The dynamic stiffness matrix of a coupled axial-bending Timoshenko beam is developed to investigate the free vibration behaviour such beams and their assemblies. Applying Hamilton's principle, governing differential equations motion in derived by considering coupling effect arising from mass axis eccentricity with elastic cross-section. are then solved an exact sense, giving expressions for axi...

In this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. To approach this aim the analytical formulas of secant stiffness matrix are presented. The models were validated and used to perform inve...

Deployable trusses that are widely applied in space missions utilize many hinged members to adapt to different geometrical shapes and work conditions. This paper presents two improved finite elements for a link and a bending beam to calculate dynamic characteristics of non-jointed and jointed trusses. First, the axial and transverse wave motion equations of a beam are used to get the shape func...

in the present paper, the aeroelastic stability of helicopter rotor blade is determined using aeroelastic frequency response function. the aeroelastic model of blade is obtained by combining dowell - hodges beam model with loewy unsteady aerodynamic theory which considers an unsteady wake beneath the rotor. equations are formed and aeroelastic frequency response functions are obtained by invert...

Starting from the solutions of governing differential equations motion in free vibration, frequency dependent mass and stiffness matrices bar beam elements have been derived this paper, but importantly, their equivalency with corresponding dynamic matrix is established. In sharp contrast to series solutions, reported literature, explicit expressions for each term are generated concise form thro...

where x is a vector of displacements of structural coordinates, M is a positive definite mass matrix, C is a non-negative definite damping matrix, and K is a non-negative definite stiffness matrix. The nonlinear restoring forces are given in R(x, ẋ) and f ext(t) is a vector of external dynamic loads. At any point in time, t = ti+1 = (i+ 1)h, we may solve for the accelerations in terms of the di...

in the current study, the effects of interactions of the moving loads and the attached mass-spring-damper systems of the composite plates on the resulting dynamic responses are investigated comprehensively, for the first time, using the classical plate theory. the solution of the coupled governing system of equations is accomplished through tracing the spatial variations using a navier-type sol...

Elements based on the exact stiffness matrix method contain an embedded analytical solution that can capture detailed local fields, enabling more efficient mesh independent finite element analysis. In the present study, this method was applied to adhesively bonded joints. The adherends were modeled as Euler-Bernoulli beams, and the adhesive layer was modeled as a bed of linear shear and normal ...

This study firstly proposes some representative simple methods to obtain the suboptimal passive damping and stiffness parameters from the optimal control gain matrix since it is not possible to add the exact optimal damping and stiffness parameters to the structure in practice. It is shown numerically that modifying the structural damping and the stiffness in the proposed suboptimal ways may su...