Dynamic Response Of Cantilever Beam Research Articles

On the Efficacy of a Novel Optimized Tuned Mass Damper for Minimizing Dynamic Responses of Cantilever Beams

This study examines the optimal design of a tuned mass damper (TMD) in the frequency domain so that the dynamic response of cantilever beams can be decreased. Random vibration theory is applied to identify the mean square acceleration of the endpoint of a cantilever beam as the objective function to be reduced. In addition, to determine the optimal TMD coefficient of mass, stiffness, and damping, a differential evolution (DE) optimization algorithm is employed. The upper and lower limit values of these parameters are taken into account. A majority of the previous studies have concentrated on determining just the stiffness and damping parameters of TMD. Nonetheless, in this study there is also the optimization of TMD mass parameters to determine the mass quantity. In addition, there has been inefficient use of the stochastic DE optimization algorithm method for the optimization of TMD parameters in previous studies. Hence, to obtain optimal TMD parameters, this algorithm is precisely used on the objective function. Tests are carried out on the cantilever beam with the TMD system following this optimization method with harmonic base excitations that resonate the foremost modes of the beam and white noise excitation. The method proposed here is reasonably practical and successful regarding the optimal TMD design. When a TMD is designed appropriately, the response of the cantilever beam under dynamic interactions undergoes a considerable reduction.

Effect of approximation of curvature/inertia on the nonlinear vibrations of cantilever beam

The nonlinear dynamic response of cantilever beams under transverse harmonic excitation is investigated experimentally and numerically. The experimental set up, finite element formulation with accurate representation of curvature/inertia nonlinearities, multi-modal transverse displacement approximation and solution methodology for the periodic solution of the resulting nonlinear equations of motion are described. The experimental and numerical results of nonlinear periodic response are compared and the detailed study is carried out to investigate the effects of approximation of curvature/inertia nonlinearities and transverse displacement on the nature/degree of nonlinearity.

Minimum dynamic response of cantilever beams supported by optimal elastic springs

In this study, optimal distribution of springs which supports a cantilever beam is investigated to minimize two objective functions defined. The optimal size and location of the springs are ascertained to minimize the tip deflection of the cantilever beam. Afterwards, the optimization problem of springs is set up to minimize the tip absolute acceleration of the beam. The Fourier Transform is applied on the equation of motion and the response of the structure is defined in terms of transfer functions. By using any structural mode, the proposed method is applied to find optimal stiffness and location of springs which supports a cantilever beam. The stiffness coefficients of springs are chosen as the design variables. There is an active constraint on the sum of the stiffness coefficients and there are passive constraints on the upper and lower bounds of the stiffness coefficients. Optimality criteria are derived by using the Lagrange Multipliers. Gradient information required for solution of the optimization problem is analytically derived. Optimal designs obtained are compared with the uniform design in terms of frequency responses and time response. Numerical results show that the proposed method is considerably effective to determine optimal stiffness coefficients and locations of the springs.

Dynamic Response Analysis of Cantilever Beam under Moving Mass by Time-Discontinuous Galerkin Finite Element Method

A time-discontinuous Galerkin (TDG) finite element method for analyzing the dynamic response of cantilever beam subjected to moving force or moving mass is presented. The cantilever beam is discretized in space by finite element method, and the time-varying dynamic equations are derived. The TDG finite element method by which both the displacements and velocities are approximated as piecewise linear functions in time domain and discontinuous at the discrete time levels is adopted to solve the differential equations. This method inherits third order accuracy and the unconditionally stable behavior, moreover, it is endowed with large stability limits and controllable numerical dissipation. The numerical solutions are accord with analytic ones, which validates the feasibility and superiority of this method for solving the dynamic response of cantilever beam under moving force or moving mass.

On the detection threshold for fatigue cracks in welded steel beams using vibration analysis

In this paper the influence of a surface fatigue crack on vibration behaviour of tee-welded plates was studied and results compared to the influence of machined through-thickness cuts on the dynamic response of cantilever beams. Comparison of experimental data with two and three dimension finite element modelling results was also carried out and discussed. Detection threshold using natural frequencies shift was found and compared to literature. The influence of naturally grown fatigue cracks on the oscillation frequencies was analysed and compared to two and three-dimensional numerical modelling results. An experimental detection threshold was found using the variation of the first mode natural frequencies. The power density spectra of the acceleration signals were analysed. Crack shape was found important for the detection threshold of the method. It was found that small size semicircular fatigue cracks do not noticeably modify the beam natural frequency but generate integer harmonics of the vibration modes that provoked stresses at the samples surface affected by the crack. The harmonics found were found to be generated by the breathing behaviour of the fatigue crack. A detection threshold using this spectral analysis was found to be lower than those found by using frequency shifts. The results obtained showed the ability of the experimental technique to detect cracks from a size of 0.6% of the cross section area, at 55% of the fatigue lifespan, 35% earlier than the other method studied.

