Transient Waves in Anisotropic Laminated Plates, Part 1: Theory

1991 ◽  
Vol 113 (2) ◽  
pp. 230-234 ◽  
Author(s):  
G. R. Liu ◽  
J. Tani ◽  
T. Ohyoshi ◽  
K. Watanabe
Keyword(s):  
Numerical Method ◽  
Fourier Transforms ◽  
Dynamic Equilibrium ◽  
Virtual Work ◽  
Laminated Plates ◽  
The Finite Element Method ◽  
Equilibrium Equations ◽  
Transient Waves ◽  
Plate Elements ◽  
Hybrid Numerical Method

A hybrid numerical method in which the finite element method and the method of Fourier transforms are combined is proposed for computing the transient waves in anisotropic laminated plates excited by impact loads. The anisotropic laminated plate is divided into N plate elements, and the principle of virtual work is used to develop approximate dynamic equilibrium equations for three- and two-dimensional problems. The displacement response is determined by employing the Fourier transformation and the modal analysis. This hybrid numerical method is straightforward and easy to use.

Transient Waves in Anisotropic Laminated Plates, Part 2: Application

1991 ◽  
Vol 113 (2) ◽  
pp. 235-239 ◽  
Author(s):  
G. R. Liu ◽  
J. Tani ◽  
T. Ohyoshi ◽  
K. Watanabe
Keyword(s):  
Numerical Method ◽  
Impact Load ◽  
Three Dimensional ◽  
Point Load ◽  
Laminated Plates ◽  
Impact Loads ◽  
Dimensional Problem ◽  
Transient Waves ◽  
Isotropic Plates ◽  
Hybrid Numerical Method

The application of the hybrid numerical method proposed in the previous paper by the present authors to the computation of transient waves in composite material plates excited by step-impact loads is presented in this paper. Both the two-dimensional problem (line step-impact load) and the three-dimensional problem (point step-impact load) are considered. First, the displacement responses of isotropic plates are computed by using the hybrid numerical method and the results are compared with those obtained by the method of the head of the pulse approximation and the method of generalized rays. Next, the displacement responses of a hybrid composite laminated plate excited by a line step-impact load and a point load are calculated, and some interesting results are obtained.

scholarly journals Investigation on the Dynamics of an On-Board Rotor-Bearing System

2012 ◽  
Author(s):  
Mzaki Dakel ◽  
Sébastien Baguet ◽  
Régis Dufour
Keyword(s):  
Dynamic Behavior ◽  
Fourier Transforms ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Beam Theory ◽  
Rigid Base ◽  
The Finite Element Method ◽  
Mass Unbalance ◽  
Motion Display

In ship and aircraft turbine rotors, the rotating mass unbalance and the different movements of the rotor base are among the main causes of vibrations in bending. The goal of this paper is to investigate the dynamic behavior of an on-board rotor under rigid base excitations. The modeling takes into consideration six types of base deterministic motions (rotations and translations) when the kinetic and strain energies in addition to the virtual work of the rotating flexible rotor components are computed. The finite element method is used in the rotor modeling by employing the Timoshenko beam theory. The proposed on-board rotor model takes into account the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of shaft and/or rigid disk. The Lagrange’s equations are applied to establish the differential equations of the rotor in bending with respect to the rigid base which represents a noninertial reference frame. The linear equations of motion display periodic parametric coefficients due to the asymmetry of the rotor and time-varying parametric coefficients due to the base rotational motions. In the proposed applications, the rotor mounted on rigid/elastic bearings is excited by a rotating mass unbalance associated with sinusoidal vibrations of the rigid base. The dynamic behavior of the rotor is analyzed by means of orbits of the rotor as well as fast Fourier transforms (FFTs).

NONLINEAR ELASTO-DYNAMIC ANALYSIS OF I-BEAMS CURVED IN-PLAN

2009 ◽  
Vol 09 (02) ◽  
pp. 213-241 ◽  
Author(s):  
R. EMRE ERKMEN ◽  
MARK A. BRADFORD
Keyword(s):  
Dynamic Equilibrium ◽  
Virtual Work ◽  
Numerical Models ◽  
Time History ◽  
Element Formulation ◽  
Nonlinear Behaviour ◽  
Equilibrium Equations ◽  
Geometric Nonlinearities ◽  
Initial Curvature ◽  
Straight Beam

The elastic response of curved beams subjected to moving vertical loads and dynamic loads is investigated. Incremental dynamic equilibrium equations are derived by using the principle of virtual work. Newmark's step-by-step procedure is adopted to discretise the dynamic equilibrium equations and obtain the time history response. Geometric nonlinearities due to large deflections and rotations are taken into account. A total Lagrangian finite element formulation is developed. The numerical models are compared with the existing analytical solutions and employed to show the effects of geometric nonlinearities as well as the initial curvature on the dynamic behaviour of curved I-beams. It is shown that the geometric nonlinearities are significant even for service loads. The nonlinear behaviour of a curved beam is substantially different from the nonlinear behaviour of a straight beam when the initial curvature is not small.

scholarly journals Dynamic Equilibrium Equations in Unified Mechanics Theory

2021 ◽  
Vol 2 (1) ◽  
pp. 63-80
Author(s):  
Noushad Bin Jamal Bin Jamal M ◽  
Hsiao Wei Lee ◽  
Chebolu Lakshmana Rao ◽  
Cemal Basaran
Keyword(s):  
Energy Loss ◽  
Entropy Generation ◽  
Equilibrium Equation ◽  
Dynamic Equilibrium ◽  
Free Vibration Analysis ◽  
Newtonian Mechanics ◽  
Equilibrium Equations ◽  
Time Coordinate ◽  
Proposed Model ◽  
Laws Of Thermodynamics

Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.

scholarly journals Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Jianhui Tian ◽  
Guoquan Jing ◽  
Xingben Han ◽  
Guangchu Hu ◽  
Shilin Huo
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Heat Source ◽  
Numerical Method ◽  
Functionally Graded ◽  
Thermal Problem ◽  
Linear Heat ◽  
Hybrid Numerical Method ◽  
Linear Heat Source ◽  
Gradient Parameter

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

A Hybrid Numerical Method for Loaded Highly Resonant Single Mode Cavities

1998 ◽  
Vol 142 (2) ◽  
pp. 506-520 ◽  
Author(s):  
Cheryl V. Hile ◽  
Gregory A. Kriegsmann
Keyword(s):  
Numerical Method ◽  
Single Mode ◽  
Hybrid Numerical Method

scholarly journals Analysis of a hybrid numerical method – decomposing leaf hydraulic conductance

2018 ◽  
Vol 5 (1) ◽  
pp. 98-112
Author(s):  
Frank H. Lynch ◽  
Gretchen B. North ◽  
Breeanna S. Page ◽  
Cullen J. Faulwell
Keyword(s):  
Numerical Method ◽  
Hydraulic Conductance ◽  
Leaf Hydraulic Conductance ◽  
Hybrid Numerical Method
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