This paper extends the Wittrick-Williams (W-W) algorithm for hybrid dynamic stiffness (DS) models connecting any combinations of line and point nodes. The principal novelties lie in development both DS formulation solution technique a sufficiently systematic general manner. parent structure is considered to be form two dimensional elements with nodes, which can connected rigid/spring supports/c...

Abstract. The presence of damage can strongly affect the residual carrying capacity and dynamic properties frame structures. uncertainty in position intensity implies difficulty adopting for practical purposes deterministic analyses, which rigorously require complicated calculations. In this paper, multi-cracked frames are studied considering crack positions as whereas intensities uncertain. Ex...

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...

A spectral dynamic stiffness (SDS) model for plate assemblies stiffened by beams is proposed. The theory sufficiently general where the can be subjected to any arbitrary boundary conditions (BCs), but importantly, beam stiffeners of open or closed cross-sections, and maybe connected plates with without eccentricity. First, using modified Fourier series, SDS formulations different are developed ...

An exact dynamic stiffness method is proposed for the free vibration analysis of multi-body systems consisting flexible beams and rigid bodies. The theory sufficiently general in that bodies can be any shape or size, but importantly, permits connections to number at arbitrary points oriented angles. For beam members, a range theories including Bernoulli-Euler Timoshenko are applied. assembly pr...

Closed-form dynamic stiffness (DS) formulations coupled with an efficient eigen-solution technique are proposed for exact longitudinal free vibration analyses of rods and trusses by using classical, Rayleigh-Love, Rayleigh-Bishop Mindlin–Hermann theories. First, the general solutions governing differential equations four rod theories developed. Then substituted into generalized displacement for...

Several models within the framework of continuum mechanics have been proposed over years to solve free vibration problem micro beams. Foremost amongst these are those based on non-local elasticity, classical couple stress, gradient elasticity and modified stress theories. Many retain basic features Bernoulli–Euler or Timoshenko–Ehrenfest theories, but they introduce one more material scale leng...

Let Fq be a finite field with q elements with prime power q and let r > 1 be an integer with q ≡ 1 (mod r). In this paper, we present a refinement of the Cipolla-Lehmer type algorithm given by H. C. Williams, and subsequently improved by K. S. Williams and K. Hardy. For a given r-th power residue c ∈ Fq where r is an odd prime, the algorithm of H. C. Williams determines a solution of X = c in O...

This paper discusses the security of the Rabin-Williams publickey signature system with a deterministic signing algorithm that computes “standard signatures.” The paper proves that any generic attack on standard Rabin-Williams signatures can be mechanically converted into a factorization algorithm with comparable speed and approximately the same effectiveness. “Comparable” and “approximately” a...