Active vibration isolation of machinery and sensitive equipment using H ∞ control criterion and particle swarm optimization method

Isolating the sensitive equipment from vibrating base or the foundation from machinery vibration is of practical importance in a number of engineering fields. With the development of the vibration control techniques and increasing requirements for the higher-performance vibration isolation in industry and everyday life, active vibration isolation exhibits the best performances. In this paper, active vibration isolation reducing vibration transmitted from vibrating base to sensitive equipment and from machinery to foundation was investigated. Controller as static output feedback was considered to design components of active isolation system. An active control is provided by using H _∞ control criteria to design this controller. This criterion is presented as a cost function and then optimized by Particle Swarm Optimization (PSO) algorithm. The approach is validated using numerical simulation. Results show that this static output feedback H _∞ controller using PSO algorithm can get good performance to reduce the effect of unwanted vibration and disturbances.     

An efficient method to solve the strongly coupled nonlinear differential equations of impact dampers

In this paper, ongoing studies to solve nonlinear differential equations are extended by combining the Newmark-beta integration method and the piecewise linearization approach. The discussed method is illustrated with a practical example. In doing so, the coupled nonlinear differential equations of an impact oscillator, which incorporates the Hertzian contact, are derived. To investigate this problem, an object-oriented computer code, based on the presented method, is written in MATLAB. Furthermore, the discussed problem is solved numerically using the Runge–Kutta commercial code. To verify the calculated results, the contact durations, which are obtained using the discussed methods, are compared with the previous analytical results. In this study, accuracy of solution and the process time (cost) are selected as two main parameters of the solution method. The so-called adequacy factor is presented to combine the two main parameters of solution. Finally, it is shown that in the case of Hertzian contact, the presented method can be more adequate than the Runge–Kutta method.     

Finding the buckling load of non-uniform columns using the iteration perturbation method

The aim of this study is to calculate the critical load of variable inertia columns. The example studied in this paper can be used as a paradigm for other non-uniform columns. The wavelength of equivalent vibratory system is used to calculate the critical load of the trigonometrically varied inertia column. In doing so, the equilibrium equation of the column is theoretically studied using the perturbation method. Accuracy of the calculated results is evaluated by comparing the solution with numerical results. Effect of improving the initial guess on the solution accuracy is investigated. Effects of varying parameters of the trigonometrically varied inertia and the uniformly tapered columns on their stability behavior are studied. Finally, using the so-called “perfectibility” parameter, two design goals, i.e., being lightweight and being strong, are studied for the discussed columns.     

Effects of a small length scale on vibrations of an embedded double-walled carbon nanotube

Extensive continuum analyses are carried out to estimate the influence of matrix stiffness, a small length scale, and intertubular radial displacements on free vibrations of an individual double-walled carbon nanotybe. The analyses are based on both local and classical Euler–Bernoulli and Timoshenko elasticity theories with concentricity and nonconcentricity assumptions. The effect of a small length scale is incorporated in the formulations. New intertubular resonant frequencies are calculated based on these theories. Detailed results are demonstrated for the resonant frequencies as functions of matrix stiffness and the small length scale. The results indicate that the internal radial displacement and the stiffness of the surrounding matrix can greatly affect the resonant frequencies, especially at higher frequencies, and thus the latter does not keep the otherwise concentric structure at ultrahigh frequencies. More over, at high frequencies and small aspect ratios, the effect of the small length scale be comes more significant.     

Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization

The solutions to H _∞ and H ₂ optimization problems of a variant dynamic vibration absorber (DVA) applied to suppress vibration in beam structures are derived analytically. The H _∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the resonant vibration amplitude, as well as, the H ₂ optimum parameters to minimize the total vibration energy or the mean square motion of a beam under random force excitation as analytical formulas. The reduction in maximum amplitude responses and mean square motion of a beam using the traditional vibration absorber is compared with the proposed dynamic absorber. Numerical results show the non-traditional DVA under optimum conditions has better vibration suppression performance on beam structures than the traditional design of DVA. Furthermore, comparing H _∞ and H ₂ optimization procedures shows that for a beam under random force excitation, use of H₂ optimum parameters resulting in smaller mean square motion than the other optimization.     

A novel scheme for nonlinear displacement-dependent dampers

In this paper, a novel scheme for nonlinear displacement-dependent (NDD) damper is introduced. The damper is attached to a simple mass-spring-damper vibration system. The vibration system equipped with a NDD damper is mathematically modeled and the nonlinear governing differential equation of the system is derived. To obtain the displacement of the system, the approximate analytical solution of the governing equation is elaborated using the multiple scales method. The advised approximate analytical algorithm is performed for several case studies and is also verified by the numerical fourth-order Runge?CKutta method. In addition, the performance of the NDD damper is analyzed and compared with the performance of the traditional linear damper. It is found that the proposed NDD damper scheme along with the multiple scales method is not only feasible for vibration reduction but also yields satisfactory response performance rather than the existing traditional linear damper.     

Analytic solution of transversal oscillation of quintic non-linear beam with energy balance method and global residue harmonic balance method

Beams are very important element in structures because of its widespread usage in steel construction such as buildings, bridges, aircraft arm, aerospace vehicles and many other industrial usages. To attain a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode which in turn yields the natural frequency of the system. The main objective of present study is to obtain highly accurate analytical solutions for vibrations of a beam with quintic nonlinearity. Two new analytical methods are the improved energy balance method, and the global residue harmonic balance method. Subsequently, the analytical results are compared with the numerical solution of the exact equation in order to evaluate the correctness of the applied approaches.     

Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems

The global homoclinic bifurcation and transition to chaotic behavior of a nonlinear gear system are studied by means of Melnikov analytical analysis. It is also an effective approach to analyze homoclinic bifurcation and detect chaotic behavior. A generalized nonlinear time varying (NLTV) dynamic model of a spur gear pair is formulated, where the backlash, time varying stiffness, external excitation, and static transmission error are included. From Melnikov method, the threshold values of the control parameter for the occurrence of homoclinic bifurcation and onset of chaos are predicted. Additionally, the numerical bifurcation analysis and numerical simulation of the system including bifurcation diagrams, phase plane portraits, time histories, power spectras, and Poincare sections are used to confirm the analytical predictions and show the transition to chaos.     

Numerical study of mixed convection heat transfer inside a vertical microchannel with two-phase approach

Journal of Thermal Analysis and Calorimetry - The current study investigates the laminar and two-phase nanofluid flow inside a two-dimensional rectangular microchannel with the ratio of length to...