.In this paper the harmonic balance method (HBM) is adopted for solving a special group of oscillators with strong nonlinear damping and elastic forces. The nonlinearity is of polynomial type. The motion is described ...
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.In this paper the harmonic balance method (HBM) is adopted for solving a special group of oscillators with strong nonlinear damping and elastic forces. The nonlinearity is of polynomial type. The motion is described with a strong nonlinear differential equation, whose approximate solution is assumed as a suitable sum of trigonometric functions. To find the most convenient combination of trigonometric functions as the probe function is the most important part of this investigation. Introducing the procedure of equating the terms with the same order of the trigonometric functions to zero, the problem is transformed into solving a system of nonlinear algebraic equations. Solving these equations the parameters of the solution up to high-order approximation are obtained. In the paper, the suggested solving procedure is applied for two nonlinear oscillator problems: free vibrations of a restrained uniform beam carrying an intermediate lumped mass and of a particle on a rotating parabola. The obtained approximate analytic solutions are compared with the already published results and with the numerically obtained solution. The solution up to third-order approximation is calculated. It is proved that the HBM with the suggested function gives more accurate results than the previous applied ones. Besides, the difference between the third-order approximate analytical solution and the numerical one is negligible. The method works well for different, even high, values of initial amplitudes.
In this paper, new bounds for the exponential function with cotangent are found by using the recurrence relation between coefficients in the expansion of power series of the function In(1 - 2x(2)/15 - px(6)) and a new...
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In this paper, new bounds for the exponential function with cotangent are found by using the recurrence relation between coefficients in the expansion of power series of the function In(1 - 2x(2)/15 - px(6)) and a new criterion for the monotonicity of the quotient of two power series.
The (G'/G)-expansion method is used to study ion-acoustic waves equations in plasma physic for the first time. Many new exact traveling wave solutions of the Schamel equation, Schamel-KdV (S-KdV), and the two-dime...
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The (G'/G)-expansion method is used to study ion-acoustic waves equations in plasma physic for the first time. Many new exact traveling wave solutions of the Schamel equation, Schamel-KdV (S-KdV), and the two-dimensional modified KP (Kadomtsev-Petviashvili) equation with square root nonlinearity are constructed. The traveling wave solutions obtained via this method are expressed by hyperbolic functions, the trigonometric functions, and the rational functions. In addition to solitary waves solutions, a variety of special solutions like kink shaped, antikink shaped, and bell type solitary solutions are obtained when the choice of parameters is taken at special values. Two- and three-dimensional plots are drawn to illustrate the nature of solutions. Moreover, the solution obtained via this method is in good agreement with previously obtained solutions of other researchers.
The G'/G-expansion method is a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems. In our work, exact traveling wave solutions of a generalized KdV typ...
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The G'/G-expansion method is a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems. In our work, exact traveling wave solutions of a generalized KdV type equation of neglecting the highest order infinitesimal term, which is an important water wave model, are discussed by the G '/G-expansion method and its variants. As a result, many new exact solutions involving parameters, expressed by Jacobi elliptic functions, hyperbolic functions, trigonometric function, and the rational functions, are obtained. These methods are more effective and simple than other methods and a number of solutions can be obtained at the same time. The related results are enriched.
A general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method, and the extended auxiliary function method with computerized symbolic co...
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A general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method, and the extended auxiliary function method with computerized symbolic computation is proposed to construct more new exact solutions for coupled Schrodinger-Boussinesq equations. As a result, several families of new generalized Jacobi elliptic function wave solutions are obtained by using this method, some of them are degenerated to solitary wave solutions and trigonometric function solutions in the limited cases, which shows that the general method is more powerful than plenty of traditional methods and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.
A disguise algorithm about DEM data is proposed in this paper, and it is based on matrix transformation and cryptographic algorithm. In this algorithm, a terrain is generated with a parametric surface, which is genera...
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ISBN:
(纸本)9781467390996
A disguise algorithm about DEM data is proposed in this paper, and it is based on matrix transformation and cryptographic algorithm. In this algorithm, a terrain is generated with a parametric surface, which is generated by the two element trigonometric function. The security communication of DEM data is realized through the discretization of the real DEM data and the terrain. Experiments prove that this algorithm is safe and efficient. This scheme can be used widely in DEM data protection field.
FLANN and generalized FLANN filters exploiting trigonometric functions are often used in active noise control. However, they cannot approximate arbitrarily well every causal, time-invariant, finite-memory, nonlinear s...
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ISBN:
(纸本)9781467310680
FLANN and generalized FLANN filters exploiting trigonometric functions are often used in active noise control. However, they cannot approximate arbitrarily well every causal, time-invariant, finite-memory, nonlinear system, i.e., they are not universal approximators as the Volterra filters. In this paper, we propose a novel class of FLANN filters, called Complete FLANN filters, which satisfy the Stone-Weierstrass theorem, and thus can arbitrarily well approximate any nonlinear, time-invariant, finite-memory, continuous system. CFLANN filters are members of the class of nonlinear filters characterized by the property that their output depends linearly on the filter coefficients. As a consequence, they can be efficiently implemented in the form of a filter bank and adapted using algorithms simply derived from those applied to linear filters. In the paper, we apply a nonlinearly Filtered-X NLMS algorithmfor CFLANN filters and describe some useful applications in the area of nonlinear active noise control.
This paper shows that the representation with the quaternions improves the efficiency in optimization of rotation matrix. The effects of vibration caused by oscillating objects can be suppressed if the object is fixed...
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ISBN:
(纸本)9781479978632
This paper shows that the representation with the quaternions improves the efficiency in optimization of rotation matrix. The effects of vibration caused by oscillating objects can be suppressed if the object is fixed with the adequate attitude. In general, Euler angles are widely known as a representation of rotation matrices, however it is difficult to optimize the attitude angle by using Euler angles. This is because Euler angles have trigonometric functions. Contrarily, rotation matrices described by the quaternions do not include trigonometric functions and the effectiveness of the quaternions has already recognized in the field such as computer vision and robotics. This paper demonstrates the effectiveness of the quaternions representation for optimization problems through a numerical example.
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