A general higher-order shell theory based on the analytical dynamics of constrained continuum systems

This paper presents new formulations on the higher order motion energies that are applied in the dynamic study of multibody mechanical systems in keeping with the researches of the main author. The analysis performed in this paper highlights the importance of motion energies of higher order in the study of dynamic behavior of fast moving mechanical systems, as well as in transient phase of motion. In these situations, are developed higher order time variations of the linear and angular accelerations. As a result, in the final part of this paper is presented an application that emphasizes this essential dynamic aspect regarding the higher order acceleration energies.

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A shell theory with scale effects and higher order gradients

International Journal of Solids and Structures ◽

10.1016/j.ijsolstr.2013.03.031 ◽

2013 ◽

Vol 50 (14-15) ◽

pp. 2271-2280 ◽

Cited By ~ 2

Author(s):

C. Sansour ◽

S. Skatulla ◽

M. Hjiaj

Keyword(s):

Shell Theory ◽

Scale Effects ◽

Higher Order

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Formulation of a Non-linear Higher-Order Shell Theory Using the Convective Description

PAMM ◽

10.1002/pamm.200310239 ◽

2003 ◽

Vol 2 (1) ◽

pp. 515-516

Author(s):

H. Sparr ◽

V. Ulbricht

Keyword(s):

Shell Theory ◽

Higher Order ◽

Non Linear

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A New Approach in Analytical Dynamics of Mechanical Systems

Symmetry ◽

10.3390/sym12010095 ◽

2020 ◽

Vol 12 (1) ◽

pp. 95 ◽

Cited By ~ 6

Author(s):

Iuliu Negrean ◽

Adina-Veronica Crișan ◽

Sorin Vlase

Keyword(s):

Fast Moving ◽

Mechanical Systems ◽

Higher Order ◽

Matrix Form ◽

Final Part ◽

Analytical Dynamics ◽

Research Papers ◽

New Approach ◽

D’Alembert Principle ◽

Matrix Exponentials

This paper presents a new approach to the advanced dynamics of mechanical systems. It is known that in the movements corresponding to some mechanical systems (e.g., robots), accelerations of higher order are developed. Higher-order accelerations are an integral part of higher-order acceleration energies. Unlike other research papers devoted to these advanced notions, the main purpose of the paper is to present, in a matrix form, the defining expressions for the acceleration energies of a higher order. Following the differential principle in generalized form (a generalization of the Lagrange–D’Alembert principle), the equations of the dynamics of fast-moving systems include, instead of kinetic energies, the acceleration energies of higher-order. To establish the equations which characterize both the energies of accelerations and the advanced dynamics, the following input parameters are considered: matrix exponentials and higher-order differential matrices. An application of a 5 d.o.f robot structure is presented in the final part of the paper. This is used to illustrate the validity of the presented mathematical formulations.

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Efficient higher-order shell theory for laminated composites

Composite Structures ◽

10.1016/0263-8223(95)00145-x ◽

1996 ◽

Vol 34 (2) ◽

pp. 197-212 ◽

Cited By ~ 46

Author(s):

Maenghyo Cho ◽

Ki-Ook Kim ◽

Min-Ho Kim

Keyword(s):

Shell Theory ◽

Laminated Composites ◽

Higher Order

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New Formulations on Motion Equations in Analytical Dynamics

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.823.49 ◽

2016 ◽

Vol 823 ◽

pp. 49-54 ◽

Cited By ~ 1

Author(s):

Iuliu Negrean ◽

Kalman Kacso ◽

Claudiu Schonstein ◽

Adina Duca ◽

Florina Rusu ◽

...

Keyword(s):

Differential Equations ◽

Multibody Systems ◽

Equations Of Motion ◽

Mechanical Systems ◽

Higher Order ◽

Analytical Dynamics ◽

Lagrange Principle ◽

Motion Equations ◽

Differential Motion

Using the main author's researches on the energies of acceleration and higher order equations of motion, this paper is devoted to new formulations in analytical dynamics of mechanical multibody systems (MBS). Integral parts of these systems are the mechanical robot structures, serial, parallel or mobile on which an application will be presented in order to highlight the importance of the differential motion equations in dynamics behavior. When the components of multibody mechanical systems or in its entirety presents rapid movements or is in transitory motion, are developed higher order variations in respect to time of linear and angular accelerations. According to research of the main author, they are integrated into higher order energies and these in differential equations of motion in higher order, which will lead to variations in time of generalized forces which dominate these types of mechanical systems. The establishing of these differential equations of motion, it is based on a generalization of a principle of analytical differential mechanics, known as the D`Alembert – Lagrange Principle.

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