In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called t...In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called the Krylov-Bogoliubov-Mitropolsky(KBM)method and the multiple scales method(MSM).All mentioned methods are applied to obtain some accurate and stable approximations to the proposed problem without decoupling the original problem.All obtained approximations are discussed graphically using different numerical values to the relevant parameters.Moreover,all obtained approximate solutions are compared with the 4thorder Runge-Kutta(RK4)numerical approximation.The maximum residual distance error(MRDE)is also estimated,in order to verify the high accuracy of the obtained analytic approximations.展开更多
The onset of the movement of particles placed on a horizontal rough surface subject to a vertical sinusoidal vibration is investigated through tracking experiments,theoretical analysis,and numerical simulations. The f...The onset of the movement of particles placed on a horizontal rough surface subject to a vertical sinusoidal vibration is investigated through tracking experiments,theoretical analysis,and numerical simulations. The frequency of vibration needed to move particles decays exponentially with the amplitude of the oscillatory input.This behavior is explained through a simple mechanism in which a forced damped harmonic oscillator with a spring constant represents all the interactions between the particle and the surface.The numerical results compare well with experimental data,demonstrating that the forces included in the numerical calculations suitably account for the main particle response,even though the complexity of the surface is not fully taken into account.Describing the way in which frequency varies with amplitude could be relevant to technological applications such as cleaning of material surfaces.展开更多
A turn control strategy is proposed in order to improve environmental adaptability of a quasi-passive walking robot by utilizing a mechanical oscillator. The target trajectory of the fmechanical oscillator is determin...A turn control strategy is proposed in order to improve environmental adaptability of a quasi-passive walking robot by utilizing a mechanical oscillator. The target trajectory of the fmechanical oscillator is determined by online planning of its period, phase, amplitude and angle of the central axis of oscillation. The motion of the mechanical oscillator is always entrained with the rocking motion of the robot based on forced entrainment in order to stabilize the robot. The turn radius can be controlled by adjusting the inclination angle of the central axis of the mechanical oscillator movement, and the control method is numerically and experimentally examined. Results show that the robot can turn with different radius and it is possible for the robot to walk in various environments. Finally, the gait of turn is compared with that of straight walking and analyzed in terms of mechanical work and energy.展开更多
The quantization of the forced harmonic oscillator is studied with the quantum variable (<em>x</em>, <span style="white-space:nowrap;"><em><sub>v</sub><sup style="...The quantization of the forced harmonic oscillator is studied with the quantum variable (<em>x</em>, <span style="white-space:nowrap;"><em><sub>v</sub><sup style="margin-left:-8px;">∧</sup></em></span>), with the commutation relation <img src="Edit_28f5b839-7de4-41e5-9ed8-69dc1bf72c2c.bmp" alt="" />, and using a Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span></span>dinger’s like equation on these variable, and associating a linear operator to a constant of motion <em>K</em> (<em>x, v, t</em>) of the classical system, The comparison with the quantization in the space (<em>x, p</em>) is done with the usual Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span></span>dinger’s equation for the Hamiltonian <em>H</em><span style="white-space:normal;">(</span><em style="white-space:normal;">x, p, t</em><span style="white-space:normal;">)</span>, and with the commutation relation <img src="Edit_cca7e318-5b35-4c55-8f09-6089970ce9a2.bmp" alt="" />. It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em><sub>v</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization has fewer oscillations than the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>p</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization, the average energy of the system is higher in (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>p</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization than on the (<em style="white-space:normal;">x</em><span style="white-space:normal;">,展开更多
A new method to construct coherent states of a time-dependent forced harmonic oscillator was given. The close relation to the classical forced oscillator and the minimum uncertainty relation were investigated. The app...A new method to construct coherent states of a time-dependent forced harmonic oscillator was given. The close relation to the classical forced oscillator and the minimum uncertainty relation were investigated. The applied periodic force (off-resonance case), in general, will attenuate the AA phase.展开更多
Abstract: This work studies the active control of chemical oscillations governed by a forced modified Van der Pol-Duffing oscillator. We considered the dynamics of nonlinear chemical systems subjected to an external s...Abstract: This work studies the active control of chemical oscillations governed by a forced modified Van der Pol-Duffing oscillator. We considered the dynamics of nonlinear chemical systems subjected to an external sinusoidal excitation. The approximative solution to the first order of the modified Van der Pol-Duffing oscillator is found using the Lindstedt’s perturbation method. The harmonic balance method is used to find the amplitudes of the oscillatory states of the system under control. The effects of the constraint parameter and the control parameter of the model on the amplitude of oscillations are presented. The effects of the active control on the behaviors of the model are analyzed and it appears that with the appropriate selection of the coupling parameter, the chaotic behavior of the model has given way to periodic movements. Numerical simulations are used to validate and complete the analytical results obtained.展开更多
基金the Deputyship for Research&Innovation,Ministry of Education in Saudi Arabia for funding this research work through the project number RI-44-0143
文摘In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called the Krylov-Bogoliubov-Mitropolsky(KBM)method and the multiple scales method(MSM).All mentioned methods are applied to obtain some accurate and stable approximations to the proposed problem without decoupling the original problem.All obtained approximations are discussed graphically using different numerical values to the relevant parameters.Moreover,all obtained approximate solutions are compared with the 4thorder Runge-Kutta(RK4)numerical approximation.The maximum residual distance error(MRDE)is also estimated,in order to verify the high accuracy of the obtained analytic approximations.
