Mohammad H. Dado

A comprehensive crack identification algorithm for beams under different end conditions

Abstract This paper presents a direct mathematical model for the prediction and identification of transverse cracks in beams with different end conditions. The input data for this algorithm are the natural frequencies of the first two bending modes of vibrations of the damaged beam. Using these two input values, and with the availability of accurate frequency measurements and ideal end conditions, the crack location and depth are identified in terms of known beam parameters. Four different end conditions are considered: pinned-pinned, clamped-free, clamped-pinned and clamped-clamped. This mathematical model is based on the assumption that the beam is an Euler-Bernoulli beam and considers open, straight, and transverse cracks in beams with rectangular cross-sections. Although this method assumes high accuracy in measurements and ideal end conditions, requirements that are not always guaranteed in practice, the results obtained help as an initial estimate of the severity and proper location of a crack.

Variable parametric pseudo-rigid-body model for large-deflection beams with end loads

Abstract This paper presents a variable parametric pseudo-rigid-body model for large-deflection beams with end loads. The values of the applied load ( P ) and joint stiffness of pseudo-rigid-body model ( k ) are expressed in terms of its kinematic parameters: the characteristic length ( γ ) and the “pseudo-rigid-body angle” (Θ). The expressions cover practical range of applications using a single equation for each variable. The accuracy of the expressions is excellent with correlation coefficients of (0.999) and (0.995). The accuracy of the end deflections generated by these expressions is shown to be much more greater than using the constant values for ( γ ) and ( k ). The new model is used for the analysis of two compliant mechanisms with different modes of analysis. The advantages of the new model and how it blends itself very smoothly in the analysis algorithm is illustrated through these examples.

PERFORMANCE SIMULATION OF A FOUR-STROKE ENGINE WITH VARIABLE STROKE-LENGTH AND COMPRESSION RATIO

The engine consists of a coupled four-bar, slider-crank and inverted slider-crank mechanisms. The variations in stroke length and compression ratio are obtained through varying the location of the pivot of the four-bar rocker arm. The engine power characteristics are based on the power cycle of the piston inside the cylinder. Several pivot locations are considered giving a range of stroke lengths and corresponding compression ratios. A simulation model is developed and verified with experimental results from the literature for both constant and variable-stroke engines. The simulation results clearly indicate the advantages and utility of variable-stroke engines in fuel-economy issues.

Crack parameter estimation in structures using finite element modeling

This paper addresses the problem of linear crack quantification, crack depth estimation and localization, in structures. An optimization technique based on a finite element model for cracked structural elements is employed in the estimation of crack parameters for beam, truss and two-dimensional frame structures. The modal data for the cracked structures are obtained by solving the corresponding eigenvalue problem. The error in the modal data is simulated by an additive noise that follows the normal distribution. The simulated reduced modal data is expanded using the eigenvector projection method. Numerical examples showed that this technique gives good results for cracks with high depth ratio. The accuracy of the estimated crack parameters depends on (1) the number of modes used, (2) the error level in the cracked structure modal data and (3) the number of measured degrees of freedom in the case of reduced modal data.

Dynamic simulation model for mixed-loop planar robots with flexible joint drives

A dynamic simulation model for mixed-loop planar robots with flexible joint drive and servo-motor control is developed. The motion of the links is coupled with the deflection of the drive shaft at the joints. The virtual work method is used for the derivation of the mathematical model. The drive signal at the motor is based on the error between the desired and actual motions using proper position and velocity gains. Different motion programs are considered in the simulation for the time histories of the angular displacements and velocities of the links and motors. The driving torques and the total error produced at the end-effector are computed. The simulation results for a five-link, three degrees of freedom manipulator show that the model presented is capable of simulating the coupling effect of joint flexibility and rigid body motion for planar robots.

Modeling and verification of the kinematics of passenger falls on escalators

Passenger falls on escalators are one of the major causes of accidents. Falls can either be passenger caused or escalator caused. Unplanned stops of escalators can cause passenger falls and consequential injury in the form of cuts, bruises, finger entrapment and, in certain cases, crushing leading to suffocation. In order to better understand the kinematics of passenger falls on escalators, MATLAB-based software has been developed. It simulates the effect of an acceleration signal on a rectangular block. The most important parameter of the rectangular solid block is the center of gravity ratio, which is defined relative to the axis around which the fall can take place. The model is then practically verified by subjecting an actual wooden rectangular block of a specific center of gravity ratio to an acceleration signal and taking a video of the fall. The acceleration signal is measured and fed into the model. The video is analyzed frame by frame in order to use time-lapse photography to compare the falling block with the output of the model. Good agreement has been achieved. Data on the human body is analyzed in order to arrive at an appropriate value of the center of gravity ratio for the human body. This value is further adjusted to account for variability in the human body, and expected human behavior, up to a value of 10. This result is then used to arrive at a limit on the maximum value of acceleration form the escalator braking system in order to prevent escalator-initiated passenger falls. Applying knowledge of the variability of the expected maximum acceleration from successive escalator stops is then applied to arrive at the final value of 1.16 m·s–2 as the recommended value to be used as a design and acceptance value for escalator braking system performance in order to prevent passenger falls.

An Accurate Numerical Scheme for Large Deflection Analysis of Non-Prismatic Inextensible Slender Beams Subjected to General Loading and Boundary Conditions

This paper studies the large deflection behavior of prismatic and non-prismatic inextensible beams subjected to various types of loading and boundary conditions. The formulation is based on representing the angle of rotation by a power series and substituting it into the derived governing nonlinear differential equation. The coefficients of the power series are obtained by minimizing the integral of the residual error over the deflected beam axis. Several numerical examples are presented covering prismatic and non-prismatic beams subjected to uniform and non-uniform distributed loads. A large displacement finite element analysis using the package MSC/NASTRAN was used to check the accuracy and efficiency of the present numerical method. Excellent agreement was observed between the two numerical schemes.