The comparative analysis of the fully nonlinear, the linear elastic and the consistently linearized equations of motion of the 2D elastic pendulum

2004 ◽  
Vol 82 (11-12) ◽  
pp. 863-870 ◽  
Author(s):  
Yu. Vetyukov ◽  
J. Gerstmayr ◽  
H. Irschik
Keyword(s):  
Comparative Analysis ◽  
Equations Of Motion ◽  
Fully Nonlinear ◽  
Linearized Equations ◽  
Linear Elastic ◽  
Elastic Pendulum

scholarly journals COMPARATIVE ANALYSIS OF THE PARAMETERS OF FINITE-ELEMENT MODELS OF SOILS OBTAINED BY NUMERICAL METHODS

2017 ◽  
pp. 23-31
Author(s):  
Vladimir Ivanovich Matselya ◽  
Igor Nikolaevich Seelev ◽  
Alexey Valentinovich Lekontsev ◽  
Robert Rafaelevich Khafizov ◽  
Pavel Viktorovich Yakovlev ◽  
...  
Keyword(s):  
Finite Element ◽  
Comparative Analysis ◽  
Numerical Methods ◽  
Small Deformation ◽  
Finite Element Models ◽  
Linear Elastic ◽  
Industrial Buildings ◽  
Test Models ◽  
Weak Points ◽  
Plaxis 3D

The popularity of numerical methods for modeling soil bases determines the increased demand for the accuracy of calculations. The choice of a model that meets the requirements of accuracy of calculations and minimization of costs is determined by comparative analysis of common soil models described in scientific literature and used in calculations of sediments and dynamic effects of buildings (finite element linear elastic, elastic, ideal-plastic, Mora - Coulomb with strengthening, elasto-plastic with strengthening at small deformation). The results have been obtained on test models using finite element method in the environment of PLAXIS 3D and SCAD Office programs. In order to compare results obtained, subject to requirements of the current regulatory documents, a comparative analysis of soils was carried out according to the model of Body of rules 22.13330.2011 "Foundations of buildings and structures". The analysis results were used for choosing an optimal model of soil bases of industrial buildings estimated in earthquake-proof design. It should be noted that the strong and weak points identified for each model justify the choice of the best model for each particular case.

Non-Linear Vibrations of Plates Under Thermal and Mechanical Loads

2005 ◽  
Author(s):  
P. Ribeiro
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Implicit Time ◽  
Linear Elastic ◽  
Time Integration Method ◽  
Thermal Fields ◽  
Non Linear ◽  
Linear Vibrations ◽  
The Time Domain ◽  
Constitutive Material

The geometrically non-linear vibrations of plates under the combined effect of thermal fields and mechanical excitations are analyzed. With this purpose, an accurate model based on a p-version, hierarchical, first-order shear deformation finite element is employed. The constitutive material of the plates is linear elastic and isotropic. The equations of motion are solved in the time domain by an implicit time integration method. The temperature and the amplitude of the mechanical excitation are varied, and transitions from periodic to non-periodic motions are found.

scholarly journals Linear Vibration Analysis of Shells Using a Seven-Parameter Spectral/hp Finite Element Model

2020 ◽  
Vol 10 (15) ◽  
pp. 5102
Author(s):  
Carlos Valencia Murillo ◽  
Miguel Gutierrez Rivera ◽  
Junuthula N. Reddy
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Variable Thickness ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Linear Elastic ◽  
Commercial Code ◽  
The Finite Element Model ◽  
Hp Finite Element

In this paper, a seven-parameter spectral/hp finite element model to obtain natural frequencies in shell type structures is presented. This model accounts for constant and variable thickness of shell structures. The finite element model is based on a Higher-order Shear Deformation Theory, and the equations of motion are obtained by means of Hamilton’s principle. Analysis is performed for isotropic linear elastic shells. A validation of the formulation is made by comparing the present results with those reported in the literature and with simulations in the commercial code ANSYS. Finally, results for shell like structures with variable thickness are presented, and their behavior for different ratios r/h and L/r is studied.

