Bending, Buckling and Vibration of Orthotropic Plate-Beam Structures

1968 ◽  
Vol 12 (04) ◽  
pp. 249-268 ◽  
Author(s):  
C. S. Smith
Keyword(s):  
Orthotropic Plate ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Elastic Buckling ◽  
Lateral Loads ◽  
Orthotropic Plates ◽  
Approximate Methods ◽  
Buckling Loads ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration

A method is described of estimating elastic deflections and stresses in systems of interconnected rectangular orthotropic plates and single-direction beams, under distributed or concentrated lateral loads combined with compressive or tensile stresses applied either normal to or in the direction of the beams. The effects of initial deformation of beams and plates are included. Elastic buckling loads and modes and natural frequencies and modes of vibration may be computed. The methods described have been incorporated in a family of FORTRAN IV computer programs which are used to obtain a number of illustrative solutions, including:(/) deflections and stresses in an orthogonally stiffened, three-dimensional ship compartment; these are compared with results computed by an alternative finite element method; (//) buckling loads and modes and natural frequencies and modes of vibration for a typical deck structure; these are compared with results calculated by more approximate methods commonly used in design.

scholarly journals Investigation of natural frequencies of axially loaded thin-walled columns

2018 ◽  
Vol 219 ◽  
pp. 02018
Author(s):  
Łukasz Żmuda-Trzebiatowski
Keyword(s):  
Applied Load ◽  
Natural Frequencies ◽  
Elastic Buckling ◽  
Correlation Technique ◽  
Buckling Loads ◽  
Perfectly Plastic ◽  
Linear Buckling ◽  
Thin Walled ◽  
Elastic Perfectly Plastic ◽  
Flexural Torsional Buckling

The paper deals with correlation between natural frequencies of two steel thin-walled columns and the corresponding applied load. The structures are made of cold-formed lipped channel sections. The columns lengths were assumed to follow two buckling patterns – global flexural and flexural-torsional buckling. In the thicker structure two material models were considered – linearly-elastic and elastic-perfectly plastic. Numerical computations cover dynamic eigenvalue problem, linear buckling and geometrically (and materially) non-linear analysis. The correlation between squares of natural frequencies and the applied load is linear in both columns. The first natural frequencies drop to zero due to structural buckling. This method, called the Vibration Correlation Technique, allows to predict buckling loads on the basis of measured vibration frequencies of the structures. Plasticity does not affect the corresponding curves – the use of the presented technique is limited to the structures exhibiting elastic buckling behaviour.

Modeling and simulation of the dynamic behavior of the macaw palm fruit-rachilla system

SIMULATION ◽  
2021 ◽  
pp. 003754972110437
Author(s):  
Mariana Ribeiro Pereira ◽  
Fábio Lúcio Santos ◽  
Nara Silveira Velloso ◽  
Flora Maria de Melo Villar ◽  
Mateus Resende Rodrigues
Keyword(s):  
Dynamic Behavior ◽  
Elasticity Modulus ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Palm Tree ◽  
Specific Mass ◽  
Palm Fruit ◽  
Modes Of Vibration ◽  
Macaw Palm ◽  
Three Dimensional Models

The macaw palm ( Acrocomia aculeata) is a palm tree native to tropical forests that stand out due to its great potential for oil production. This study was developed with the objective of constructing a high-fidelity model of the macaw palm fruit-rachilla system for the purpose of simulating its dynamic behavior when subjected to mechanical vibrations. The finite element method was used to determine the natural frequencies and modes of vibration of the system. The three-dimensional models of the fruit-rachilla systems were elaborated using CAD3D Fusion 360 software. The modal properties of the fruit-rachilla systems were obtained based on the models developed by varying the elasticity modulus values of the system. The parameters of greatest influence in the estimation of natural frequencies are the elasticity modulus, especially that of the fruit-rachilla joint, and the specific mass. The models that take into account the three-dimensional strains along the rachilla are the least sensitive to variations in the mechanical properties (elasticity modulus and specific mass) and are shown to be more representative of the actual physical system.

scholarly journals A Novel Highly Accurate Finite-Element Family

2017 ◽  
Vol 2017 ◽  
pp. 1-20
Author(s):  
Giovanni Bernardini ◽  
Fabio Cetta ◽  
Luigi Morino
Keyword(s):  
Finite Element ◽  
Structural Dynamics ◽  
Hermite Interpolation ◽  
Natural Frequencies ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Numerical Results ◽  
Small Thickness ◽  
Modes Of Vibration ◽  
Patch Technique

A novel Nth order finite element for interior acoustics and structural dynamics is presented, with N arbitrarily large. The element is based upon a three-dimensional extension of the Coons patch technique, which combines high-order Lagrange and Hermite interpolation schemes. Numerical applications are presented, which include the evaluation of the natural frequencies and modes of vibration of (1) air inside a cavity (interior acoustics) and (2) finite-thickness beams and plates (structural dynamics). The numerical results presented are assessed through a comparison with analytical and numerical results. They show that the proposed methodology is highly accurate. The main advantages however are (1) its flexibility in obtaining different level of accuracy (p-convergence) simply by increasing the number of nodes, as one would do for h-convergence, (2) the applicability to arbitrarily complex configurations, and (3) the ability to treat beam- and shell-like structures as three-dimensional small-thickness elements.