文摘The onset of the movement of particles placed on a horizontal rough surface subject to a vertical sinusoidal vibration is investigated through tracking experiments,theoretical analysis,and numerical simulations. The frequency of vibration needed to move particles decays exponentially with the amplitude of the oscillatory input.This behavior is explained through a simple mechanism in which a forced damped harmonic oscillator with a spring constant represents all the interactions between the particle and the surface.The numerical results compare well with experimental data,demonstrating that the forces included in the numerical calculations suitably account for the main particle response,even though the complexity of the surface is not fully taken into account.Describing the way in which frequency varies with amplitude could be relevant to technological applications such as cleaning of material surfaces.
文摘A turn control strategy is proposed in order to improve environmental adaptability of a quasi-passive walking robot by utilizing a mechanical oscillator. The target trajectory of the fmechanical oscillator is determined by online planning of its period, phase, amplitude and angle of the central axis of oscillation. The motion of the mechanical oscillator is always entrained with the rocking motion of the robot based on forced entrainment in order to stabilize the robot. The turn radius can be controlled by adjusting the inclination angle of the central axis of the mechanical oscillator movement, and the control method is numerically and experimentally examined. Results show that the robot can turn with different radius and it is possible for the robot to walk in various environments. Finally, the gait of turn is compared with that of straight walking and analyzed in terms of mechanical work and energy.
文摘The quantization of the forced harmonic oscillator is studied with the quantum variable (<em>x</em>, <span style="white-space:nowrap;"><em><sub>v</sub><sup style="margin-left:-8px;">∧</sup></em></span>), with the commutation relation <img src="Edit_28f5b839-7de4-41e5-9ed8-69dc1bf72c2c.bmp" alt="" />, and using a Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span></span>dinger’s like equation on these variable, and associating a linear operator to a constant of motion <em>K</em> (<em>x, v, t</em>) of the classical system, The comparison with the quantization in the space (<em>x, p</em>) is done with the usual Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span></span>dinger’s equation for the Hamiltonian <em>H</em><span style="white-space:normal;">(</span><em style="white-space:normal;">x, p, t</em><span style="white-space:normal;">)</span>, and with the commutation relation <img src="Edit_cca7e318-5b35-4c55-8f09-6089970ce9a2.bmp" alt="" />. It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em><sub>v</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization has fewer oscillations than the (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>p</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization, the average energy of the system is higher in (<em style="white-space:normal;">x</em><span style="white-space:normal;">, </span><em style="white-space:normal;"><sub>p</sub><sup style="margin-left:-8px;">∧</sup></em>) quantization than on the (<em style="white-space:normal;">x</em><span style="white-space:normal;">,
文摘A new method to construct coherent states of a time-dependent forced harmonic oscillator was given. The close relation to the classical forced oscillator and the minimum uncertainty relation were investigated. The applied periodic force (off-resonance case), in general, will attenuate the AA phase.
文摘Abstract: This work studies the active control of chemical oscillations governed by a forced modified Van der Pol-Duffing oscillator. We considered the dynamics of nonlinear chemical systems subjected to an external sinusoidal excitation. The approximative solution to the first order of the modified Van der Pol-Duffing oscillator is found using the Lindstedt’s perturbation method. The harmonic balance method is used to find the amplitudes of the oscillatory states of the system under control. The effects of the constraint parameter and the control parameter of the model on the amplitude of oscillations are presented. The effects of the active control on the behaviors of the model are analyzed and it appears that with the appropriate selection of the coupling parameter, the chaotic behavior of the model has given way to periodic movements. Numerical simulations are used to validate and complete the analytical results obtained.
