End Effects in Laminated Anisotropic Beams—Part II

1995 ◽  
Vol 117 (4) ◽  
pp. 285-289
Author(s):  
J. A. Ackermann ◽  
T. J. Kozik
Keyword(s):  
Normal Load ◽  
Analysis Procedure ◽  
Normal Stresses ◽  
Timoshenko Theory ◽  
End Effects ◽  
Laminated Beam ◽  
Analytical Technique ◽  
Simply Supported ◽  
Aluminum Beam ◽  
Combination Of Material

An analytical method of examining the stress field near the edge of a simply supported, laminated beam was developed in Part I of this paper. The result was a system of second-order, ordinary, linear, nonhomogeneous differential equations. A numerical and analytical technique for solving these equations is presented in this paper. The method is a versatile stress analysis procedure which can accommodate any combination of material lay-up and can simulate any prescribed distribution of normal load on the upper and lower surfaces. The reactions at the ends of the beam may be distributed over the surface edges in a fashion most accurately characterizing the physical supports. An all-steel lay-up is examined as a basis for comparison with Bernoulli-Euler and Timoshenko theory; and a two-layered steel/aluminum beam is examined to simply demonstrate the method’s capability of determining the interlaminar transverse shear and normal stresses.

End Effects in Laminated Anisotropic Beams — Part I

1995 ◽  
Vol 117 (4) ◽  
pp. 279-284
Author(s):  
J. A. Ackermann ◽  
T. J. Kozik
Keyword(s):  
Stress Field ◽  
Normal Stress ◽  
Transverse Shear ◽  
Analytical Method ◽  
Normal Load ◽  
End Effects ◽  
Laminated Beam ◽  
Simply Supported ◽  
Combination Of Material

The derivation of an analytical method to examine the stress field near the end of a simply supported, laminated beam is presented. Specific effort has been directed to accurately calculate the transverse-shear and normal stress by incorporating the exact displacement relations derived, by Kozik (1970). The method accommodates any combination of material lay-up and any type of normal load on the upper and lower surfaces. The reactions at the ends of the beam may be distributed over the surface edges in a fashion most accurately characterizing the physical supports. The solution and application of the method is presented in Part II of this paper.

Damage Detection Using Piezoelectrics Modal Analysis and PSD Technique

2000 ◽  
Author(s):  
Sauro Liberatore ◽  
Gregory P. Carman
Keyword(s):  
Theoretical Model ◽  
Damage Detection ◽  
State Space Model ◽  
Piezoelectric Sensor ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Power Spectral ◽  
Frequency Changes ◽  
Set Up ◽  
Aluminum Beam

Abstract A damage detection method has been implemented on a simply supported beam structure. The method is developed with both a theoretical model and experimental results. The simply supported beam contains one piezoelectric actuator and one piezoelectric sensor. The theoretical model was obtained from an energy formulation and a Rayleigh-Ritz approach. Matrices were composed in a State Space model to reproduce the input-output system between actuator and sensor. The damage was modeled with material properties variations. The experimental set up consisted of an aluminum beam with damage introduced by adding different weights in various locations. The dynamic changes produced were investigated and compared with theoretical prediction with reasonable agreement obtained. In order to quantify the size of damage, Power Spectral Density approach was used. To locate damage, frequency changes were used.

Eigenfrequencies of Continuous Plates With Arbitrary Number of Equal Spans

1979 ◽  
Vol 46 (3) ◽  
pp. 656-662 ◽  
Author(s):  
Isaac Elishakoff ◽  
Alexander Sternberg
Keyword(s):  
Arbitrary Number ◽  
Wave Number ◽  
Analytical Technique ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Simple Support ◽  
Transcendental Equations ◽  
Rigid Supports ◽  
Numerical Complexity

An approximate analytical technique is developed for determination of the eigenfrequencies of rectangular isotropic plates continuous over rigid supports at regular intervals with arbitrary number of spans. All possible combinations of simple support and clamping at the edges are considered. The solution is given by the modified Bolotin method, which involves solution of two problems of the Voigt-Le´vy type in conjunction with a postulated eigenfrequency/wave-number relationship. These auxiliary problems yield a pair of transcendental equations in the unknown wave numbers. The number of spans figures explicitly in one of the transcendental equations, so that numerical complexity does not increase with the number of spans. It is shown that the number of eigenfrequencies associated with a given pair of mode numbers equals that of spans. The essential advantage of the proposed method is the possibility of finding the eigenfrequencies for any prescribed pair of mode numbers. Moreover, for plates simply supported at two opposite edges and continuous over rigid supports perpendicular to those edges, the result is identical with the exact solution.