Finite Element Modeling of Annular-Like Acoustic Cavities

1985 ◽  
Vol 107 (1) ◽  
pp. 81-85
Author(s):  
Chaw-Hua Kung ◽  
Rajendra Singh
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Pressure Oscillation ◽  
Transient Heat Conduction ◽  
Natural Frequencies And Modes ◽  
Acoustic Cavities ◽  
Eigen Solutions ◽  
Element Technique ◽  
Good Agreement

A finite element technique has been developed to find natural frequencies and modes of undamped three-dimensional acoustic cavities. This method utilizes the analogy between a special form of the discretized transient heat conduction equations and discretized equations of acoustic pressure oscillation. The proposed technique is verified by applying it to several cavities of known theoretical eigen-solutions. Computed results for an acoustic ring, an acoustic disk, and a pure annular cavity match extremely well with exact solutions. In addition, the condensation scheme is investigated and guidelines of selecting acoustic master nodes appropriately are also discussed in the paper. Using the validated finite element method along with suitable condensation, the eigenvalue problem of an annular-like cavity is solved. Since the exact solution for this case is not possible, finite element computations for natural frequencies and modes are compared with the measured results obtained using an acoustic modal analysis experimental technique; again very good agreement has been found.

Natural frequencies of cooling tower shells

1967 ◽  
Vol 2 (2) ◽  
pp. 127-133 ◽  
Author(s):  
B G Neal
Keyword(s):  
Cooling Tower ◽  
Natural Frequencies ◽  
Support Condition ◽  
Theoretical Determination ◽  
Electro Deposition ◽  
Horizontal Fracture ◽  
Natural Frequencies And Modes ◽  
Modes Of Vibration ◽  
Hyperbolic Cooling Tower

A theoretical determination of the lowest natural frequencies of inextensional vibrations of hyperbolic cooling tower shells is first presented. It is shown that inextensional behaviour is only possible for certain types of support condition at the base, one of which consists of four pairs of inclined columns evenly spaced round the circumference which, at their points of attachment, only permit displacements normal to the plane of the shell. Experiments to determine the natural frequencies and modes of vibration of a model shell are then described. This model, which was made by the electro-deposition of copper on a Perspex mould, could be supported at its base by up to forty pairs of inclined columns. Using only four evenly spaced pairs of columns the lowest natural frequencies of inextensional vibrations were first determined, and found to agree well with the theoretical values. The natural frequencies and modes of the extensional vibrations which occurred when the shell was supported by forty pairs of columns were then explored. Finally, the effect of removing some of the supports, thereby simulating a horizontal fracture in part of the shell, was studied. The possibility of wind-induced vibrations occurring in practice is then considered. It is concluded that these are unlikely to occur unless the shell has already suffered damage, as for example by experiencing a horizontal fracture over part of its circumference near the base.

On The Theory Of Bending Of A Thick Orthotropic Plate Without Consideration Of Simplifying Hypothesis

2011 ◽  
Vol 3 ◽  
Author(s):  
Makhamatali Koraboyevich Usarov
Keyword(s):  
Analytical Solution ◽  
Orthotropic Plate ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Orthotropic Plates

The problem of bending of a thick orthotropic plate is considered as a three-dimensional problem of the theory ofelasticity. On the basic of the method of expansion of thesolution into the series, a three-dimensional problem isreduced to two independent two –dimensional problems.The theory of thick orthotropic plates free from simplifiedhypothesis is developed: An analytical solution of equationis given. Maximum values of displacements and stressesfor upper, middle and lower surfaces of the plate are calculated.

scholarly journals On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times

2004 ◽  
Vol 2004 (1) ◽  
pp. 69-83 ◽  
Author(s):  
K. L. Verma ◽  
Norio Hasebe
Keyword(s):  
Orthotropic Plate ◽  
Finite Thickness ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Orthotropic Plates ◽  
Special Cases ◽  
Thermal Relaxation Times ◽  
Modes Of Vibration ◽  
The Waves ◽  
Thermoelastic Waves

Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. Numerical solution of the frequency equations for orthotropic plate is carried out, and the dispersion curves for the first six modes are presented for a representative orthotropic plate. The three motions, namely, longitudinal, transverse, and thermal, of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves gets modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.

Effect of a Change in Position of a Support on the Natural Frequencies and Modes of Vibration of a System

1965 ◽  
Vol 7 (3) ◽  
pp. 271-278 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Torsional Vibration ◽  
Simple Formula ◽  
Natural Frequencies ◽  
Static Deflection ◽  
Deflection Curve ◽  
Natural Frequencies And Modes ◽  
Method Of Solution ◽  
Modes Of Vibration ◽  
Frequency Changes ◽  
Small Change

The effect of a small change in position of one of the supports on the natural frequencies and modes of a structure, which is ‘continuous’ over a number of supports, is examined in this paper. Using energy and receptance methods a simple formula is obtained for the change in natural frequency of a beam when the support displacement is infinitesimal. The corresponding displacements of other nodal points are also obtained. When the support displacement is finite, but not large, changes in mode and frequency are determined by iteration. The method of solution is extended to the coupled flexural and torsional vibration of a non-symmetrical beam. In the case of a rectangular plate with stiffeners parallel to an edge, frequency changes due to the change in position of a stiffener may be determined by the same method. Alternative approximate formulae, based on the static deflection curve, are derived for the change of fundamental frequency.

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