Propagation of a nonlinear seismic pulse in an anelastic homogeneous medium

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 949-963 ◽  
Author(s):  
Dan W. Kosik
Keyword(s):  
Wave Propagation ◽  
Equations Of Motion ◽  
Surrounding Medium ◽  
Homogeneous Medium ◽  
Seismic Surveys ◽  
Linear Elastic ◽  
Cylindrically Symmetric ◽  
Unconsolidated Material ◽  
Linear Pulse ◽  
Implicit Finite Difference

Seismic surveys are often conducted using dynamite charges buried near the surface in unconsolidated material. In such material a large zone near the source should exist wherein nonlinear anelastic wave propagation, can be expected to take place, and have a significant impact on the way in which a seismic pulse forms and how its energy gets distributed into the surrounding medium. To obtain a solution for a propagating pulse in this zone, the equations of motion for nonlinear anelastic wave propagation, good to second order in the displacements, are solved numerically for the problem of a Gaussian pressure pulse acting on the interior cavity of a cylindrically symmetric hole in the medium. An implicit finite‐difference algorithm is used for the solution to the equations of motion for this problem. The anelastic medium is characterized by multivalued stress‐strain relations that exhibit hysteresis, and therefore a loss of energy per cycle, corresponding to a medium with a constant Q factor. Several numerical examples are calculated contrasting the nonlinear anelastic, linear anelastic, and linear elastic propagating pulses to one another. The nonlinear anelastic propagating pulse is found to have an amplitude that is several times larger than would be expected for a pulse in a linear medium and has a peak propagation velocity that is slightly less than that for a linear pulse. Dispersive effects are also evident for the nonlinear pulse.

Comparative Analysis of Frame-Core Wall Structure for Seismic Design

2012 ◽  
Vol 256-259 ◽  
pp. 2028-2033
Author(s):  
Jing Yang ◽  
Jiang Fan ◽  
Ji Xing Yuan ◽  
Qing Zhang
Keyword(s):  
Comparative Analysis ◽  
Dynamic Response ◽  
Seismic Performance ◽  
Seismic Design ◽  
Dynamic Characteristics ◽  
Wall Structure ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Plastic Phase

In this paper a skyscrapers frame-core wall structure as an example in Kun Ming, using two independent software, SATWE and ETABS, analyzed the dynamic characteristics and dynamic response of structures with earthquake in linear elastic phase and the elastic-plastic phase respectively, so that could evaluate rationality of the design of the structure as a whole and seismic performance superior or not, and it could provide an idea for audit drawing or proofread their own.

Unilateral Impact and Contact of Elastic Structures Using Lagrangian Multipliers

2011 ◽  
Author(s):  
Sebastian Tatzko
Keyword(s):  
Equations Of Motion ◽  
Structural Equations ◽  
Contact Forces ◽  
Integration Scheme ◽  
Lagrangian Multiplier ◽  
Elastic Structures ◽  
Lagrangian Multipliers ◽  
Linear Elastic ◽  
Time Stepping ◽  
Numerical Effort

This paper deals with linear elastic structures exposed to impact and contact phenomena. Within a time stepping integration scheme contact forces are computed with a Lagrangian multiplier approach. The main focus is turned on a simplified solving method of the linear complementarity problem for the frictionless contact. Numerical effort is reduced by applying a Craig-Bampton transformation to the structural equations of motion.

The Use of Normal Modes in Problems of Forced Vibration and Impact

1957 ◽  
Vol 61 (560) ◽  
pp. 552-559
Author(s):  
R. P. N. Jones
Keyword(s):  
Forced Vibration ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Very High Frequency ◽  
Linear Elastic ◽  
Modes Of Vibration ◽  
Fundamental Equations ◽  
Very High ◽  
Simple Exposition

SummaryA simple exposition, using d'Alembert's principle and methods of virtual work, is given of the properties and applications of the normal modes of vibration of a linear elastic system. The use of the normal modes in problems of free and forced vibration and dynamic loading is discussed with the aid of simple examples, and it is shown that by these methods dynamical problems for any linear system may be solved without the use of the fundamental equations of motion, provided the natural frequencies and modes of the system are known. In most problems the solutions converge rapidly, so that only the first few modes of vibration need be considered, and in these cases the solution may be modified to give further improvement in convergence. Unsatisfactory convergence may be obtained, however, in problems where there is an exciting force of very high frequency, or an impact of short duration. An approximate allowance may be made for damping, provided this is small.

