Sentence examples for by utilizing the integral from inspiring English sources
In the present study, finite element formulations are derived for static bending, linear buckling and free vibration analysis of nanobeam structures by utilizing the integral form of Eringen nonlocal model.
By utilizing the integral Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded.
By utilizing the integral-type Lyapunov function, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded.
The second purpose of this paper is to establish some interesting Hermite-Hadamard type inequalities involving Hadamard fractional integrals for the functions satisfying monotonicity, convexity and s-e-condition by utilizing the left-type Hadamard fractional integral identities.
The generalized definition of the Jk-integral is recast into a domain independent form composed of line and area integrals by utilizing the constitutive relations of plane orthotropic thermoelasticity.
By utilizing the following identity for the exponential integral function given in ([43], Eq. (06.34.06.0007.01), when z→0, we get { {E_{1}}}!left z right) propto -ln z) + O(1).
A formal integral expression for the radiated pressure field in the frequency domain is obtained by utilizing the spatial Fourier transform along the shell axis and Fourier series expansion in the circumferential direction.
For the integral of time multiplied by absolute error (ITAE) reference model tracking, a chain observer is designed to establish the virtual estimated states for the decoupled subsystems by utilizing the obtained approximated continuous-time models.
Utilizing the integration by parts formula for the Riemann-Stieltjes integral and the reduction of the Riemann-Stieltjes integral to a Riemann integral (see, for instance, [48]) we have: (2.6).
In the present paper, analytical method for the steady state vibration of non-linear system including subharmonic vibration is proposed by utilizing convolution integral and the impulse response.
