Piezoelectrically induced snap-through buckling in a buckled beam bonded with a segmented actuator

2018 ◽  
Vol 29 (9) ◽  
pp. 1862-1874 ◽  
Author(s):  
Sontipee Aimmanee ◽  
Kasarn Tichakorn
Keyword(s):  
Piezoelectric Material ◽  
Ritz Method ◽  
Hessian Matrix ◽  
Sudden Change ◽  
Energy Principle ◽  
Straight Beam ◽  
Smart Beam ◽  
Support Conditions ◽  
The Stability ◽  
Minimum Potential Energy Principle

In this article, a mathematical model is developed to analyze piezoelectrically induced deformations of bistable smart beams with various geometric configurations and boundary conditions. The model delineates a straight beam bonded with a segmented piezoelectric material. Three types of support conditions are considered, namely, simple, clamped–clamped, and clamped–pinned supports. The beam is buckled into two possible stable curved shapes by means of edge shortening compression. A sudden change in transverse deflection from one to the other stable shape, so-called snap-through action, can be stimulated by electrical activation given to the piezoelectric material. The minimum potential energy principle associated with the modified Ritz method is used to predict developing shapes of the smart beam and the snap-through voltage. Principal minors of bordered Hessian matrix are calculated to determine the stability of the shapes obtained. Experiments were also conducted to corroborate the computational results in the case of the simply-supported smart beam. Comparisons between the two approaches reveal very good agreements in both mid-span displacements of buckled shapes and snap-through voltages. Finally, size and location of the segmented piezoelectric actuator are varied to search for the minimum critical electrical field for each support condition.

scholarly journals Postbuckling Analysis Of A Rectangular Plate Loaded In Compression

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Jozef Havran ◽  
Martin Psotný
Keyword(s):  
Rectangular Plate ◽  
User Program ◽  
Nonlinear Fem ◽  
Buckling Mode ◽  
Energy Principle ◽  
Initial Imperfections ◽  
Potential Energy Principle ◽  
Total Potential ◽  
The Stability ◽  
Minimum Total Potential Energy

Abstract The stability analysis of a thin rectangular plate loaded in compression is presented. The nonlinear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user program. Special attention is paid to the influence of imperfections on the post-critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. Full Newton-Raphson procedure has been applied.

Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam

1995 ◽  
Author(s):  
Régis Dufour ◽  
Alain Berlioz ◽  
Thomas Streule
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

Abstract In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

scholarly journals On the stability of the Rayleigh–Ritz method for eigenvalues

2017 ◽  
Vol 137 (2) ◽  
pp. 339-351 ◽  
Author(s):  
D. Gallistl ◽  
P. Huber ◽  
D. Peterseim
Keyword(s):  
Ritz Method ◽  
The Stability

A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)

1994 ◽  
Vol 61 (4) ◽  
pp. 914-918 ◽  
Author(s):  
J. E. Taylor
Keyword(s):  
Potential Energy ◽  
Problem Formulation ◽  
Extremum Problem ◽  
Equilibrium Analysis ◽  
Minimum Potential Energy ◽  
Problem Statement ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

Theoretical and Experimental Investigations on Shear Lag Effect of Double-Box Composite Beam with Wide Flange under Symmetrical Loading

2015 ◽  
Vol 31 (6) ◽  
pp. 653-663 ◽  
Author(s):  
S.-W. Hu ◽  
J. Yu ◽  
Y.-Q. Huang ◽  
S.-Y. Xiao
Keyword(s):  
Composite Beam ◽  
Experimental Investigations ◽  
Shear Lag ◽  
Shear Lag Effect ◽  
Theoretical Derivation ◽  
Energy Principle ◽  
Lag Effect ◽  
Symmetrical Loading ◽  
Stress Behaviors ◽  
Minimum Potential Energy Principle

ABSTRACTA new type of steel-concrete composite beam with double-box cross-section is proposed in this paper. In order to investigate stress behaviors and deflection characteristics of such composite beam with wide flange considering the shear lag effect, theoretical analysis and experimental study are launched simultaneously. Based on the minimum potential energy principle, governing differential equations in view of the shear lag effect are deduced by energy variational method, and analytical solutions of it's stress and deflection under the effect of symmetrical loading are calculated. The preceding analyses show that relative error is less than 14.71%, with a good agreement, and farther show that this method of theoretical derivation, which is used for analyzing shear lag effect of composite beam with wide flange, has certain reference and guidance.

