scholarly journals On the applicability limits of refined theories in describing of the flexural edge wave in plates

2020 ◽  
pp. 206-213
Author(s):  
Мария Владимировна Вильде ◽  
Янина Александровна Парфенова ◽  
Мария Юрьевна Сурова
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Theory ◽  
Wave Dispersion ◽  
Excitation Amplitude ◽  
Edge Wave ◽  
Numerical Comparison ◽  
Plate Bending ◽  
Classical Boundary ◽  
Kirchhoff Theory ◽  
3D Problem

Исследуются пределы применимости уточненных теорий изгиба пластины при описании дисперсии изгибной краевой волны и амплитуды её возбуждения парой сосредоточенных скручивающих моментов, приложенных на торце. Методом численного сравнения с решением трехмерной задачи показано, что теория типа Тимошенко пригодна для описания краевой волны на частотах, не превосходящих 30% от первой частоты запирания. Уточненная теория изгиба пластин с приведенной инерцией в сочетании с классическими граничными условиями позволяет уточнить скорость волны по сравнению с теорией Кирхгофа, но значительно искажает амплитуду. The applicability limits of refined plate bending theories in describing of the flexural edge wave dispersion and its excitation amplitude are investigated. The wave is excited by a pair of twisting couples applied to the edge of the plate. Numerical comparison with the solution of 3D problem shows that Uflyand-Mindlin theory is applicable at the frequencies up to 30% of the first cut-off. The higher order asymptotic theory of plate bending with modified inertia and classical boundary conditions allows to improve the describing of the velocity comparing to Kirchhoff theory, but leads to a considerable error in describing of the amplitude.

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

Pull-In Instability of Functionally Graded Cantilever Nanoactuators Incorporating Effects of Microstructure, Surface Energy and Intermolecular Forces

2018 ◽  
Vol 10 (08) ◽  
pp. 1850091 ◽  
Author(s):  
Mohamed A. Attia ◽  
Salwa A. Mohamed
Keyword(s):  
Residual Stress ◽  
Surface Energy ◽  
Boundary Conditions ◽  
Van Der Waals ◽  
Surface Elasticity ◽  
Van Der Waals Forces ◽  
Functionally Graded ◽  
Surface Residual Stress ◽  
Electrically Actuated ◽  
Classical Boundary

In this paper, an integrated non-classical continuum model is developed to investigate the pull-in instability of electrostatically actuated functionally graded nanocantilevers. The model accounts for the simultaneous effects of local-microstructure, surface elasticity and surface residual in the presence of fringing field as well as Casimir and van der Waals forces. The modified couple stress and Gurtin–Murdoch surface elasticity theories are employed to conduct the scaling effects of microstructure and surface energy, respectively, in the context of Euler–Bernoulli beam hypothesis. Bulk and surface material properties are varied according to the power-law distribution through the beam thickness. The physical neutral axis position for mentioned FG nanobeams is considered. Hamilton principle is employed to derive the nonlinear size-dependent governing equations and the non-classical boundary conditions. The resulting nonlinear differential equations are solved utilizing the generalized differential quadrature method (GDQM). In addition, the non-classical boundary conditions of nanocantilever beams due to surface residual stress are exactly implemented. After validation of the obtained results by previously available data in the literature, the influences of different geometrical and material parameters on the pull-in instability of the FG nanocantilevers are examined in detail. It is concluded that the pull-in behavior of electrically actuated FG micro/nanocantilevers is significantly influenced by the material distribution, material length scale parameter, surface elasticity constant, surface residual stress, initial gap, slenderness ratio, Casimir, and van der Waals forces. The obtained results can be considered for modeling and analysis of electrically actuated FG nanocantilevers.

An Experimental Approach to the Design of PVDF Modal Sensors

2001 ◽  
Author(s):  
Daniel Cuhat ◽  
Patricia Davies
Keyword(s):  
Boundary Conditions ◽  
Experimental Approach ◽  
Experimental Methodology ◽  
Laser Doppler Velocimeter ◽  
Piezoelectric Film ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Arbitrary Boundary ◽  
Classical Boundary ◽  
Euler Bernoulli Beam

Abstract The principle of modal sensing is based on the use of a shaped PVDF piezoelectric film measuring strains on the surface of a bending beam and acting as a modal filter. So far, the use of this type of sensors has remained confined to studies involving uniform structures with classical boundary conditions. The goal of this paper is to present an experimental methodology for the design of a shaped modal sensor applicable to an non-uniform Euler-Bernoulli beam with arbitrary boundary conditions. This approach is illustrated with test data collected on a cantilever beam structure with a laser Doppler velocimeter.

Unified Solution on Skew Plate Bending with Four Edges Supported under Arbitrary Load

2011 ◽  
Vol 243-249 ◽  
pp. 5994-5998
Author(s):  
Lang Cao ◽  
Xing Jie Xing ◽  
Feng Guang Ge
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourier Series ◽  
Boundary Conditions ◽  
Engineering Design ◽  
Plate Bending ◽  
The Finite Element Method ◽  
Arbitrary Load ◽  
Skew Plate ◽  
Good Agreement

According to the bending equation and boundary conditions of skew plate in the oblique coordinates system parallel to the edge of the plate, expanding deflection and load into form of Fourier series, the paper derives and obtains unified solution of bending problem for the four-edge-supported skew plate under arbitrary load. Programmed and calculated by mathematica language, the paper also comes with deflections and moments under the condition of any oblique angles, ratios of side length and Poisson ratios. The results of the paper is compared with those by the finite element method in the example, and they’re in good agreement with each other. The paper extends the bending theory of rectangular plate to the skew plate of any angle. The theory being reliable and the result being accurate, the research of the paper can provide reference for engineering design.

scholarly journals Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Qingshan Wang ◽  
Dongyan Shi ◽  
Fuzhen Pang ◽  
Qian Liang
Keyword(s):  
Boundary Conditions ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Computational Effort ◽  
General Boundary Condition ◽  
Shells Of Revolution ◽  
Elastic Boundary ◽  
Boundary Force ◽  
Classical Boundary ◽  
The Common

AbstractA Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with θ = 0 and 2π. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.

Boundary Conditions for Plate Bending in One-dimensional Hexagonal Quasicrystals

2006 ◽  
Vol 86 (3) ◽  
pp. 221-233 ◽  
Author(s):  
Yang Gao ◽  
Si-peng Xu ◽  
Bao-sheng Zhao
Keyword(s):  
Boundary Conditions ◽  
Plate Bending ◽  
One Dimensional
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