Dynamic Characteristics of Large Repetitive Framelike Structures

1984 ◽  
Vol 51 (3) ◽  
pp. 510-518 ◽  
Author(s):  
Adnan H. Nayfeh ◽  
Michael S. Hartle
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Characteristics ◽  
Building Block ◽  
Equations Of Motion ◽  
Single Element ◽  
Two Dimensional ◽  
Energy Equivalent ◽  
Theoretical Predictions ◽  
Block Approach

Using a building block approach and starting with a single element, expressions for the energy of various two-dimensional frametype gridwork configurations are derived. These are then used to develop energy equivalent continua for the grid-works. Equations of motion and associated boundary conditions are obtained for the continua. Some dynamic characteristics of these continua are investigated and compared with corresponding results obtained from finite element codes and also with some available theoretical predictions.

Random Base Excitation of Timoshenko Beam Traversed by Moving Load

2011 ◽  
Author(s):  
Fahim Javid ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Base Excitation ◽  
Lateral Direction ◽  
Beam Dynamic

The study of dynamic response of Timoshenko beam traversed by moving load subjected to random base excitation is carried out. By applying the theory of dynamic response of Timoshenko beam as well as finite element theory, beam finite element governing equations of motion are developed and they are solved using Galerkin method. To validate the model, some results of the model are compared with those available in literatures and very close agreement is achieved. The beam is subjected to travelling load and random base excitation in lateral direction simultaneously. Three types of boundary conditions, namely, hinged-hinged, hinged-clamped, and the clamped-clamped ends, are considered and beam dynamic behavior; such as deflection, velocity, and bending moment of beam midpoint, with all so-called boundary conditions are studied. To get better understanding of base excitation effects on the beam dynamic performance, all the results are presented with and without base excitation, in which considerably difference is observed. Moreover, the effect of base excitation on beam with different span-length is monitored.

scholarly journals Vectorized Matlab Codes for Linear Two-Dimensional Elasticity

2007 ◽  
Vol 15 (3) ◽  
pp. 157-172 ◽  
Author(s):  
Jonas Koko
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Linear Elasticity ◽  
Numerical Experiments ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Linear Finite Element ◽  
Matlab Implementation

A vectorized Matlab implementation for the linear finite element is provided for the two-dimensional linear elasticity with mixed boundary conditions. Vectorization means that there is no loop over triangles. Numerical experiments show that our implementation is more efficient than the standard implementation with a loop over all triangles.

Polynomial Based Elasticity Solutions of Beams and their Numerical Validation: A Review

2011 ◽  
Vol 311-313 ◽  
pp. 2315-2321
Author(s):  
Sebin Jose ◽  
Sunil Bhat
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Stress Problem ◽  
Elasticity Solutions ◽  
Harmonic Equation ◽  
Complex Cases ◽  
Good Agreement

Solution of two-dimensional stress problem is reduced to integration of bi-harmonic equation[1].A polynomial is chosen as Airy’s stress function.Constants of the polynomial[2] are found by fulfilling the boundary conditions. Stress solutions are obtained from.The paper presents polynomial based stress solutions of beams for complex cases involving offset loads and other combinations with offset loads.The results are compared with those obtained from finite element analysis[3] and conventional methods.The results are in good agreement with each other.

scholarly journals An effective high-order element for analysis of two-dimensional linear problem using SBFEM

2021 ◽  
Vol 15 (3) ◽  
pp. 109-122
Author(s):  
Nguyen Van Chung ◽  
Nguyen Thanh Him ◽  
Bui Quoc Khiem ◽  
Pham Ngoc Tien
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Linear Problem ◽  
High Order ◽  
Surface Load ◽  
Two Dimensional ◽  
High Order Element ◽  
Scaled Boundary Finite Element ◽  
Element Method

The scaled boundary finite element method (SBFEM) is a semi-analytical method, whose versatility, accuracy, and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using an efficient high-order polynomial element in the SBFEM to form the approximation in the circumferential direction. The governing equations are formulated from the classical linear elasticity theory via the SBFEM technique. The scaled boundary finite element equations are formulated within a general framework integrating the influence of the distributed body source, mixed boundary conditions, contributions the side face with either prescribed surface load or prescribed displacement. The position of scaling center is considered for modeling problem. The proposed method is evaluated by solving two-dimensional linear problem. A selected set of results is reported to demonstrate the accuracy and convergence of the proposed method for solving problems in general boundary conditions.