Effects of In-plane Load on Flutter of Homogeneous Laminated Beam Plates with Delamination

2000 ◽  
Vol 123 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Le-Chung Shiau ◽  
Yuan-Shih Chen
Keyword(s):  
Mach Number ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Compressive Load ◽  
Two Dimensional ◽  
Plate Model ◽  
Laminated Beam ◽  
Simply Supported ◽  
Flutter Boundary ◽  
Homogeneous Beam

The effects of in-plane load on flutter characteristics of delaminated two-dimensional homogeneous beam plates at high supersonic Mach number are investigated theoretically. Linear plate theory and quasi-steady supersonic aerodynamic theory are employed. A simple beam-plate model is developed to predict the effects of in-plane load on flutter boundaries for the delaminated beam plates with simply supported ends. Results reveal that the presence of an in-plane compressive load degrades the stiffness and natural frequencies of the plate and thereby decreases the flutter boundary for the plate. However, for certain geometry, the flutter boundaries were raised due to flutter coalescence modes of the plate altered by the presence of the in-plane load on the plate.

scholarly journals Assessment of Theories for Free Vibration Analysis of Homogeneous and Multilayered Plates

2004 ◽  
Vol 11 (3-4) ◽  
pp. 261-270 ◽  
Author(s):  
Erasmo Carrera
Keyword(s):  
Vibration Analysis ◽  
Single Layer ◽  
Free Vibration Analysis ◽  
Normal Stresses ◽  
Displacement Fields ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Vibrational Response ◽  
Multilayered Plates ◽  
Electric Materials

This paper assesses classical and advanced theories for free vibrational response of homogeneous and multilayered simply supported plates. Closed form solutions are given for thick and thin geometries. Single layer and multilayered plates made of metallic, composite and piezo-electric materials, are considered. Classical theories based on Kirchhoff and Reissner-Mindlin assumptions are compared with refined theories obtained by enhancing the order of the expansion of the displacement fields in the thickness directionz. The effect of the Zig-Zag form of the displacement distribution inzas well as of the Interlaminar Continuity of transverse shear and normal stresses at the layer interface were evaluated. A number of conclusions have been drawn. These conclusions could be used as desk-bed in order to choose the most valuable theories for a given problem.

An In Vivo Method for Measuring Turbulence in Mechanical Prosthesis Leakage Jets

2004 ◽  
Vol 126 (1) ◽  
pp. 26-35 ◽  
Author(s):  
Brandon R. Travis ◽  
Thomas D. Christensen ◽  
Morten Smerup ◽  
Morten S. Olsen ◽  
J. Michael Hasenkam ◽  
...  
Keyword(s):  
Mechanical Heart Valve ◽  
Maximum Velocity ◽  
Shear Stresses ◽  
Normal Stresses ◽  
Mechanical Prosthesis ◽  
Analytical Technique ◽  
In Vivo Measurement ◽  
Measurement And Analysis

This work introduces a method for the in vivo measurement and analysis of turbulence within the leakage of a mechanical heart valve. Several analysis techniques were applied to ultrasound measurements acquired within the atrium of a pig, and error associated with these techniques was analyzed. The technique chosen applies cyclic averaging to mean and maximum velocity measurements within small, normalized phase windows to calculate Reynolds normal stresses in the direction of the ultrasound beam. Maximum shear stresses are estimated from these normal stresses using an analytical technique. The stresses observed were smaller than those reported from previous in vitro simulations.

scholarly journals The mechanisms underlying long-term shaft resistance enhancement of energy pile in clays

2020 ◽  
Author(s):  
Saeed Yazdani ◽  
Sam Helwany ◽  
Guney Olgun
Keyword(s):  
Normal Load ◽  
Comprehensive Analysis ◽  
Normal Stresses ◽  
Lateral Stress ◽  
Energy Pile ◽  
Shaft Resistance ◽  
Energy Piles ◽  
Constant Normal Stiffness ◽  
Constant Normal Load

