scholarly journals Multibody Dynamics of Nonsymmetric Planar 3PRR Parallel Manipulator with Fully Flexible Links

2020 ◽  
Vol 10 (14) ◽  
pp. 4816 ◽  
Author(s):  
Abdur Rosyid ◽  
Bashar El-Khasawneh
Keyword(s):  
Boundary Conditions ◽  
Multibody Dynamics ◽  
Parallel Manipulator ◽  
Flexible Multibody Dynamics ◽  
Elastic Displacement ◽  
Bernoulli Beam ◽  
Finite Element Approximations ◽  
Different Types ◽  
Floating Frame ◽  
Euler Bernoulli Beam

This paper presents the implementation of the floating frame of reference formulation to model the flexible multibody dynamics of a nonsymmetric planar 3PRR parallel manipulator. All of the links, including the moving platform, of the manipulator under study are assumed flexible whereas the joints are assumed rigid. Using the Euler-Bernoulli beam, the flexibility of the links is modeled by using the Rayleigh-Ritz and finite element approximations. In both approximations, fixed-free boundary conditions are applied to the elastic coordinates of the links. These boundary conditions enable the evaluation of the elastic displacement at a link tip coincident with the end-effector of the manipulator which is of interest in the high precision robotics application. Both the approximations were compared by applying two different types of loads to the manipulator. It is shown that the elastic displacements obtained by using both the approximations have an agreement with a slight difference in the magnitude. In addition, the sensitivity analysis shows that the rigidity of the manipulator is much affected by the in-plane depth of the manipulator links’ cross section.

Exact solutions for the bending of Timoshenko beams using Eringen’s two-phase nonlocal model

2018 ◽  
Vol 24 (3) ◽  
pp. 559-572 ◽  
Author(s):  
Yuanbin Wang ◽  
Kai Huang ◽  
Xiaowu Zhu ◽  
Zhimei Lou
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Model ◽  
Bernoulli Beam ◽  
Two Phase ◽  
Differential Model ◽  
Euler Bernoulli Beam

Eringen’s nonlocal differential model has been widely used in the literature to predict the size effect in nanostructures. However, this model often gives rise to paradoxes, such as the cantilever beam under end-point loading. Recent studies of the nonlocal integral models based on Euler–Bernoulli beam theory overcome the aforementioned inconsistency. In this paper, we carry out an analytical study of the bending problem based on Eringen’s two-phase nonlocal model and Timoshenko beam theory, which accounts for a better representation of the bending behavior of short, stubby nanobeams where the nonlocal effect and transverse shear deformation are significant. The governing equations are established by the principal of virtual work, which turns out to be a system of integro-differential equations. With the help of a reduction method, the complicated system is reduced to a system of differential equations with mixed boundary conditions. After some detailed calculations, exact analytical solutions are obtained explicitly for four types of boundary conditions. Asymptotic analysis of the exact solutions reveals clearly that the nonlocal parameter has the effect of increasing the deflections. In addition, as compared with nonlocal Euler–Bernoulli beam, the shear effect is evident, and an additional scale effect is captured, indicating the importance of applying higher-order beam theories in the analysis of nanostructures.

An Experimental Approach to the Design of PVDF Modal Sensors

2001 ◽  
Author(s):  
Daniel Cuhat ◽  
Patricia Davies
Keyword(s):  
Boundary Conditions ◽  
Experimental Approach ◽  
Experimental Methodology ◽  
Laser Doppler Velocimeter ◽  
Piezoelectric Film ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Arbitrary Boundary ◽  
Classical Boundary ◽  
Euler Bernoulli Beam

Abstract The principle of modal sensing is based on the use of a shaped PVDF piezoelectric film measuring strains on the surface of a bending beam and acting as a modal filter. So far, the use of this type of sensors has remained confined to studies involving uniform structures with classical boundary conditions. The goal of this paper is to present an experimental methodology for the design of a shaped modal sensor applicable to an non-uniform Euler-Bernoulli beam with arbitrary boundary conditions. This approach is illustrated with test data collected on a cantilever beam structure with a laser Doppler velocimeter.

Influence of Axial Force on the Vibration of Euler-Bernoulli Beam Structures Solved by DQEM Using EDQ

2006 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Axial Force ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Bernoulli Beam ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Euler Bernoulli Beam ◽  
Element Boundary

The influence of axial force on the vibration of Euler-Bernoulli beam structures is analyzed by differential quadrature element method (DQEM) using extended differential quadrature (EDQ). The DQEM uses the differential quadrature to discretize the governing differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

Influence of Axially Distributed Force on the Vibration of Euler-Bernoulli Beam Structures Solved by DQEM Using EDQ

2007 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Bernoulli Beam ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Euler Bernoulli Beam ◽  
Element Boundary

The influence of axially distributed force on the vibration of Euler-Bernoulli beam structures is analyzed by differential quadrature element method (DQEM) using extended differential quadrature (EDQ). The DQEM uses the differential quadrature to discretize the governing differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

scholarly journals The Vibration of a Beam under a Traversing Load

2021 ◽  
Author(s):  
Kan-Chen Jane Wu
Keyword(s):  
Boundary Conditions ◽  
Constant Velocity ◽  
Equation Of Motion ◽  
Linear Strain ◽  
Bernoulli Beam ◽  
Simply Supported ◽  
Runge Kutta Method ◽  
Extended Hamilton’S Principle ◽  
Gyroscopic Forces ◽  
Euler Bernoulli Beam

The objective of this study is to investigate the response of an Euler-Bernoulli beam under a force or mass traversing with constant velocity. Simply-supported and clamped-clamped boundary conditions are considered. The linear strain-displacement scenario is applied to both boundary conditions, while the von Kármán nonlinear scenario is applied only to the former boundary condition. The governing equation of motion is derived via the extended Hamilton's principle. Simulations are performed with the fourth-order Runge-Kutta method via Matlab software. The equation of motion is first validated and then used to investigate the effects of the beam second moment of area, the magnitude of the traversing velocity, and centrifugal and gyroscopic forces.

scholarly journals The Exact Frequency Equations for the Euler-Bernoulli Beam Subject to Boundary Damping

2020 ◽  
Vol 25 (2) ◽  
pp. 183-189
Author(s):  
Angela Biselli ◽  
Matthew P. Coleman
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Methods ◽  
Bernoulli Beam ◽  
Boundary Damping ◽  
Numerical Examples ◽  
Wave Numbers ◽  
Complex Wave ◽  
Energy Conserving ◽  
Vibrating Beams ◽  
Euler Bernoulli Beam

The Euler-Bernoulli (E-B) beam is the most commonly utilized model in the study of vibrating beams. The exact frequency equations for this problem, subject to energy-conserving boundary conditions, are well-known; however, the corresponding dissipative problem has been solved only approximately, via asymptotic methods. These methods, of course, are not accurate when looking at the low end of the spectrum. Here, we solve for the exact frequency equations for the E-B beam subject to boundary damping. Numerous numerical examples are provided, showing plots of both the complex wave numbers and the exponential damping rates for the first five frequencies in each case. Some of these results are surprising.

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