ROD MODELING OF STRUCTURES LEVERING MECHANISMS WITH DISTRIBUTED INERTIA

To reduce inertia of moving links into resultant force and moment vectors and to represent center of mass as node in finite element models are widely-used in mechanical calculations of linkage mechanisms. Considering distributed inertia of motion makes possible to create more precise finite element models in spatial linkage structures. By algebraically summing all the distributed inertial loads acting in both directions, perpendicular and along the axis of a constant cross section link, we can show that their intensity varies linearly along the length of link. Using this approach together with Chasles theorem for a point of free rigid body in projections onto the moving axes in the finite element method for rectilinear homogeneous rod, we reach to a more precise finite element model considering analytically distributed inertia of motion. Besides, we obtained subvectors in matrix relation which binds the generalized reaction forces acting at the contact points of the rod element with nodal generalized elastic movements. These subvectors includes the weight and inertia of a distributed spatial movement of link.

Elastic bending wave on the edge of a semi-infinite plate reinforced by a strip plate

Elastic waves localised near the edge of a semi-infinite plate reinforced by a strip plate are considered within the framework of the 2D classical theory for plate bending. The boundary value problem for the strip plate is subject to asymptotic analysis, assuming that a typical wavelength is much greater than the strip thickness. As a result, effective conditions along the interface corresponding to a plate reinforced by a beam with a narrow rectangular cross-section are established. They support an approximate dispersion relation perturbing that for a homogeneous plate with a free edge. The accuracy of the approximate dispersion relation is tested by comparison with the numerical data obtained from the ‘exact’ matrix relation for a composite plate. The effect of the problem parameters on the localisation rate is studied.

Evaluation of Planar Harmonic Impedance for Periodic Elastic Strips of Rectangular Cross Section by Plate Mode Expansion

A system of periodic elastic strips (each one considered as a piece of a plate) is characterized by a matrix relation between the Bloch series of displacement and traction at the bottom side of the system. Both these mechanical fields are involved in the boundary conditions at the contact plane between the strips and the substrate supporting a Rayleigh wave. The analysis exploits the mechanical field expansion over the plate modes, including complex modes; numerical results satisfy the energy conservation law satisfactorily. The derived planar harmonic Green’s function provides an alternative tool for investigation of surface waves propagation under periodic elastic strips, with respect to pure numerical methods mostly applied in the surface acoustic wave devices literature. Perfect agreement of the presented theory with the experimentally verified perturbation model of thin strips is demonstrated.

The Zone Method: A New Explicit Matrix Relation to Calculate the Total Exchange Areas in Anisotropically Scattering Medium Bounded by Anisotropically Reflecting Walls

A new explicit matrix relation for the calculation of the total exchange areas (TEA) in emitting, absorbing and anisotropically scattering semi-transparent medium bounded by emitting, absorbing and anisotropically reflecting walls has been established. It has been used to directly determine the TEA as a function of radiative properties and geometry of the medium and its boundaries. Computation calls for direct exchange areas (DEA) and indirect exchange areas (IEA). A new definition of these exchange areas reduces their integration order and provides practical energy balance relations for their computation in the case of complex geometry elements. The new formulation is applied in the case of an emitting, absorbing and linearly anisotropic scattering semi-transparent slab bounded by black surfaces. This method is also applicable to nongray medium using the weighted sum of gray gases model.