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The dynamics of nonlinear thin plates under influence of relatively heavy moving masses is considered. By expansion of the solution as a series of mode functions, the governing equations of motion are reduced to an ordinary differential equation for time development of vibration amplitude, which is Duffing's oscillator with time varying coefficients. Through the application of Banach's fixed-point theorem, the periodic solutions are predicted. The method presented in this paper is general so that the response of plate to moving force systems can also be considered. © 2002 Published by Elsevier Science Ltd  

This study aims to evaluate the amount of energy transfers through the bridge in Setar, a Persian long-necked lute, Stringed musical instruments are among the most complicated acoustical systems. When the string is plucked, its vibration distributes into the entire vibrating system (i.e. body, string, air enclosure) and produces sound. The resultant sound consists of three parts: the first is the string's direct sound; the second is that part of sound-box vibration being excited by string's direct sound, and the third is the part of sound-box vibration being excited by string force passing through bridge. The last part believed to have the major share and the others have minor effect. For... 

A large number of people are exposed to whole body vibration in their occupational life. Measuring vibration is an important tool in rehabilitation and biomechanical fields of research. We have proposed image processing as a new method to record and determine the frequency response of human body. The arranged set up for forced vibration consisted of an AC motor, a variable speed drive unit and a shaking table for producing one directional sinusoidal vibration. Volunteers were asked to stand on the shaking table at a relaxed posture. Two digital camcorders were used to capture the motion of colored pencil-dot markers on the skin of human body (forehead) and on the edge of the shaking table.... 

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses  

In this paper, forced vibration analysis of an extended dynamic model of the milling process is investigated, in the presence of internal resonance. Regenerative chatter, structural nonlinearity, tool wear and process damping effects are included in the proposed model. Taking into account the average and first order expansion of Fourier series for cutting force components; their closed form expressions are derived. Moreover, in the presence of large vibration amplitudes, the loss of contact effect is included in this model. Analytical approximate response of the nonlinear system is constructed through the multiple-scales approach. Dynamics of the system is studied for two cases of primary... 

The nonlinear vibrational properties of single layer graphene sheets (SLGSs) are investigated using a membrane model. The nonlinear equation of motion is considered for the SLGSs by including the effects of stretching due to large amplitudes. The equation of motion is numerically solved utilizing the finite difference method for SLGSs with different initial and boundary conditions, sizes and pretensions. It is concluded that the nonlinear fundamental frequency of SLGSs increases by increasing the pretension and initial velocity. In addition, it is observed that an increase in the pretension weakens the effects of the initial velocity on the fundamental frequency, such that the fundamental... 

This technical note addresses the free vibration problem of an elastically restrained Euler-Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses  

This paper deals with the coupling flexural-torsional vibration analysis of a grid formed by two members. A mass-spring system is attached to the grid at the intersecting joint. The members of the grid are assumed to resist torsion as well as bending and shear. Moreover, the mechanical and geometrical properties of each member are different. In order to analyze the problem, a closed-form solution is obtained. In doing so, the governing differential equations of the system along with the pertinent boundary and compatibility conditions of the system are introduced. Then, the frequency parameters of the mechanical system under study are derived and given for the first five modes of vibration.... 

Iterative methods for modification of vibratory characteristics of dynamic systems have attracted a lot of attention as a convenient and more economical way when compared to the traditional and costly structural dynamic optimization processes. Many complicated structures, such as telecommunication towers, chimneys and tall buildings, may be modeled as simple spring-mass systems. This paper presents an iterative method for modification of the frequencies of simple vibrating system consisting of springs and masses. The proposed algorithm may be used to adjust any of the vibration frequencies of a simple vibrating system to the target values within the desired level of accuracy. The method... 

A new predictive model for evaluating the vibration of a sawing machine was developed using a new rock classification system. The predictors are machine parameters and a rock sawability index. The new rock classification system includes four major parameters of the rock: uniaxial compressive strength, abrasivity index, mean Moh's hardness, and Young's modulus. The FAHP approach was used when determining the weights of these parameters by six decision makers. Two groups of carbonate rocks were sawn using a fully-instrumented laboratory sawing rig at different feed rates and depths of cut. During the sawing trials system vibration was monitored as a measure of saw performance. Then, a new... 

In this paper, the dynamic instability of a nonlinear system has been studied using the stochastic vibration analysis and employing statistical properties of the system response. In this method neither the time domain analysis nor limit cycle oscillations were used. A two degrees-of-freedom airfoil subjected to an aerodynamic quasi-steady flow with a nonlinear torsional spring was considered as the case study. The spring nonlinearity was examined in hardening and softening states. A random force in the form of the white noise with Gaussian function was added to the aerodynamic lift force. The statistical linearization and random vibration analysis were applied to the nonlinear system to... 

This paper presents an active suspension system for passenger cars, using adaptive critic-based neurofuzzy controller. The model is described by a system with seven degrees of freedom. The car is subjected to excitation from a rode surface and wheel unbalance. The main superiority of the proposed controller over previous analogous fuzzy logic controller designed approaches, e.g., genetic fuzzy logic controller, is its online tuning characteristic and remarkable reduced amount of computations used for parameter adaptation, which makes it desirable for real time applications. Considering the simplicity of this controller and its independence from the system model, this control method has the... 

This paper aims to develop a boundary control solution for complicated gantry crane coupled motions. In addition to the large angle sway motion, the crane cable has a flexural transverse vibration. The Hamilton principle has been utilized to derive the governing partial differential equations of motion. The control objectives which are sought include: moving the payload to the desired position; reducing the payload swing with large sway angle; and finally suppressing the cable transverse vibrations in the presence of boundary disturbances simultaneously. These simultaneous boundary control objectives make the problem challenging. The proposed control approach is based on the original... 

This study introduces a novel Bayesian framework for online and real-time vibration control of beam type structures, which represent a comprehensive control system associated with input-state algorithms. Control design systems typically require knowledge of system states, which in structures are displacements and velocities at some degrees of freedom. Currently, full-field measurements of displacements and velocities in large structural systems are not feasible. Also, properties of the moving inertial loads as key parameters in control designs are assumed known; however, in practice, measuring their characteristics is a challenging issue. As a remedy, an observer is required to estimate... 

Magnetorheological (MR) damper is a prominent semi-active control device to vibrate mitigation of structures. Due to the inherent non-linear nature of MR damper, an intelligent non-linear neuro-fuzzy control strategy is designed to control wave-induced vibration of an offshore steel jacket platform equipped with MR dampers. In the proposed control system, a dynamic-feedback neural network is adapted to model non-linear dynamic system, and the fuzzy logic controller is used to determine the control forces of MR dampers. By use of two feedforward neural networks required voltages and actual MR damper forces are obtained, in which the first neural network and the second one acts as the inverse...