A Laminated Beam Theory With Interlayer Slip

1984 ◽  
Vol 51 (3) ◽  
pp. 551-559 ◽  
Author(s):  
H. Murakami
Keyword(s):  
Virtual Work ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Transverse Shear Strain ◽  
Beam Model ◽  
Euler Beam ◽  
Concentrated Load ◽  
Laminated Beam ◽  
Wide Range ◽  
Interlayer Slip

A Timoshenko beam theory with built-in interlayer slip is developed to facilitate analytical means of simulating the effect of interlayer slip on the stiffness degradation of laminated beam structures. The proposed theory is unique in the sense that any well-structures interlay slip law can be adopted in the beam model. Based on the principle of virtual work, well-posed boundary value problems of the proposed beam theory are defined. It is shown that the proposed theory reduces to the existing Bernoulli-Euler beam theory with interlayer slip by introducing the kinematic constraint of zero transverse shear strain. As a demonstration of the theory the load-deflection curves of a simply supported sandwich beam subjected to a concentrated load at the center are computed for several characteristic interlayer slip laws. It is found that the proposed model has the capability of simulating the deformation of beams with wide range of interlayer bond qualities, from interface with perfect bond to interface without connectors.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

Dynamic Formulations and Energy Analysis of Rotating Flexible-Shaft/Multi-Flexible-Disk System With Eddy-Current Brake

2000 ◽  
Vol 122 (4) ◽  
pp. 365-375 ◽  
Author(s):  
Rong-Fong Fung ◽  
Shih-Ming Hsu
Keyword(s):  
Eddy Current ◽  
Energy Analysis ◽  
Virtual Work ◽  
Beam Theory ◽  
Brake System ◽  
Euler Beam ◽  
Disk System ◽  
Coupling System ◽  
Flexible Disk ◽  
Work Done

In this paper, the rotating flexible-Timoshenko-shaft/flexible-disk coupling system is formulated by introducing the kinetic and strain energies, and the virtual work done by the eddy-current brake system into Hamilton’s principle. The attachment of disk to shaft becomes flexible for Timoshenko-beam theory and rigid for Euler-beam theory. It is found that the eddy-current brake system can be used to decrease speed and suppress flexible and shear vibrations simultaneously. From the dynamic formulations and energy analysis, some important discussions are made. Numerical results are provided to validate the theoretical analysis. [S0739-3717(00)01504-X]

Vibration of Steel–Concrete Composite Beams Using the Timoshenko Beam Model

2005 ◽  
Vol 11 (6) ◽  
pp. 829-848 ◽  
Author(s):  
Stefan Berczyński ◽  
Tomasz Wróblewski
Keyword(s):  
Dynamic Behavior ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Composite Beams ◽  
Free Vibrations ◽  
Timoshenko Beam Theory ◽  
Analytical Models ◽  
Beam Model ◽  
Euler Beam ◽  
Flexural Vibrations

In this paper we present a solution of the problem of free vibrations of steel–concrete composite beams. Three analytical models describing the dynamic behavior of this type of constructions have been formulated: two of these are based on Euler beam theory, and one on Timoshenko beam theory. All three models have been used to analyze the steel–concrete composite beam researched by others. We also give a comparison of the results obtained from the models with the results determined experimentally. The model based on Timoshenko beam theory describes in the best way the dynamic behavior of this type of construction. The results obtained on the basis of the Timoshenko beam theory model achieve the highest conformity with the experimental results, both for higher and lower modes of flexural vibrations of the beam. Because the frequencies of higher modes of flexural vibrations prove to be highly sensitive to damage occurring in the constructions, this model may be used to detect any damage taking place in such constructions.

Free Vibration of Cross Ply Laminated Beams with Multiple Distributed Piezoelectric Actuators

2012 ◽  
Vol 28 (1) ◽  
pp. 217-227 ◽  
Author(s):  
A. A. Khdeir ◽  
E. Darraj ◽  
O. J. Aldraihem
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Piezoelectric Actuators ◽  
Mode Shapes ◽  
Beam Model ◽  
Laminated Beams ◽  
State Space Approach ◽  
Laminated Beam ◽  
Beam Surface

ABSTRACTAnalytical solution is obtained for the free vibration of cross-ply laminated beams with multiple distributed extension piezoelectric actuators. The piezoelectric actuators are bonded at local position on the beam surface. The beam structure can contain one pair or two pairs or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The equations of motion and associated boundary conditions are derived for the beam model using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures revealing the influences of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam for different type of piezoelectric actuators cases. The first order shear deformation beam theory (FOBT) is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded at a local position on the beam surface.

