Vibrations of a beam elastically restrained against rotation at one end and carrying a guided mass at the other

An exact solution to the title problem is obtained in the present paper using classical beam theory. Natural frequencies and mode shapes are determined as a function of the end flexibility coefficient and of the ratio concerned, end mass/beam mass.     

Forced vibrations of a continuous beam with ends elastically restrained against rotation

A survey of the literature shows that the title problem has not been studied to any great extent. In the present paper an approximate solution is obtained in the case of a beam with ends elastically restrained against rotation and an intermediate support. A sinusoidally varying excitation is assumed.     

Large amplitude axisymmetric vibrations of orthotropic circular plates elastically restrained against rotation

A finite element formulation is employed to obtain the linear and non-linear frequencies of orthotropic circular plates with elastically restrained edges. Results are presented in the form of linear frequency parameters and ratios of non-linear to linear periods for several values of the spring constants, orthotropy parameter and central deflections.     

Transverse vibrations of rectangular plates with edges elastically restrained against translation and rotation

The fundamental frequency coefficient for a rectangular plate with edges elastically restrained against both translation and rotation is calculated by using polynomial coordinate functions and the Rayleigh-Ritz method. The approach is simple and straightforward and allows the solution of a rather difficult elastodynamics problem. Complicating factors (orthotropic properties, in-plane forces, concentrated masses, etc.) can also be taken into account without formal difficulties.     

In-plane vibrations of an elastically cantilevered circular arc with a tip mass

Upper and lower bounds are determined for the fundamental frequency of in-plane, transverse vibration of the structural system described in the title in the case of constant cross-section and moment of inertia. The upper bound is determined by approximating the fundamental mode shape with a polynomial co-ordinate function in the angular co-ordinate which includes an exponential optimization parameter. The fundamental frequency equation is generated by means of the Rayleigh-Ritz method and the resulting upper bound is minimized with respect to the previously mentioned exponential parameter. The lower bound for the frequency coefficient is obtained by means of an extension of Dunkerley's method. It is felt that the methodologies developed in the present study are especially useful in the case of variable cross-section of the arch structure, presence of internal supports, etc.     

Free vibrations of a rectangular plate of variable thickness elastically restrained against rotation along three edges and free on the fourth edge

A literature search has shown that the title problem has received no treatment.In this paper solutions are presented as obtained (I) by use of the Ritz method with deflection functions which are simple polynomials, and (II) by use of the extended Kantorovich Method. The natural boundary conditions along the free edge are not satisfied in the first case, while they are complied with approximately when using the second approach. The fundamental frequency coefficient is determined and good agreement is shown to exist between the results obtained by the two methods.     

Vibrations of a beam fixed at one end and carrying a guided mass at the other

This paper presents an exact solution of the title problem, using classical beam theory. It is also assumed that the tip mass is guided in such a manner that the end of the beam does not rotate.     

Vibrations of a timoshenko beam clamped at one end and carrying a finite mass at the other

The present paper deals with an exact solution of the title problem. Modal shapes and natural frequency coefficients are determined for a significant range of the mechanical and geometric parameters that come into play. When the parameter I/AL² (where I is cross-sectional moment of inertia, A is cross-sectional area, and L beam length) approaches zero, the beam dynamic characteristics agree with values already available in the open literature.