Although there are several studies indicating that heating increases the long-term shaft resistance of energy piles, the mechanisms by which heating causes this increase have not been adequately evaluated yet. This article aims to perform comprehensive analysis and discussion to assess the important factors contributing to this increase by integrating the findings from three recently published papers studying the thermo-mechanical behavior of clay and clay-pile interface. In these three studies, reconstituted kaolin clay was used, and cyclic and monotonic heat ranging between 24° C and 34°C were applied to the clay and interface. The interface was sheared under two stiffness boundary conditions; Constant Normal Stiffness (CNS) and Constant Normal Load (CNL), where the normal stresses varied between 100 kPa and 300 kPa. The analysis performed in this article reveals that the increase in strength of interface under CNL condition is primarily attributed to clay stiffening at interface. However, the increase in shaft resistance under CNS condition is primarily attributed to the heating-induced increase of effective lateral stress, although clay stiffening at interface also partially contributes to the total increase of shaft resistance.

Temperature Field in Simply Supported Laminated Beam

2012 ◽  
Vol 430-432 ◽  
pp. 181-184
Author(s):  
Hai Qian ◽  
Ding Zhou ◽  
Wei Qing Liu
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Single Layer ◽  
Lower Surface ◽  
Continuity Condition ◽  
Two Dimensional ◽  
Laminated Beam ◽  
Surface Conditions ◽  
Simply Supported

According to the two-dimensional thermal theory, the temperature distribution in a simply supported laminated beam is studied. Firstly, the temperature distribution in a single-layer simply supported beam is analytically derived. Then, based on the continuity condition of the temperature and heat flux between the connected layers, the temperature and heat flux relations between the lowest layer and the top layer of the beam are recurrently obtained. Finally, the unknown coefficients are determined by the upper and lower surface conditions of the laminated beam. The temperature in the beam is given by substituting the unknown coefficients back to the recurrent formulae.

scholarly journals Frictional slip of a rigid punch on an elastic half-plane

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160352 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Half Plane ◽  
Applied Load ◽  
Normal Load ◽  
Slip Zone ◽  
Slip Model ◽  
Normal Stresses ◽  
Rigid Punch ◽  
The Coefficient Of Friction ◽  
Slip Displacement ◽  
Frictional Slip

If a rigid punch is perfectly bonded to an elastic half-plane, the stress state possesses a well-known oscillating singularity. Because the shear and normal stresses are out of phase with each other, the application of a frictional slip model is expected to result in a slip zone at each of the corners. A solution exists in the literature if the punch is subjected to a normal load. It was shown that the extent of the slip zone is an eigenvalue which depends upon Poisson’s ratio and the coefficient of friction, but is independent of the magnitude of the applied load. In this investigation, the extent of the slip zone as well as the slip displacement is determined from the perfect bond solution. The analysis is valid if the length of the slip zone is small compared with the punch width. However, the results are shown to be in excellent agreement with the solution in the literature even when the total length of the slip zones is equal to half of the punch width. A solution is then obtained for combined normal and tangential loading. This work, and its extensions, is expected to be applicable in the study of the mechanics of fretting.

Computation of the Optimal Normal Load for a Mistuned and Frictionally Damped Bladed Disk Assembly Under Different Types of Excitation

2001 ◽  
Author(s):  
D. Cha ◽  
A. Sinha
Keyword(s):  
Harmonic Balance ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Random Excitation ◽  
Friction Dampers ◽  
Analytical Technique ◽  
Bladed Disk ◽  
Different Types ◽  
Bladed Disk Assembly ◽  
Sinusoidal Excitation

Using non-dimensional variables, the performances of friction dampers of a mistuned bladed disk assembly are examined for different types of excitation: white noise excitation, independent narrow band random excitation and sinusoidal excitation with unknown amplitudes. Based on the harmonic balance method, an analytical technique is developed to compute the statistics of response for sinusoidal excitation with unknown amplitudes. The performances of blade-to-blade and blade-to-ground dampers are compared under different types of excitation. It is found that non-dimensional optimal normal loads of friction dampers are almost independent of the nature of excitation. Therefore, optimal normal loads of friction dampers can be chosen without any knowledge of the nature of excitation.

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