Analysis of Nonlinear Vibration and Instability of Electrostatically Actuated Fluid-Conveying Micro Beams

2019 ◽  
Vol 29 (07) ◽  
pp. 1950088
Author(s):  
Yan Yan ◽  
Wen-Quan Wang ◽  
G. R. Liu
Keyword(s):  
Nonlinear Vibration ◽  
Optimization Design ◽  
Phase Plane ◽  
Initial Conditions ◽  
Beam Theory ◽  
Phase Portraits ◽  
Curved Beams ◽  
Euler Beam ◽  
Homoclinic Connections ◽  
Wide Range

Based on the Euler beam theory and a Galerkin formulation using natural modes, the nonlinear vibration behavior and stability of electrostatic driving fluid-conveying micro (straight or curved) beams are studied in the paper. The focus of this study is on the critical coupling of fluidic, mechanical and electrostatic effects in the nonlinear system. Under these effects, micro devices may exhibit (dynamic) snap-through or/and pull-in instabilities. Our study reveals, for the first time, the effects of the velocity of the inner fluid on the bifurcation diagrams for complex nonlinear systems. It is also found that fluid can be utilized to efficiently tune the frequency of straight beams over a wide range. For curved beams, the tuning can be achieved easily by adjusting the voltage. These findings are beneficial in many applications of the electrostatic microelectronic mechanical systems (MEMS). In addition, phase plane analyses are performed in this study, and more complicated phase portraits for different initial conditions are obtained as well. It is found that the homoclinic connections on the phase plane are directly related to the dynamic snap-through or dynamic pull-in instabilities; and the periodic orbits are directly related to the periodic motions of micro beams. These findings can provide reasonable explanations for the experimentally-observed phenomena for micro sensors, and are beneficial to the optimization design of MEMS.

scholarly journals Dynamic Gust Load Analysis for Rotors

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Yuting Dai ◽  
Linpeng Wang ◽  
Chao Yang ◽  
Xintan Zhang
Keyword(s):  
Structural Model ◽  
Beam Theory ◽  
Bending Moment ◽  
Iteration Algorithm ◽  
Beam Model ◽  
Euler Beam ◽  
Helicopter Rotors ◽  
Aeroelastic Model ◽  
Flap Deflection ◽  
The Time Domain

Dynamic load of helicopter rotors due to gust directly affects the structural stress and flight performance for helicopters. Based on a large deflection beam theory, an aeroelastic model for isolated helicopter rotors in the time domain is constructed. The dynamic response and structural load for a rotor under the impulse gust and slope-shape gust are calculated, respectively. First, a nonlinear Euler beam model with 36 degrees-of-freedoms per element is applied to depict the structural dynamics for an isolated rotor. The generalized dynamic wake model and Leishman-Beddoes dynamic stall model are applied to calculate the nonlinear unsteady aerodynamic forces on rotors. Then, we transformed the differential aeroelastic governing equation to an algebraic one. Hence, the widely used Newton-Raphson iteration algorithm is employed to simulate the dynamic gust load. An isolated helicopter rotor with four blades is studied to validate the structural model and the aeroelastic model. The modal frequencies based on the Euler beam model agree well with published ones by CAMRAD. The flap deflection due to impulse gust with the speed of 2m/s increases twice to the one without gust. In this numerical example, results indicate that the bending moment at the blade root is alleviated due to elastic effect.

