Large amplitude flexural vibration analysis of tapered plates with edges elastically restrained against rotation using DQM

A modified Fourier–Ritz method is developed for the flexural and in-plane vibration analysis of plates with two rectangular cutouts with arbitrary boundary conditions, aiming to provide a unified solving process for cases that the plate has various locations or sizes of cutout, and different kinds of boundary conditions. Under the current framework, modifying the position of the cutout or the boundary conditions of the plate is just as changing the geometric parameters of the plate, and there is no need to change the solution procedures. The arbitrary boundary conditions can be obtained by setting the stiffness constant of the boundary springs which are fixed uniformly along the edges of the plate at proper values. The strain and kinetic energy functions of a plate with rectangular cutout are derived in detail. The convergence and accuracy of the present method are demonstrated by comparing the present results with those obtained from the FEM software. In this paper, free in-plane and flexural vibration characteristics of the plate with rectangular cutout under general boundary conditions are studied. From the results, it can be found that the geometric parameters and positions of the cutout and the boundary conditions of the plate will obviously influence the natural vibration characteristics of the structures.

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Free vibration analysis of elastically restrained functionally graded curved beams based on the Mori–Tanaka scheme

Mechanics of Advanced Materials and Structures ◽

10.1080/15376494.2018.1452318 ◽

2018 ◽

Vol 26 (21) ◽

pp. 1821-1831 ◽

Cited By ~ 7

Author(s):

Cheng Zhang ◽

Qingshan Wang

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Curved Beams ◽

Elastically Restrained

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Large Amplitude Forced Vibration Analysis of Stiffened Plates under Harmonic Excitation

Dynamic Methods and Process Advancements in Mechanical, Manufacturing, and Materials Engineering ◽

10.4018/978-1-4666-1867-1.ch002 ◽

2012 ◽

pp. 26-61

Author(s):

Anirban Mitra ◽

Prasanta Sahoo ◽

Kashinath Saha

Keyword(s):

Free Vibration ◽

Forced Vibration ◽

Large Amplitude ◽

Vibration Analysis ◽

Mathematical Formulation ◽

Free Vibration Analysis ◽

Harmonic Excitation ◽

Stiffened Plates ◽

Backbone Curve ◽

Forced Vibration Analysis

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

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