Direct Linearization of Continuous and Hybrid Dynamical Systems

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Julie J. Parish ◽  
John E. Hurtado ◽  
Andrew J. Sinclair
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Equations ◽  
Equilibrium Configuration ◽  
Equations Of Motion ◽  
Hybrid Dynamical Systems ◽  
Linearized Equations ◽  
Direct Linearization ◽  
Taylor Series Expansions ◽  
Nonlinear Equations Of Motion ◽  
And Control

Nonlinear equations of motion are often linearized, especially for stability analysis and control design applications. Traditionally, the full nonlinear equations are formed and then linearized about the desired equilibrium configuration using methods such as Taylor series expansions. However, it has been shown that the quadratic form of the Lagrangian function can be used to directly linearize the equations of motion for discrete dynamical systems. This procedure is extended to directly generate linearized equations of motion for both continuous and hybrid dynamical systems. The results presented require only velocity-level kinematics to form the Lagrangian and find equilibrium configuration(s) for the system. A set of selected partial derivatives of the Lagrangian are then computed and used to directly construct the linearized equations of motion about the equilibrium configuration of interest, without first generating the entire nonlinear equations of motion. Given an equilibrium configuration of interest, the directly constructed linearized equations of motion allow one to bypass first forming the full nonlinear governing equations for the system. Examples are presented to illustrate the method for both continuous and hybrid systems.

An Efficient Method for Predicting the Vibratory Response of Linear Structures With Friction Interfaces

1986 ◽  
Vol 108 (4) ◽  
pp. 633-640 ◽  
Author(s):  
E. Bazan ◽  
J. Bielak ◽  
J. H. Griffin
Keyword(s):  
Equations Of Motion ◽  
Solution Procedure ◽  
System Response ◽  
Steady State Response ◽  
Friction Forces ◽  
Practical Applications ◽  
Linear Elastic ◽  
State Response ◽  
Vibratory Response ◽  
Parametric Studies

A simple methodology to study the steady-state response of systems consisting of linear elastic substructures connected by friction interfaces is presented. Assuming that only the first Fourier components of the friction forces contribute significantly to the system response, the differential equations of motion are transformed into a system of algebraic complex equations. Then, an efficient linearized procedure to solve these equations for different normal loads in the friction interfaces is developed. As part of the solution procedure, a criterion to determine the slip-to-stuck transitions in the joint is proposed. Within the assumption that the response is harmonic, any desired accuracy can be obtained with this methodology. Selected numerical examples are presented to illustrate practical applications and the relevant features of the methodology. Due to its simplicity, this methodology is particularly appropriate for performing parametric studies that require solutions for many values of normal loads.

General linearized equations of wave propagation in strained elastic solids of cylindrical shapes using a simple perturbation method

2002 ◽  
Vol 216 (6) ◽  
pp. 683-690
Author(s):  
A Sinaie ◽  
A Ziaie
Keyword(s):  
Wave Propagation ◽  
Perturbation Method ◽  
Equations Of Motion ◽  
Particle Displacement ◽  
Elastic Solids ◽  
Cylindrical Coordinates ◽  
Linearized Equations ◽  
Practical Applications ◽  
Linear Partial Differential Equations ◽  
Static Part

The equations of particle motion in an elastic isotropic stressed medium are first derived in Cartesian coordinates and then transformed into cylindrical coordinates. The three components of the equations of motion are non-linear partial differential equations and cannot be of use in practical applications. However, noting that the particle displacement is composed of a small dynamic part superimposed on a large static part, these equations are linearized via a simple perturbation method. The linearized equations are presented in closed form. They contain variables, which may be measured and experimented upon in practice, in the field of acoustoelasticity.

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