...C. C. Hong The thermal vibration study of magnetostrictive functionally graded material (FGM) plate under rapid heating is computed by using the generalized differential quadrature (GDQ) method. The dynamic equilibrium differential equations with displacements and shear rotations...

..., a special case of a cantilever microbeam is studied and modeled as a distributed-parameter system, which is attached to the PCB. These lumped-distributed and distributed-distributed models are discretized into ordinary differential equations, using the Galerkin method, which are then integrated numerically...

... or tensile) and other parameters of the PVC layers on the vibration characteristics of flexible structure have been investigated. The Hamilton principle in conjunction with finite element method is used to derive the differential equations of motion. Using proportional feedback controllers, the complex...

... is of great importance. In this paper, the free vibration of an inclined taut cable is further investigated by accounting for the factor of the weight component parallel to the cable chord. Two coupled linear differential equations describing two-dimensional in-plane motion of the cable are derived based...

...Peng Lan; Ahmed A. Shabana The goal of this study is to develop the dynamic differential equations of the first finite element based on the rational absolute nodal coordinate formulation (RANCF) and to demonstrate its use in the nonlinear dynamic and vibration analysis of flexible bodies...

... differential equation of motion. Frequency equations for an annular plate for two different combinations of edge conditions have been obtained employing Chebyshev collocation technique. Numerical results thus obtained have been presented in the form of tables and graphs. The effect of foundation parameter...

... were used to represent the active material while the inertia, viscous losses, and compressibility of the fluid were included using differential equations. Factors affecting system performance are identified and the inclusion of fluid inertia in the model is also justified. The starting point...

... leads to a homogeneous differential equation. This is similar to the definition of free vibration in the case of SDoF systems with constant parameters. The physical meaning associated with condition (i) is that it represents a case when the absolute velocity of the entering or exiting mass is negligible...

..., and show that this leads to a significantly improved quality. Our idea also works for operators of order greater than 1. damping differential equations integration mathematical operators numerical analysis vibrations fractional derivative numerical method Yuan–Agrawal method...

... quantification, which generally require an efficient and robust sensitivity calculation method. In this paper, the sensitivity of the milling process, which can be modeled by a set of time delay differential equations, to variations in the input parameters is calculated. The semi-analytical derivative...

..., namely, a formulation where the governing differential equation had constant coefficients. In the present study, when the foundation is narrower than the plate and its spatial footprint varies in time, the equation of motion presents time-varying coefficients, and motion is excited both parametrically...

..., a stiff differential equation with analytical results is adopted to be solved using the symplectic precise integration method, precise integration method, and general Runge–Kutta method. The Hamiltonian of this system is 72 H = 1 2 m 1 x ̇ 1 2 + 1 2 m 2 x ̇ 2 2...

... the governing differential equations of motion that describe the deformations of the beam element according to the trigonometric shear deformation theory, which include the sinusoidal variation of the axial displacement over the cross section of the beam. The application of the dynamic stiffness matrix...

.... This work demonstrates that the parameters of a system of ordinary differential equations may be adjusted via an evolutionary algorithm to produce excitations that improve the sensitivity and robustness to extraneous noise of state-space based damage detection features extracted from the structural response...

...Igor V. Andrianov; Jan Awrejcewicz; Alexander A. Diskovsky A novel asymptotical approach to integrate differential equations governing quasi-regular structures, particularly suitable on the stage of construction design, is proposed. 02 12 2004 21 02 2006 periodic structures...

... degrees of freedom, viz., three translational components along the cylindrical coordinates and two rotational components of the normal to the middle surface. Then the strain and kinetic energy expressions are obtained in terms of these displacement fields. The differential equation governing the vibration...

...Z. S. Liu,; D. T. Song, and; C. Huang; D. J. Wang; S. H. Chen 21 03 2005 vibrations damping approximation theory matrix algebra differential equations eigenvalues and eigenfunctions We appreciate S. M. Shahruz for his interest in our paper and for the useful comments...

...L. Starek; D. J. Inman, Fellow ASME This paper summarizes the authors’ previous efforts on solving inverse eigenvalue problems for linear vibrating systems described by a vector differential equations with constant coefficient matrices and nonproportional damping. The inverse problem of interest...

... of governing partial differential equations is reduced to a “special form” of a system of the first order ordinary differential equations. Then, they are integrated by the “Modified Transfer Matrix Method (with Interpolation Polynomials).” The mode shapes and the natural frequencies of the composite system...

... characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P = P 0 + P t cos θ t are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed...