,Summary In this report, the Kron eigenvalue procedure is established by the application of Hamilton's principle to a constrained primitive Lagrangian, comprising the characteristics of the various subsystems into which a composite system is 'torn' to facilitate analysis. The computational merits of the method are outlined-particularly in relation to a scanning algorithm derived from a procedur...

This paper proposes an efficient and reliable eigenvalue solution technique for analytical stochastic dynamic stiffness (SDS) formulations of beam built-up structures with parametric uncertainties. The SDS are developed based on frequency-dependent shape functions in conjunction both random-variable random-field structural parameters. overall numerical framework is aimed towards representing th...

As the length of single sling increases, double slings with transverse connections are gradually becoming one effective measures to control undesirable vibration slings. In analysis dynamic characteristics system, this paper firstly deduces stiffness matrix elastically connected system by method (DSM), solves frequency equation evolved from using Wittrick-Williams (W-W) algorithm, and obtains s...

In this paper, the free vibration characteristics of Sigmoid Functionally Graded Material (S-FGM) Levy-type plates are investigated by developing Dynamic Stiffness Method (DSM) through application Wittrick-Williams algorithm, as solution technique. Kirchoff-Love Plate Theory (KLPT) and Hamilton principle utilised to derive governing equation motion associated natural boundary conditions. Based ...

Size-dependent dynamic responses of small-size frames are modelled by stress-driven nonlocal elasticity and assessed a consistent finite-element methodology. Starting from uncoupled axial bending differential equations, the exact stiffness matrix two-node beam element is evaluated in closed form. The relevant global an arbitrarily-shaped frame, where every member made single element, built stan...

This paper proposes two significant developments of the Wittrick–Williams (W–W) algorithm for an exact wave propagation analysis lattice structures based on analytical dynamic stiffness (DS) model each unit cell structures. Based Bloch’s theorem, combination both DS and W–W makes efficient in contrast to existing methods such as finite element method (FEM). Any number or order natural frequenci...

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...

Abstract. A novel approach for free vibration analysis of train body structures is introduced by using the Carrera Unified Formulation (CUF) and Dynamic Stiffness Method (DSM). Higher-order kinematic fields are developed Formulation, which allows straightforward implementation any-order theory without need ad hoc formulations, in case beam theories. In particular, parallel axis theorem on basis...

A Newtonian (vectorial) approach is used to develop the governing differential equations of motion for a three layer sandwich beam in which the uniform distribution of mass and stiffness is dealt with exactly. The model allows for each layer of material to be of unequal thickness and the effects of coupled bending and longitudinal motion are accounted for. This results in an eighth order ordina...