Viscosity measurements based on experimental investigations of composite cantilever beam eigenfrequencies in viscous media

Experimental investigations have been conducted to study the multimode dynamic response of composite cantilever beams in various viscous media and to determine their viscosity. Theoretical eigenfrequencies are computed using the analytical model proposed by Sader [J. Appl. Phys. 84, 64 (1998)] based on the analysis of the hydrodynamic function of cantilever beams. A good agreement is found between theory and experiment for the first two resonant frequencies of composite beams operated in air and in water. The same experimental approach is used to determine the viscosity of ultrapure ethanol. Thus, it is established that Sader’s model represents an accurate alternative for the determination of liquid viscosity in small volumes (about 50 μl) which might be of great importance for microfluidics applications. Finally, the limits of the method are underlined by monitoring the dynamic response of cantilever beams in silicon oil.

Control of Cantilever Vibration via Structural Tailoring and Adaptive Materials

A dual approach integrating structural tailoring and adaptive materials technology and designed to control the dynamic response of cantilever beams subjected to external excitations is presented. Whereas structural tailor- ing uses the anisotropy properties of advanced composite materials, adaptive materials technology exploits the actuating capabilities of piezoelectric materials bonded or embedded into the host structure. A control law relat- ing the piezoelectrically induced boundary bending moment with the velocity at given points of the structure is implemented and its effect on the closed-loop frequencies and dynamic response to harmonic excitations is inves- tigated. The combination of structural tailoring and control by means of adaptive materials proves very effective in damping out vibration. I. Introduction A Sthe requirements for higherexibility on high-speed aircraft increase, so do the challenges of developing innovative de- sign solutions. Whereas the increasedexibility is likely to provide enhanced aerodynamic performance, the aircraft also must be able to ful® ll a multitude of missions in complex environmental condi- tions and to feature an expanded operational envelope and longer operational life. To achieve such ambitious goals- advanced con- cepts resulting in the enhancement of static and dynamic response of the multimission- highlyexible aircraft must be developed and implemented. One way of achieving such goals consists of the in- tegration of advanced composite materials in the aircraft structure. 1 In this regard, the directionality property featured by anisotropic composite materials is capable of providing the desired elastic cou- plings through the proper selection of the ply angle. However, such a technique is passive in nature in the sense that, once the design is in place, the structure cannot respond to the variety of conditions in which it must operate. The situation can be mitigated by incorporating into the host structure adaptive materials able to respond actively to changing conditions. In a structure with adaptive capabilities, the natural fre- quencies, damping, and mode shapes can be tuned to reduce the vibration so as to avoid structural resonance andutter instability, and in general toenhance the dynamic response characteristics.The adaptivecapabilityisachievedthroughtheconversepiezoelectricef- fect,whichconsistsofthegenerationoflocalized strainsinresponse to an applied voltage. This induced strain ® eld produces, in turn, a change in the dynamic response characteristics of the structure. It is proposedheretoenhancethefreevibrationanddynamicresponseto externalexcitationsofwing structures by incorporating theadaptive capabilityreferredtoasinduced strain actuationinconjunctionwith structural tailoring. Under consideration is a cantilevered aircraft wing, modeled as a thin/thick-walled closed cross-section beam of anisotropic material. Implementation of a control law relating the applied electric ® eld to one of the mechanical quantities charac- terizing the response of the wing according to a prescribed func- tional relationship results in eigenvalue/boundary-value problems. The solution consists of closed-loop eigenvalues/dynamic response characteristics, which are functions of the applied voltage, i.e., of the feedback control gain. Investigation of static and dynamic control of aircraft wing structures via the simultaneous implementation of induced strain

Dynamic response of cantilever beams with discontinuity in thickness subjected to a point load

Cantilever beams with discontinuity in the thickness and subjected to harmonic point load have been analyzed. A beam element with 2 DOF (degrees of freedom) per node is used for the analysis. Three beam models are analyzed for possible reduction of maximum displacement and maximum stress by choosing the discontinuity at different locations. Numerical results are presented for various step-ratios in the thickness for the first three modes. The weight of the beam is kept constant for various step-ratios. It has been shown that the maximum displacement and maximum stress decreases for a certain type of thickness variations presented in this paper.

Experimental Investigation of Non-Linear Modal Coupling in the Response of Cantilever Beams

The results of an experimental investigation of non-linear one-to-one modal coupling in the dynamic response of cantilever beams excited by a periodic transverse base excitation are presented. The experimental results are in excellent agreement with previously published analytical predictions based on a set of non-linear differential equations which consider the effects of non-linear curvature and non-linear inertia. The effects of base stiffness, small imperfections along the beam span, and linear and non-linear damping are considered in this work.