A Two-Stage Optimization Procedure for the Design of an EAP-Actuated Soft Gripper

2019 ◽  
Author(s):  
Wei Zhang ◽  
Jonathan Hong ◽  
Saad Ahmed ◽  
Zoubeida Ounaies ◽  
Mary Frecker
Keyword(s):  
Design Optimization ◽  
Compliant Mechanisms ◽  
Optimization Problems ◽  
Beam Theory ◽  
Optimization Procedure ◽  
Analytical Models ◽  
Euler Beam ◽  
Two Stage ◽  
Nsga Ii ◽  
Wide Range

Abstract An increasing range of engineering applications require soft grippers, which use compliant mechanisms instead of stiff components to achieve grasping action, have high conformability and exert gentle contact with target objects compared to traditional grippers. In this study, a three-fingered gripper is first designed based on a notched self-folding mechanism actuated using an electrostrictive PVDF-based terpolymer. Then the design optimization problem is formulated, where the design objectives are to maximize the free deflection Δfree and the blocked force Fb. A computationally efficient two-stage design optimization procedure is proposed and successfully applied in the gripper design. NSGA-II is adopted as the optimization algorithm for its capacity to deal with multi-objective optimization problems and to find the global optima with high design variables and large design domains. In stage one, computationally less expensive analytical models are developed based on Bernoulli-Euler beam theory and Castigliano’s theorem to calculate Δfree and Fb. Utility function is applied to determine the best design in the last generation of stage one. In stage two, 3D FEA models are developed, using the dimensions determined by the best design from stage one, to investigate effect of the shape of segment surfaces on the design objectives. Overall, the proposed two-stage optimization procedure is successfully applied in the actuator design and shows the potential to solve a wide range of structural optimization problems.

scholarly journals Substructural Identification of Flexural Rigidity for Beam-Like Structures

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Ki-Young Koo ◽  
Jin-Hak Yi
Keyword(s):  
Boundary Conditions ◽  
Flexural Rigidity ◽  
Beam Theory ◽  
Beam Model ◽  
Single Variable ◽  
Euler Beam ◽  
Identification Method ◽  
Bridge Model ◽  
Euler Beam Theory ◽  
Girder Bridge

This study proposes a novel substructural identification method based on the Bernoulli-Euler beam theory with a single variable optimization scheme to estimate the flexural rigidity of a beam-like structure such as a bridge deck, which is one of the major structural integrity indices of a structure. In ordinary bridges, the boundary condition of a superstructure can be significantly altered by aging and environmental variations, and the actual boundary conditions are generally unknown or difficult to be estimated correctly. To efficiently bypass the problems related to boundary conditions, a substructural identification method is proposed to evaluate the flexural rigidity regardless of the actual boundary conditions by isolating an identification region within the internal substructure. The proposed method is very simple and effective as it utilizes the single variable optimization based on the transfer function formulated utilizing Bernoulli Euler beam theory for the inverse analysis to obtain the flexural rigidity. This novel method is also rigorously investigated by applying it for estimating the flexural rigidity of a simply supported beam model with different boundary conditions, a concrete plate-girder bridge model with different length of an internal substructure, a cantilever-type wind turbine tower structure with different type of excitation, and a steel box-girder bridge model with internal structural damages.

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

scholarly journals Dynamic Analysis of Honeycomb Sandwich Beam with Multiple Debonds

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
B. Saraswathy ◽  
R. Ramesh Kumar ◽  
Lalu Mangal
Keyword(s):  
Analytical Solution ◽  
Transient Analysis ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Beam Length ◽  
Honeycomb Core ◽  
Element Analysis ◽  
Fast Fourier Transform Analysis ◽  
Honeycomb Sandwich ◽  
Nonlinear Transient

Analytical formulation for the evaluation of frequency of CFRP sandwich beam with debond, following the split beam theory, generally underestimates the stiffness, as the contact between the honeycomb core and the skin during vibration is not considered in the region of debond. The validation of the present analytical solution for multiple-debond size is established through 3D finite element analysis, wherein geometry of honeycomb core is modeled as it is, with contact element introduced in the debond region. Nonlinear transient analysis is followed by fast Fourier transform analysis to obtain the frequency response functions. Frequencies are obtained for two types of model having single debond and double debond, at different spacing between them, with debond size up to 40% of beam length. The analytical solution is validated for a debond length of 15% of the beam length, and with the presence of two debonds of same size, the reduction in frequency with respect to that of an intact beam is the same as that of a single-debond case, when the debonds are well separated by three times the size of debond. It is also observed that a single long debond can result in significant reduction in the frequencies of the beam than multiple debond of comparable length.

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