are extended to a dynamical case using series of initial and additional deflections and Galerkin's procedure, the governing equation for an admissible mode time function is established using this single assumed modal deflection, and assuming built-in edge fiee to move in the inplane directions.
Abstract: Von Karman field equations for flexible oblique plates with an initial curvature are extended to a dynamical case Using series iepresentation of initial and additional deflections and Galerkin's procedure, the governing equation for an admissible mode time function is established Using this single assumed modal deflection, and assuming built-in edge fiee to move in the inplane directions, the following particular cases are discussed: buckling of an oblique plate under uniaxial compressive load, free linear vibrations of a square plate, large deflections of a uniformly loaded square plate, snap-through phenomena of a curved oblique plate under uniform transverse load, and free nonlinear vibrations A numeiical example concerning a rhombic plate is discussed in more detail The well-known fact of a decrease of the period of nonlinear vibrations with an increasing amplitude is corroborated, this relation being less pronounced for larger sweep angles
20 citations
TL;DR: In this paper, the large amplitude free flexural vibration of thin, elastic orthotropic stiffened plates is studied and the governing dynamic equations are derived in terms of non-dimensional parameters describing the stiffening achieved, and the solutions are obtained on the basis of an assumed one-term vibration mode shape for various stiffener combinations.
19 citations