AIMED CONTROL OF THE FREQUENCY SPECTRUM OF EIGENVIBRATIONS OF ELASTIC PLATES WITH A FINITE NUMBER OF DEGREES OF MASS FREEDOM BY INTRODUCING ADDITIONAL GENERALIZED KINEMATIC DEVICES

As is known, targeted regulation of the frequency spectrum of natural vibrations of elastic systems with a finite number of degrees of mass freedom can be performed by introducing additional generalized constraints and generalized kinematic devices. Each targeted generalized constraint increases, and each generalized kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and all forms of natural vibrations (natural modes). To date, for some elastic systems with a finite number of degrees of freedom of masses, in which the directions of mass movement are parallel and lie in the same plane, special methods have been already developed for creating additional constraints and generalized kinematic devices that change the frequency spectrum of natural vibrations in a targeted manner. In particular, a theory and an algorithm for the creation of targeted generalized constraints and generalized kinematic devices have been developed for rods. It was previously proved that the method of forming a matrix of additional stiffness coefficients, specifying targeted generalized constraint, in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. In particular, such systems include plates. The distinctive paper shows that the method of forming a matrix for taking into account the action of additional inertial forces, specifying targeted kinematic devices in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. However, the algorithms for the creation of targeted generalized kinematic devices developed for rods based on the properties of rope polygons cannot be used without significant changes in a similar problem for plates. The method of creation of computational schemes of kinematic devices that precisely change the frequency spectrum of natural vibrations of elastic plates with a finite number of degrees of mass freedom is a separate problem and will be considered in a subsequent paper.

Using a Point-Line-Plane Representation for Unified Simulation of Planar and Spherical Mechanisms

This paper presents a geometric constraints driven approach to unified kinematic simulation of n-bar planar and spherical linkage mechanisms consisting of both revolute and prismatic joints. Generalized constraint equations using point, line, and plane coordinates have been proposed which unify simulation of planar and spherical linkages and are demonstrably scalable to spatial mechanisms. As opposed to some of the existing approaches, which seek to derive loop-closure equations for each type of mechanism separately, we have shown that the simulation can be made simpler and more efficient by using unified version of the geometric constraints on joints and links. This is facilitated using homogeneous coordinates and constraints on geometric primitives, such as point, line, and plane. Furthermore, the approach enables simpler programming, real-time computation, and ability to handle any type of planar and spherical mechanism. This work facilitates creation of practical and intuitive design tools for mechanism designers.

Using a Point-Line-Plane Representation for Unified Simulation of Planar and Spherical Mechanisms

This paper presents a geometric constraints driven approach to unified kinematic simulation of n-bar planar and spherical linkage mechanisms consisting of both revolute and prismatic joints. Generalized constraint equations using point, line and plane coordinates have been proposed which unify simulation of planar and spherical linkages and are demonstrably scalable to spatial mechanisms. As opposed to some of the existing approaches, which seek to derive loop-closure equations for each type of mechanism separately, we have shown that the simulation can be made simpler and more efficient by using unified version of the geometric constraints on joints and links. This is facilitated using homogeneous coordinates and constraints on geometric primitives, such as point, line, and plane. Furthermore, the approach enables simpler programming, real-time computation, and ability to handle any type of planar and spherical mechanism. This work facilitates creation of practical and intuitive design tools for mechanism designers.