A Pseudo-Static Model for Dynamic Analysis on Frequency Domain of Distributed Compliant Mechanisms

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Mingxiang Ling ◽  
Larry L. Howell ◽  
Junyi Cao ◽  
Zhou Jiang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Modeling ◽  
Stiffness Matrix ◽  
Compliant Mechanisms ◽  
Dynamic Stiffness ◽  
Elastic Beam ◽  
Static Model ◽  
Flexible Beam ◽  
Element Analysis ◽  
Static Modeling

This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way based on D'alembert's principle. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo-static model. The superiority of the proposed method is that when it is used for the dynamic modeling of compliant mechanisms, the traditional dynamic modeling procedures, such as calculation of the elastic and kinetic energies as well as using Lagrange's equation, are avoided and the dynamic modeling is converted to a statics-similar problem. Comparison of the proposed method with an elastic-beam-based model in previous literature and finite element analysis for an exemplary XY precision positioning stage reveals its high accuracy and easy operation.

Frequency domain-based analysis of floor vibrations using the dynamic stiffness matrix method

2018 ◽  
Vol 25 (4) ◽  
pp. 763-776 ◽  
Author(s):  
Tong Guo ◽  
Zhiliang Cao ◽  
Zhiqiang Zhang ◽  
Aiqun Li
Keyword(s):  
Finite Element ◽  
Frequency Domain ◽  
Stiffness Matrix ◽  
Road Traffic ◽  
Dynamic Stiffness ◽  
Design Stage ◽  
Element Analysis ◽  
Frequency Spectra ◽  
Dynamic Stiffness Matrix ◽  
Floor Vibrations

Buildings may experience excessive floor vibrations due to inner excitations such as walking people and running machines, or ground motion caused by the road traffic. Therefore, it is often necessary to evaluate the vibration level at the design stage. In this paper, a frequency domain-based model for predicting vertical vibrations of a building floor is provided, where the floor is simplified as a rectangular plate stiffened by beams in two orthogonal directions, while vertical motion and rotation of the slab–column joints are viewed as the unknown degrees of freedom. The dynamic stiffness matrix of the whole structure is obtained from those of the floor and column elements. To validate the proposed solution, a five-story building was analyzed, and frequency spectra were compared with those from the finite element method. Besides, a prototype building was analyzed and validated based on field measured data. It is found that the proposed solution could predict vibration responses with satisfactory accuracy, and is more computationally efficient than finite element analysis.

Dynamic Analysis of Rotating Beams with Nonuniform Cross Sections Using the Dynamic Stiffness Method

2001 ◽  
Vol 123 (4) ◽  
pp. 536-539 ◽  
Author(s):  
K. J. Huang ◽  
T. S. Liu
Keyword(s):  
Dynamic Analysis ◽  
Cross Sections ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Equation Of Motion ◽  
The Finite Element Method ◽  
Rotating Beam ◽  
Rotating Beams ◽  
Stiffness Method ◽  
Dynamic Stiffness Method

This study develops dynamic analysis based on the dynamic stiffness method for a rotating beam of nonuniform cross-section. To deal with nonuniform beams, coefficients related to material and geometric properties in the equation of motion are expressed in a polynomial form. A dynamic stiffness matrix is accordingly formulated in terms of power series. The dynamic response of the rotating beam is calculated by performing modal analysis. It is demonstrated that the present method provides an alternative to the finite element method in dealing with nonuniform rotating beams.

Pseudo-Rigid-Body Dynamic Models for Design of Compliant Members

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Vedant ◽  
James T. Allison
Keyword(s):  
Rigid Body ◽  
Dynamic Models ◽  
Compliant Mechanisms ◽  
Flexible Beam ◽  
Dynamical Response ◽  
Structural Members ◽  
Element Analysis ◽  
Rigid Body Dynamic ◽  
Revolute Joints ◽  
Body Dynamic

Abstract Movement in compliant mechanisms is achieved, at least in part, via deformable flexible members, rather than using articulating joints. These flexible members are traditionally modeled using finite element analysis (FEA)-based models. In this article, an alternative strategy for modeling compliant cantilever beams is developed with the objectives of reducing computational expense and providing accuracy with respect to design optimization solutions. The method involves approximating the response of a flexible beam with an n-link/m-joint pseudo-rigid-body dynamic model (PRBDM). Traditionally, static pseudo-rigid-body models (PRBMs) have shown an approximation of compliant elements using two or three revolute joints (2R/3R-PRBM). In this study, a more general nR-PRBDM model is developed. The first n resonant frequencies of the PRBDM are matched to exact or FEA solutions to approximate the response of the compliant system and compared with existing PRBMs. PRBDMs can be used for co-design studies of flexible structural members and are capable of modeling large deflections of compliant elements. We demonstrate PRBDMs that show dynamically accurate response for a random geometry cantilever beam by matching the steady-state and frequency response, with dynamical response accuracies up to 10% using a 5R-PRBDM.

