Cantilever Beam

In engineering, some problems can be managed with simple hand calculations and manipulations. They are many engineering problems with various complexity levels. Engineering simulation software contain many tools adapted to specific problems. In fact, the classical approach is well adapted when the problem involves a single element, few independent variables or limited degrees of freedom.
Problems involving several data with complex dynamic situations with many independent or dependent variables interacting with each other are difficult to handle using the classical approach and the generated results may also be far from the expected ones when performed using the classical problem handling methods. At a small scale, the results could be sufficiently acceptable when solving for specific locations on a beam or a pipe. That is the main reason why it is preferable to perform discretization on the analyzed model to identify and obtain the closest or most accurate results to the actual solutions. Performing discretization divides the model into many segments, increasing the degrees of freedom.  Using the software to solve for each element requires the use of engineering skills to choose the necessary inputs, apply the acting forces and defining the existing boundary conditions if any. The end result can be used as a tool to estimate or predict similar situations under given conditions.
In this report, Matlab software will be used to write interpolation and regression polynomials for single variable or multivariable data. The frequency response and time response of a cantilever and supported beams are estimated when simulated in various conditions. Data will be collected from cars to analyze correlation between several parameters and develop coding for cost optimization.

One of the most common applications of MEMS is by utilizing them as microsensors and microactuators. They have become varied in their applications and can be found almost everywhere in everyday life. The popularity of these microsensors and microactuators is mostly due to the great advantages that they posses. In addition to their small size, MEMS sensors and microactuators consume very little power and are capable of delivering accurate measurements, which are unparalleled with macro-sized sensors. Hence in this research a comparison of some common actuation mechnisms is done and the results showed why electrostatic actuation is gaining roots in recent advancements of micro devices due to its enormous advantages including fast response time and ease of integration and fabrication. Also an electrostatically actuated cantiliver beam was simulated to see the relationships between applied voltage against displacement and also applied voltage against capacitance. This simulation results...

Cantilevered beams with piezoceramic layers have been frequently used as piezoelectric vibration energy harvesters in the past five years. The literature includes several single degree-of-freedom models, a few approximate distributed parameter models and even some incorrect approaches for predicting the electromechanical behavior of these harvesters. In this paper, we present the exact analytical solution of a cantilevered piezoelectric energy harvester with Euler–Bernoulli beam assumptions. The excitation of the harvester is assumed to be due to its base motion in the form of translation in the transverse direction with small rotation, and it is not restricted to be harmonic in time. The resulting expressions for the coupled mechanical response and the electrical outputs are then reduced for the particular case of harmonic behavior in time and closed-form exact expressions are obtained. Simple expressions for the coupled mechanical response, voltage, current, and power outputs are ...

A new refined theory for laminated composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse-shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam's cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented h...

Abstract:-In the paper, the authors try to evaluate the possibility of detecting damages in different types of beams, using the vibrations by finite element method. The assumption was that for beams with the same value of transversal area, same length and different geometries, the efficiency of the procedure will be different. Relevant information obtained by calculation is the natural frequencies of the beams; common variations should indicate changes in its structure. Our first approach was to test the method on a cantilever beam, ...

For the past five years, cantilevered beams with piezoceramic layer(s) have been frequently used as piezoelectric energy harvesters for vibration-to-electric energy conversion. Typically, the energy harvester beam is located on a vibrating host structure and the dynamic strain induced in the piezoceramic layer(s) results in an alternating voltage output across the electrodes. Vibration modes of a cantilevered piezoelectric energy harvester other than the fundamental mode have certain strain nodes where the dynamic strain distribution changes sign in the direction of beam length. It is theoretically explained and experimentally demonstrated in this paper that covering the strain nodes of vibration modes with continuous electrodes results in strong cancellations of the electrical outputs. A detailed dimensionless analysis is given for predicting the locations of the strain nodes of a cantilevered beam in the absence and presence of a tip mass. Since the cancellation issue is not pecul...

Large flexible structures and aerospace structures can be studied by building a model flexible beam with an appendage. The appendage can be used as a passive or an active vibration absorber for a structure under sinusoidal and random excitation. In this study, a cantilever beam-tip mass-pendulum system is investigated by using Finite Element method (FEM). Dynamical behaviour of the model

Tapered cantilever beams, traditionally termed as leaf springs, undergo much larger deflections in comparison to a beam of constant cross-section that takes their study in the domain of geometric nonlinearity. This paper studies response of a leaf spring of parabolic shape, assumed to be made of highly elastic steel. Numerical simulation was carried out using both the small and large deflection theories to calculate the stress and the deflection of the same beam. Non-linear analysis is found to have significant effect on the beam's response under a tip load. It is seen that the actual bending stress at the fixed end, calculated by nonlinear theory, is 2.30-3.39% less in comparison to a traditional leaf spring having the same volume of material. Interestingly, the maximum stress occurs at a region far away from the fixed end of the designed parabolic leaf spring. Keywords: Parabolic leaf spring, End-shortening, Geometric nonlinearity, Equilibrium Configuration Path, Varying Cross...

Cantilevered piezoelectric energy harvesters have been extensively investigated in the literature of energy harvesting. As an alternative to conventional cantilevered beams, this article presents the L-shaped beam-mass structure as a new piezoelectric energy harvester configuration. This structure can be tuned to have the first two natural frequencies relatively close to each other, resulting in the possibility of a broader band energy harvesting system. This article describes the important features of the L-shaped piezoelectric energy harvester configuration and develops a linear distributed parameter model for predicting the electromechanically coupled voltage response and displacement response of the harvester structure. After deriving the coupled distributed parameter model, a case study is presented to investigate the electrical power generation performance of the L-shaped energy harvester. A direct application of the L-shaped piezoelectric energy harvester configuration is pro...

This paper presents the dual use of a piezoelectric self-sensing actuator for both vibration suppression and structural health monitoring (SHM) applications. For vibration suppression, positive position feedback is used for control, where the impedance method or time series autoregressive models are utilized for structural damage detection in SHM. For this approach, only a single piezoelectric transducers element is employed to reduce the number of system components, while enhancing the structural performance. To validate this technique, an analytical model is first developed using the basic principles of PZT materials and the Euler-Bernoulli beam theory. This analytical model is then experimentally verified on a cantilever beam and a three story bolted structure. This paper summarizes considerations needed to design such systems, techniques for control and signal processing, experimental procedures and results, as well as additional issues that can be used as a guideline for future...

Current research in vibration-based energy harvesting and in microelectromechanical system technology has focused renewed attention on the vibration of beams with end masses. This paper shows that the commonly accepted and frequently quoted fundamental natural frequency formula for a beam with identical end masses is incorrect. It is also shown that the higher mode frequency expressions suggested in the referred work (Haener, J., 1958, “Formulas for the Frequencies Including Higher Frequencies of Uniform Cantilever and Free-Free Beams With Additional Masses at the Ends,” ASME J. Appl. Mech. 25, pp. 412) are also incorrect. The correct characteristic (frequency) equation is derived and nondimensional comparisons are made between the results of the previously published formula and the corrected formulation using Euler–Bernoulli beam assumptions. The previous formula is shown to be accurate only for the extreme case of very large end mass to beam mass ratios. Curve fitting is used to r...