Effect of Boundary Conditions on Transient Response of Sandwich Plates with Electrorheological Fluid Core

2011 ◽  
Vol 462-463 ◽  
pp. 372-377
Author(s):  
Jafar Rahiminasab ◽  
Jalil Rezaeepazhand
Keyword(s):  
Finite Element ◽  
Electric Field ◽  
Boundary Conditions ◽  
Transient Response ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Electrorheological Fluid ◽  
Fluid Core

Electrorheological (ER) fluids are a kind of smart material whose rheological properties can be controlled by an external electric field. In the present paper, the transient vibration of a rectangular three layer sandwich plate with electrorheological fluid core is analyzed based on the classical plate theory. The Bingham plastic model is used to consider the post-yield behavior of ER fluid. The structure is modeled using a finite element method. Hamilton’s principle is employed to derive the finite element equations of motion. The constant average acceleration scheme is used to integrate the equations of motion. The effects of change in electric field and core thickness on the structure settling time and its natural frequencies are studied for various boundary conditions. The results show that the thickness of the core layer and the electric field strength has significant effects on damping behavior of the sandwich plate. When the applied electric field increases a linear decay in transient response of the structure is observed. It is also found that the electric field changes have no influence on the system natural frequencies.

Mathematical Model for Gas Bearing With Holes of Tangential Supply

1999 ◽  
Vol 121 (2) ◽  
pp. 301-305 ◽  
Author(s):  
L Q. Liu ◽  
C. Z. Chen
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Inertia Effect ◽  
Governing Equations ◽  
Gas Bearing ◽  
Typical Design

To investigate the dynamic characteristics of gas bearings with holes of tangential supply (TS bearing), drawing on the modified Reynolds equations proposed by Mori, we present new governing equations and their reasonable boundary conditions. Using this mathematical model, the inertia effect of the supplied gas on the aerodynamic film force can be evaluated properly. The governing equations are solved numerically using Finite Element Method (FEM), and the pressure distribution of the gas in the bearing, the critical whirl ratio and so on, are calculated for a typical design. Some results for a cylindrical journal bearing (CJ bearing) and ordinary bearing with holes of radial supply (RS bearing) are also provided for comparison.

A model for tidal motion and level in the Tay Estuary

1987 ◽  
Vol 92 (3-4) ◽  
pp. 257-273
Author(s):  
D. J. Gunn ◽  
O. Yenigun
Keyword(s):  
Boundary Conditions ◽  
Integral Method ◽  
Equations Of Motion ◽  
Hydrodynamic Resistance ◽  
Two Dimensional ◽  
Final Solution ◽  
The Road ◽  
Tidal Motion ◽  
Outer Estuary ◽  
Tay Estuary

SynopsisA new mathematical model has been constructed for tidal motion and level in the Tay Estuary. The model is based upon the two-dimensional vertically integrated equations of motion and gives two-dimensional vector velocities and levels from the rail bridge to the Bar, about 5 km east of Buddon Ness. The extent of the model outside the mouth of the Tay is 3 km north of Buddon Ness and 7 km south. The equations of motion are expressed in the form of central differences in space and solved explicitly in time using the Local Integral Method. The emergence and submergence of drying zones in the estuary are calculated during the tidal cycle. A representation of the hydrodynamic resistance of the road bridge was included in the model.The boundary conditions for the model were based upon estimates of river flows at the western entrance and tidal levels at the eastern, northern and southern boundaries. Boundary conditions at the eastern end of the model presented considerable complexities because of the presence of an amphidromic system to the south of the Norwegian coast. The final solution adopted was to choose tidal levels along the easterly boundaries to give velocities in the outer estuary that agreed with available tidal atlases of the region.Velocities and levels at intervals of 250 m for the period of a tide show the prevalent shoaling conditions over the estuary combined during certain periods with conditions of high velocity, giving very difficult approaches to the River Tay.

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