Elliptic integral solution of the extensible elastica with a variable length under a concentrated force

2011 ◽  
Vol 222 (3-4) ◽  
pp. 209-223 ◽  
Author(s):  
Alexander Humer
Keyword(s):  
Elliptic Integral ◽  
Integral Solution ◽  
Variable Length ◽  
Concentrated Force

scholarly journals Natural Frequency Analysis of Two Nonlinear Panels Coupled with a Cavity Using the Approximate Elliptic Integral Solution and the Method of Harmonic Residual Minimization

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Y. Y. Lee
Keyword(s):  
Natural Frequency ◽  
Frequency Analysis ◽  
Elliptic Integral ◽  
Integral Solution ◽  
Acoustic Problem ◽  
Nonlinear Structural ◽  
Homogeneous Wave ◽  
Flexible Panels ◽  
Natural Frequency Analysis ◽  
Residual Minimization

The nonlinear structural acoustic problem considered in this study is the nonlinear natural frequency analysis of flexible double panels using the elliptic integral solution method. There are very limited studies for this nonlinear structural-acoustic problem, although many nonlinear plate or linear double panel problems have been tackled and solved. A multistructural/acoustic modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibrations of the flexible panels and acoustic pressure induced within the air gap. One is the von Karman’s plate equation and the other is the homogeneous wave equation. The results obtained from the proposed method approach are verified with those from a numerical method. The effects of vibration amplitude, gap width, aspect ratio, the numbers of acoustic modes and harmonic terms, and so forth on the resonant frequencies of the in-phase and out of phase modes are examined.

scholarly journals Predicting Nonlinear Stiffness, Motion Range, and Load-Bearing Capability of Leaf-Type Isosceles-Trapezoidal Flexural Pivot Using Comprehensive Elliptic Integral Solution

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Aimei Zhang ◽  
Yanjie Gou ◽  
Xihui Yang
Keyword(s):  
Elliptic Integral ◽  
Integral Solution ◽  
Leaf Spring ◽  
Nonlinear Stiffness ◽  
Load Bearing ◽  
Large Rotation ◽  
Leaf Type ◽  
Proposed Model ◽  
Motion Range ◽  
Stiffness Characteristics

A leaf-type isosceles-trapezoidal flexural (LITF) pivot consists of two leaf springs that are situated in the same plane and intersect at a virtual center of motion outside the pivot. The LITF pivot offers many advantages, including large rotation range and monolithic structure. Each leaf spring of a LITF pivot subject to end loads is deflected into an S-shaped configuration carrying one or two inflection points, which is quite difficult to model. The kinetostatic characteristics of the LITF pivot are precisely modeled using the comprehensive elliptic integral solution for the large-deflection problem derived in our previous work, and the strength-checking method is further presented. Two cases are employed to verify the accuracy of the model. The deflected shapes and nonlinear stiffness characteristics within the range of the yield strength are discussed. The load-bearing capability and motion range of the pivot are proposed. The nonlinear finite element results validate the effectiveness and accuracy of the proposed model for LITF pivots.

Concentrated force in a cubic anisotropic solid: a single integral solution

1973 ◽  
Vol 44 (1) ◽  
pp. 7-9 ◽  
Author(s):  
John W. Goodman ◽  
Robert A. Masumura ◽  
George Sines
Keyword(s):  
Integral Solution ◽  
Concentrated Force ◽  
Anisotropic Solid ◽  
Single Integral

An Elliptic Integral Solution to the Multiple Inflections Large Deflection Beams in Compliant Mechanisms

2014 ◽  
Vol 971-973 ◽  
pp. 349-352 ◽  
Author(s):  
Jiang Yong Song
Keyword(s):  
Euler Equations ◽  
Inflection Point ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Accurate Method ◽  
Integral Solution ◽  
Large Deflections ◽  
Cantilever Beams ◽  
Inflection Points

In this paper, a solution based on the elliptic integrals is proposed for solving multiples inflection points large deflection. Application of the Bernoulli Euler equations of compliant mechanisms with large deflection equation of beam is obtained ,there is no inflection point and inflection points in two cases respectively. The elliptic integral solution which is the most accurate method at present for analyzing large deflections of cantilever beams in compliant mechanisms.

Design and Analysis of a Monolithic Compliant Dwell Mechanism

2019 ◽  
Author(s):  
Hongkuan Lin ◽  
Ayse Tekes
Keyword(s):  
Elliptic Integral ◽  
Integral Solution ◽  
Experimental Setup ◽  
Maximum Displacement ◽  
Critical Buckling Load ◽  
Lumped Model ◽  
Single Piece ◽  
Buckling Beam ◽  
Full Rotation ◽  
Polynomial Formulation

Abstract A novel, monolithic flexible translational dwell mechanism that is driven by a DC motor is designed in this study. Mechanism consists of an initially straight, large deflecting pinned-pinned buckling beam as a coupler, semi-circular compliant arc as a follower, rigid crank and a slider. An approximate dwell motion is created since the slider doesn’t move until the critical buckling load of the flexible coupler is achieved and then snaps to its maximum displacement by pushing the follower arc beam. As the maximum bending on the arc is reached, slider moves back to its initial as the crank follows a full rotation. Dynamical lumped model of the mechanism is obtained by integrating first and second kind of elliptic integral solution of pinned-pinned beam with polynomial formulation method. Optimal dimensions and geometric positions are explored using commercially available FEA program (ADAMs). Mechanism is built by 3D printing the entire mechanism as a single piece using polyethylene terephthalate glycol (PETG). Mathematical model of the mechanism is validated through experimental setup and ADAMs simulations.

A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Cantilever Beams in Compliant Mechanisms

2012 ◽  
Author(s):  
Aimei Zhang ◽  
Guimin Chen
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Accurate Method ◽  
Integral Solution ◽  
Large Deflections ◽  
Cantilever Beams ◽  
Complex Modes ◽  
Inflection Points ◽  
Moment Load

The elliptic integral solution is often considered as the most accurate method for analyzing large deflections of cantilever beams in compliant mechanisms. In this paper, by explicitly including the number of inflection points (m) and the sign of the end-moment load (SM) in the derivation, a comprehensive solution based on the elliptic integrals is proposed for solving the large deflection problems. The comprehensive solution is capable of solving large deflections of cantilever beams subject to any kind of load cases and of any kind of deflected modes. A few deflected configurations of complex modes solved by the comprehensive solution are presented and discussed. The use of the comprehensive solution in analyzing compliant mechanisms is also demonstrated by a few case studies.

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