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11.
The vibration response of a Timoshenko beam supported by a viscoelastic foundation with randomly distributed parameters along
the beam length and jected to a harmonic moving load, is studied. By means of the first-order two-dimensional regular perturbation
method and employing appropriate Green's functions, the dynamic response of the beam consisting of the mean and variance of
the deflection and of the bending moment are obtained analytically in integral forms. Results of a field measurement for a
test track are utilized to model the uncertainty of the foundation parameters. A frequency analysis is carried out and the
effect of the load speed on the response is studied. It is found that the covariance functions of the stiffness and the loss
factor both have the shape of an exponential function multiplied by a cosine function. Furthermore, it is shown that in each
frequency response there is a peak value for the frequency, which changes inversely with the load speed. It is also found
that the peak value of the mean and also standard deviation of the deflection and bending moment can be a decreasing or increasing
function of the load speed depending on its frequency.
An erratum to this article is available at . 相似文献
12.
The vibration of an Euler-Bernoulli beam, resting on a nonlinear Kelvin-Voight viscoelastic foundation, traversed by a moving load is studied in the frequency domain. The objective is to obtain the frequency responses of the beam and the effects of different parameters on the system response. The parameters include the magnitude and speed of the moving load and the foundation nonlinearity and its damping coefficient. The solution is obtained by using the Galerkin method in conjunction with the multiple scales method (MSM). The governing nonlinear partial differential equations of motion are discretized into sets of nonlinear ordinary differential equations. Subsequently, the solution is calculated for different harmonics by using the MSM as one of the powerful perturbation techniques. The steady-state responses of the main harmonic as well as its two super-harmonics are then obtained. As a case study, a conventional railway track is dynamically simulated and the jump phenomenon in the response is observed for three harmonics. Moreover, a thorough stability analysis of the system is carried out. 相似文献
13.
The frequency response of a cracked beam supported by a nonlinear viscoelastic foundation has been investigated in this study. The Galerkin method in conjunction with the multiple scales method (MSM) is employed to solve the nonlinear governing equations of motion. The steady-state solutions are derived for the two different resonant conditions. A parametric sensitivity analysis is carried out and the effects of different parameters, namely the geometry and location of crack, loading position and the linear and nonlinear foundation parameters, on the frequency-response solution are examined. 相似文献
14.
Non-linear vibration of a variable speed rotating beam is analyzed in this paper. The coupled longitudinal and bending vibration of a beam is studied and the governing equations of motion, using Hamilton’s principle, are derived. The solutions of the non-linear partial differential equations of motion are discretized to the time and position functions using the Galerkin method. The multiple scales method is then utilized to obtain the first-order approximate solution. The exact first-order solution is determined for both the stationary and non-stationary rotating speeds. A very close agreement is achieved between the simulation results obtained by the numerical integration method and the first-order exact solution one. The parameter sensitivity study is carried out and the effect of different parameters including the hub radius, structural damping, acceleration, and the deceleration rates on the vibration amplitude is investigated. 相似文献
15.
He's energy balance method (HEBM) is employed in this article to obtain the analytical approximate solution of the generalized nonlinear oscillator. Existence of periodic solutions is analytically verified and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. A number of numerical simulations are carried out and accuracy of the HEBM is then examined within an error analysis. The exact values of the natural frequency numerically obtained via the elliptic integrals are taken into account as the references bases and the relative error is then evaluated for a range of oscillation amplitudes. Excellent correlation of the approximate frequencies with the exact ones demonstrates that the approximate solutions are quite consistent even for large amplitudes of oscillation. 相似文献
16.
The suppression of chaotic motion in viscoelastic plates driven by external subsonic air flow is studied. Nonlinear oscillation of the plate is modeled by the von-Kármán plate theory. The fluid-solid interaction is taken into account. Galerkin’s approach is employed to transform the partial differential equations of the system into the time domain. The corresponding homoclinic orbits of the unperturbed Hamiltonian system are obtained. In order to study the chaotic behavior of the plate, Melnikov’s integral is analytically applied and the threshold of the excitation amplitude and frequency for the occurrence of chaos is presented. It is found that adding a parametric perturbation to the system in terms of an excitation with the same frequency of the external force can lead to eliminate chaos. Variations of the Lyapunov exponent and bifurcation diagrams are provided to analyze the chaotic and periodic responses. Two perturbation-based control strategies are proposed. In the first scenario, the amplitude of control forces reads a constant value that should be precisely determined. In the second strategy, this amplitude can be proportional to the deflection of the plate. The performance of each controller is investigated and it is found that the second scenario would be more efficient. 相似文献
17.
Free and forced vibrations of triangular plate are investigated. Diverse types of stiffeners were attached onto the plate to suppress the undesirable large-amplitude oscillations. The governing equation of motion for a triangular plate, based on the von Kármán theory, is developed and the nonlinear ordinary differential equation of the system using Galerkin approach is obtained. Closed-form expressions for the free undamped and large-amplitude vibration of an orthotropic triangular elastic plate are presented using the two well-known analytical methods, namely, the energy balance method and the variational approach. The frequency responses in the closed-form are presented and their sensitivities with respect to the initial amplitudes are studied. An error analysis is performed and the vibration behavior, as well as the accuracy of the solution methods, is evaluated. Different types of the stiffened triangular plates are considered in order to cover a wide range of practical applications. Numerical simulations are carried out and the validity of the solution procedure is explored. It is demonstrated that the two methods of energy balance and variational approach have been quite straightforward and reliable techniques to solve those nonlinear differential equations. Subsequently, due to the importance of multiple resonant responses in engineering design, multi-frequency excitations are considered. It is assumed that three periodic forces are applied to the plate in three specific positions. The multiple time scaling method is utilized to obtain approximate solutions for the frequency resonance cases. Influences of different parameters, namely, the position of applied forces, geometry and the number of stiffeners on the frequency response of the triangular plates are examined. 相似文献
18.
19.
Nonlinear harmonic oscillation of a plate-cavity system is analytically studied in this paper. Von-Karman theory is used to model a rectangular plate backed by an air cavity. Coupled nonlinear differential equations of system are analytically derived using Galerkin’s approach. The Multiple Scales Method (MSM) is then employed to solve the corresponding nonlinear equations. Primary, secondary, and combinational resonance conditions are taken into account and the corresponding closed-form frequency-amplitude relationships are derived. A parametric study is carried out and effects of different parameters on the frequency responses are investigated. 相似文献
20.
D. Younesian 《Journal of sound and vibration》2011,330(2):308-320
A new strategy for vibration suppression of a rotating beam using a time-increasing internal tensile force is proposed in this paper. Nonlinear coupled longitudinal and bending equations of motion are derived in non-dimensional form using the Hamilton principle. The first-order analytical solution of the equations of motion is obtained using the Galerkin technique combined with the multiple scales method (MSM). Numerical simulations are then performed for various increasing rates of the internal tensile force and performance of the vibration suppression strategy is studied. A very close agreement between the simulation results obtained by the numerical integration and the first-order analytical solution is achieved. Forced vibrations of the system for input excitations of either a sinusoidal or a random function with white noise time history are considered. The simulation results and dynamic performance of the suppressed system for an externally excited rotating beam show an interesting phenomenon of the form of remarkable effectiveness of the proposed vibration reduction strategy. 相似文献