Analysis of Maximum Elasto-Plastic Response of Multi-Degree-of-Freedom Oscillators Based on a Modal Combination of Equivalently Linearized Response of Each Mode

Volume 8: Seismic Engineering ◽

10.1115/pvp2016-63865 ◽

2016 ◽

Author(s):

Tomoyo Taniguchi ◽

Hiroki Nishiraku ◽

Yusuke Ono

Keyword(s):

Analytical Method ◽

Degree Of Freedom ◽

Base Excitation ◽

Plastic Response ◽

Single Degree Of Freedom ◽

Single Degree ◽

Linearized System ◽

Plastic Displacement ◽

Relationship Of ◽

Force Displacement

This study develops a new analytical method for evaluating maximum elasto-plastic displacement of multi-degree-of-freedom (MDOF) oscillators under the action of base excitation based on a modal combination. The essence is that modal frequencies, shapes and damping during yielding of any member of the MDOF oscillators are readily specified by the modal analysis with the secondary stiffness of the members being yielded. In addition, assuming that a bilinear hysteresis may describe the force-displacement relationship of each mode, an equivalently linearized system consisting of a single-degree-of-freedom (SDOF) oscillator is introduced to approximate maximum elsato-plastic displacement of each mode. Employing the SRSS-rule, the maximum elasto-plastic displacement of the MDOF oscillator subjected to Kobe-NS accelerogram is calculated and compared with that computed by the commercial software. Applicability of the proposed method to evaluating maximum elasto-plastic displacement of the MDOF oscillator is thoroughly discussed.

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An Algorithm for Analytically Calculating the Positions of the Secondary Instant Centers of Indeterminate Linkages

Journal of Mechanical Design ◽

10.1115/1.2839008 ◽

2008 ◽

Vol 130 (4) ◽

Cited By ~ 15

Author(s):

Raffaele Di Gregorio

Keyword(s):

Analytical Method ◽

Direct Application ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Planar Mechanism ◽

Single Degree ◽

Planar Linkages

In a planar mechanism, the position of the instant centers reveals important pieces of information about its static and kinematic behaviors. Such pieces of information are useful for designing the mechanism. Unfortunately, when the mechanism architecture becomes complex, common methods to locate the instant centers, which are based on the direct application of the Aronold–Kennedy theorem, fail. Indeterminate linkages are single-degree-of-freedom (single-dof) planar linkages where the secondary instant centers cannot be found by direct application of the Aronold–Kennedy theorem. This paper presents an analytical method to locate all the instant centers of any single-dof planar mechanism, which, in particular, succeeds in determining the instant centers of indeterminate linkages. In order to illustrate the proposed method, it will be applied to locate the secondary instant centers of the double butterfly linkage and of the single flier eight-bar linkage.

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Analytical method for the singularity analysis and exhaustive enumeration of the singularity conditions in single-degree-of-freedom spherical mechanisms

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406212469328 ◽

2012 ◽

Vol 227 (8) ◽

pp. 1830-1840 ◽

Cited By ~ 4

Author(s):

Raffaele Di Gregorio

Keyword(s):

Analytical Method ◽

Singularity Analysis ◽

Degree Of Freedom ◽

Systems Of Equations ◽

Single Degree Of Freedom ◽

Planar Mechanism ◽

Single Degree ◽

Geometric Conditions ◽

Spherical Mechanisms ◽

Spherical Mechanism

In spherical-mechanism kinematics, instantaneous pole axes play the same role as, in planar-mechanism kinematics, instant centres. Their locations only depend on the mechanism configuration when spherical single-degree-of-freedom mechanisms are considered. Such a property makes them a tool to visualize and/or to analyse the instantaneous kinematics of those mechanisms. This article addresses the singularity analysis of single-degree-of-freedom spherical mechanisms by exploiting the properties of instantaneous pole axes. An exhaustive enumeration of the geometric conditions which occur for all the singularity types is given, and a general analytical method based on this enumeration is proposed for implementing the singularity analysis. The proposed analytical method can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

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