Simple Beam Example Research Articles

Extraction of Opening and Closing States of Cracked Structure using Adaptive Volterra Filter Model

Fatigue cracks often exist in structures during the service life of the structure and need to detect at its earliest stage before it leads to catastrophic failure. The fatigue breathing crack problem exhibits an instantaneous change in the stiffness of the structure due to change in the state of the cracked domain from open to close and vice versa. Therefore these fatigue cracks exhibit breathing like phenomena, hence widely referred as breathing cracks. The present work attempts to separate the opening and closing of the cracked structure from the global response using adaptive Volterra Filter Model. Adaptive Volterra Filter model is a generalization of the linear convolution and the impulse response function to nonlinear structures in discrete form. The dynamical properties of the nonlinear system in the Volterra series representation or adaptive Volterra Filter Model are completely characterized by a sequence of multi-dimensional weighting function called Volterra kernels. These Volterra kernels are the backbone of adaptive Volterra filter approach in nonlinear analysis and system identification and diverse range of techniques are reported in the literature for Volterra kernel estimation. Adaptive Volterra series based Least square is used in the present work to estimate Volterra kernels. The various states of the cracked structure are then estimated using these Volterra kernels. Numerical simulation studies are carried out on a simple beam example to demonstrate the capability of the proposed adaptive Volterra filter in extracting the opening and closing state response from the global response of the cracked structure.

Design of a d 33-mode piezocomposite electricity generating element and its application to bridge monitoring

The piezoelectric effect is used in sensing applications such as in force and displacement sensors. However, the brittleness and low performance of piezoceramic lead zirconate titanate (PZT) often impede its applicability in civil structures which are subjected to large loads. The concept of a piezocomposite electricity generating element (PCGE) has been proposed for improving the electricity generation performance and overcoming the brittleness of piezoceramic wafers. The post-curing residual stress in the PZT layer constitutes a main reason for the PCGE’s enhanced performance, and the outer epoxy-based composites protect the brittle PZT layer. A d33-mode PCGE designed for bridge monitoring application was inserted in a bridge bearing to provide a permanent and simple weigh-in-motion system. The designed PCGEs were tested through a series of tests including fatigue and dynamic tests to verify their applicability for monitoring purposes in a bridge structure. A simple beam example was presented to show the applicability of the proposed bridge bearing equipped with the PCGE for adequately measuring the traffic loads.

On dispersion relations in piezoelectric coupled-platestructures

This paper presents the dispersion relations for wave propagationin piezoelectric coupled plates based on Kirchhoff and Mindlin platetheories. Two layers of piezoelectric actuators are surface bonded on theplate and poled in the transverse direction to induce flexural action. Ahalf-cosine distribution for the electric potential in the transversedirection is assumed and the Maxwell static electricity equation is imposedfor the piezoelectric layers. This assumption is verified numerically byfinite-element analysis using a simple beam example. Based on Kirchhoff plate theory, avirtually linear relationship between the non-dimensional phase velocityand the non-dimensional wave number is obtained similar to that for pureplate structure. Based on Mindlin first-order plate theory, which accountsfor the effects of both shear and rotary inertia, the phase velocity-wavenumber relationship deviates from linearity when the wave number is notsmall relative to the thickness of the beam. The phase velocity approachesa finite value, corresponding to the velocity of the Love wave, for largewave number in contrast to that based on Kirchhoff plate theory. Thecut-off frequency is found to be a function of the ratio of the shear andflexural rigidities. The presence of the piezoelectric materials has theeffect of reducing the phase velocity which is evident from the results ofboth Kirchhoff and Mindlin theories. Comparisons of the dispersivecharacteristics based on the two-plate models for different piezoelectriclayers are also conducted by using a PZT actuator and a piezo-film sensorin the numerical simulations.

Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization

Compliant mechanisms are mechanical devices that achieve motion via elastic deformation. A new method for topological synthesis of single-piece compliant mechanisms is presented, using a “design for required deflection” approach. A simple beam example is used to illustrate this concept and to provide the motivation for a new multi-criteria approach for compliant mechanism design. This new approach handles motion and loading requirements simultaneously for a given set of input force and output deflection specifications. Both a truss ground structure and a two-dimensional continuum are used in the implementation which is illustrated with design examples.

Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities

Several important issues relevant to modeling of flexible-link robotic manipulators are addressed in this paper. First, we examine the question of which inertial nonlinearities should be included in the equations of motion for purposes of simulation. A complete model incorporating all inertial terms that couple rigid-body and elastic motions is presented along with a rational scheme for classifying them. Second, the issue of geometric nonlinearities is discussed. These are terms whose origin is the geometrically nonlinear theory of elasticity, as well as the terms arising from the interbody coupling due to the elastic deformation at the link tip. Accordingly, a general way of incorporating the well-known geometric stiffening effect is presented along with several schemes for treating the elastic kinematics at the joint interconnections. In addition, the question of basis function selection for spatial discretization of the elastic displacements is also addressed. The finite element method and an eigenfunction expansion techniques are presented and compared. All issues are examined numerically in the context of a simple beam example and the Space Shuttle Remote Manipulator System. Unlike a single-link system, the results for the latter show that all terms are required for accurate simulation of faster maneuvers. Hence, the conclusions of the paper are contrary to some of the previous findings on the validity of various models for dynamics simulation of flexible-body systems.

Combining global and local approximations

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.

Algorithm for modification of parameters in vibrating systems

Concluding Remarks A global-local approximation based on a linear approximation to a scaling factor has been presented. The approximation permits us to use a global approximation based on a simple model of our problem to extend the range of usefulness of derivative-based approximations to a more refined model. The method was demonstrated for a simple beam example with a crude and more refined finite element model.

Derivation of geometric stiffness and mass matrices for finite element hybrid models

An unifying approach in deriving the geometric stiffness and mass matrices for finite element hybrid models is presented. The variational formulation is based on a modified Reissner Principle. Numerical verification is illustrated through a simple beam example. The element interchangeability in the finite element method and an alternative way of deriving the loading vector for the hybrid stress model are also discussed.