Dynamic Parameter Identification of Subject-Specific Body Segment Parameters Using Robotics Formalism: Case Study Head Complex

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Miguel Díaz-Rodríguez ◽  
Angel Valera ◽  
Alvaro Page ◽  
Antonio Besa ◽  
Vicente Mata
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Modeling ◽  
Static Model ◽  
Crash Test ◽  
Entire Body ◽  
Body Segment ◽  
Biomechanical Models ◽  
Subject Specific ◽  
Inertia Parameters

Accurate knowledge of body segment inertia parameters (BSIP) improves the assessment of dynamic analysis based on biomechanical models, which is of paramount importance in fields such as sport activities or impact crash test. Early approaches for BSIP identification rely on the experiments conducted on cadavers or through imaging techniques conducted on living subjects. Recent approaches for BSIP identification rely on inverse dynamic modeling. However, most of the approaches are focused on the entire body, and verification of BSIP for dynamic analysis for distal segment or chain of segments, which has proven to be of significant importance in impact test studies, is rarely established. Previous studies have suggested that BSIP should be obtained by using subject-specific identification techniques. To this end, our paper develops a novel approach for estimating subject-specific BSIP based on static and dynamics identification models (SIM, DIM). We test the validity of SIM and DIM by comparing the results using parameters obtained from a regression model proposed by De Leva (1996, “Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters,” J. Biomech., 29(9), pp. 1223–1230). Both SIM and DIM are developed considering robotics formalism. First, the static model allows the mass and center of gravity (COG) to be estimated. Second, the results from the static model are included in the dynamics equation allowing us to estimate the moment of inertia (MOI). As a case study, we applied the approach to evaluate the dynamics modeling of the head complex. Findings provide some insight into the validity not only of the proposed method but also of the application proposed by De Leva (1996, “Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters,” J. Biomech., 29(9), pp. 1223–1230) for dynamic modeling of body segments.

Dynamic Modeling of Compliant Mechanisms Based on 2R Pseudo-Rigid-Body Model

2012 ◽  
Vol 163 ◽  
pp. 277-280 ◽  
Author(s):  
Wen Jing Wang ◽  
Shu Sheng Bi ◽  
Li Ge Zhang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Large Deflections ◽  
Flexible Link ◽  
Flexible Links ◽  
Body Model ◽  
Rigid Body Model ◽  
New Type

Compliant mechanism is a kind of new type mechanism and its analysis is very complex because flexible links often under large deflections which introduce geometry nonlinearities. A new model (2R PRBM) can simulate accurately both the deflection path and angle of the flexible link. A new dynamic model of compliant mechanism is developed using the 2R PRBM. The dynamic equation of planar compliant mechanism is derived. The dynamic analysis on the natural frequency of compliant mechanism is obtained in the example of a planar compliant parallel-guiding mechanism. The numerical results show the advantage of the proposed method for the dynamic analysis of compliant mechanisms.

Optimal Design for Damper of Long Blade in Steam Turbine Based on Dynamic Analysis

2007 ◽  
Author(s):  
Yonghui Xie ◽  
Di Zhang
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Steam Turbine ◽  
Stiffness Matrix ◽  
Harmonic Wave ◽  
Mass Matrix ◽  
Beam Element ◽  
Friction Damper ◽  
Element Analysis ◽  
Damping Matrix

Adding damped structure can decrease dynamic stress of blade and avoid blade fatigue failure from forced vibration. Based on the structural feature of long blade with friction damper, the numerical model for dynamic analysis of damped blade in steam turbine has been developed. The blade was described by twisted beam element, the usual space beam element was adopted to analyze the frame of damper, and the slip motion between rubbing surface was modeled by a damping connector. The following matrices which are necessary for finite element analysis were obtained: the stiffness matrix, mass matrix and damping matrix of finite element for blade and damper, the stiffness matrix and damping matrix of damping connector. Then the gross finite element motion equation of the blade was got. Meanwhile, harmonic wave propagation method was adopted to improve calculation efficiency. The comparison of calculation results and experimental data of a 360mm blade shows good agreement. The dynamic characteristic of a last stage long blade in steam turbine with damper was analyzed in detail, its responses with different thickness shroud and gap between shrouds were investigated in detail too, then the optimal structure of damped shroud was obtained, the comparison for response between damped blade and freestanding blade shows the maximum response of blade with optimal damper is 42.4% of that of freestanding blade. At last, a tie wire was added to the damped blade, numerical result shows it can decrease blade response further.

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