Implement of Ameliorated ACM Element in Numerical Manifold Space for Tackling Kirchhoff Plate Bending Problems

2014 ◽  
Vol 638-640 ◽  
pp. 1710-1715
Author(s):  
Hong Wei Guo ◽  
Hong Zheng ◽  
Wei Li
Keyword(s):  
Partition Of Unity ◽  
Plate Bending ◽  
Minimum Potential Energy ◽  
Energy Principle ◽  
Displacement Boundary ◽  
Minimum Potential ◽  
Bending Problems ◽  
Minimum Potential Energy Principle ◽  
Numerical Manifold ◽  
Fourth Order Problems

Ab ridging the chasm between the prevalent ly employed continuum methods (e.g. FEM) and discontinuum methods (e.g. DDA) ,the numerical manifold (NNM) ,which utilizes two covers, namely the mathematical cover and physical cover , has evinced various advantages in solving solid mechanic al issues. The forth-order partial elliptic differential equation governing Kirchhoff plate bending makes it arduous to establish the -regular Lagrangian partition of unity ,nevertheless, this study renders a modified conforming ACM manifold element , irrespective of accreting its cover degrees, to resolve the fourth-order problems. In tandem with the forming of the finite element cover system that erected on r ectangular mesh es , a succession of n umerical manifold formulas are derived on grounds of the minimum potential energy principle and the displacement boundary conditions are executed by penalty function methods. The numerical example elucidates that , compared with the orthodox ACM element , the proposed methods bespeak the accuracy and precipitating convergence of the NMM .

ELASTO-PLASTIC BUCKLING OF PRESTRESSED ARCHES

2002 ◽  
Vol 02 (03) ◽  
pp. 295-313
Author(s):  
AMIR MIRMIRAN ◽  
AMDE M. AMDE ◽  
ZEFANG XU
Keyword(s):  
Yield Strength ◽  
Strain Hardening ◽  
Beam Element ◽  
Fabrication Technique ◽  
Linear Strain ◽  
Plastic Buckling ◽  
Buckling Mode ◽  
Hardening Material ◽  
Straight Beam ◽  
Support Conditions

Intentional buckling as a fabrication technique for arch frameworks results in prestrains at every section of the arch, which in turn affect its strength and stability. A nonlinear corotational straight beam element with elastic, linear strain hardening material has been developed to study the elasto-plastic buckling of prestressed arches. The study indicates that for prestressed arches there is an interdependence between the slenderness and steepness ratios of the arch with the ratio of prestresses to the yield strength of the material, all of which control the magnitude and shape of buckling mode. While steeper arches are generally more stable in their elastic range, the effect of steepness ratio is reduced as the prestress exceeds 55% of the yield strength. Effects of loading and support conditions have also been considered. Although fixed supports result in more stable arches, their effectiveness depends on the steepness ratio and the level of prestresses. Finally, the effect of strain hardening on the plastic buckling of the arch is more pronounced for lower values of the plastic tangent modulus.

Mixing shocks in two-phase flow

1969 ◽  
Vol 36 (4) ◽  
pp. 639-655 ◽  
Author(s):  
Jan H. Witte
Keyword(s):  
Sudden Change ◽  
Microscopic Theory ◽  
Entropy Change ◽  
Continuous Phase ◽  
Plane Shock ◽  
Two Phase ◽  
Gas Entrainment ◽  
The Stability ◽  
Air Ejector ◽  
Liquid Flows

In gas-liquid flows a certain sudden change of the flow structure may occur, which can be described as a transition from ‘jet flow’ to ‘froth flow’ accompanied by energy dissipation and pressure build-up. Upstream of this phenomenon the gas is the continuous phase; downstream the liquid is the continuous phase. The phenomenon, which has been called ‘mixing shock’, shows some similarity and also some differences with the plane shock wave in gasdynamics. In the first part of this paper the mixing shock is treated as a one-dimensional macroscopic process. With the aid of the laws of conservation of mass, momentum and energy, expressions are obtained for the pressure and entropy change across the mixing process. In addition the stability of the mixing shock in a cylindrical flow channel is treated. Next, a theory that explains the gas entrainment mechanism in the mixing shock is proposed. As an experimental tool a water-air ejector with the water as a driving medium was used. The experiments confirm the macroscopic and the microscopic theory. In the last section of this paper theoretical and experimental evidence is combined to construct a model of the processes that play a role in the shock.

scholarly journals Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

2016 ◽  
Vol 9 ◽  
pp. 9-25 ◽  
Author(s):  
Hareram Lohar ◽  
Anirban Mitra ◽  
Sarmila Sahoo
Keyword(s):  
Elastic Foundation ◽  
Static Problem ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Dimensionless Frequency ◽  
Energy Principle ◽  
Various Boundary Conditions ◽  
Non Linear ◽  
Beams On Elastic Foundation ◽  
Minimum Potential Energy Principle

A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton’s principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

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