Dynamic Stability of Elastic Systems

Abstract

REVIEWED BY M. H. RICHMAN 1 THIS WORK by John Wulff and his associates consists of four individual volumes each devoted to a different aspect of materials science. The subjects of the various volumes are as follows: (1) Structure, (2) Thermodynamics of Structures, (3) Mechanical Behavior, and (4) Electronic Properties. The series is designed to offer a comprehensive introduction to the structure, properties and behavior of solid materials-metals, polymers, and ceramics. The authors have tried to balance the physics and chemistry of solids and have placed emphasis on the principles relating properties and behavior to structure and environment. At present, only volumes 1 and 2 are available for review.

The generalized harmonic balance method for determining the combination resonance in the parametric dynamic systems

“…The most popular and very effective method is that referred to as Bolotin's method [16]. In applying it one assumes the solution on the stability limits to be of the form of a truncated Fourier series: After substitution of expression (2.6) into equations (2.1) the coefficients of the individual harmonic components are equated separately to zero; this procedure is called the harmonic balance method.…”

“…The method relies upon assuming the solution on the stability limits to be in the form of a Fourier series and applying the harmonic balance procedure. It is often referred to as Bolotin's method [16]. It is worth noting that the results as obtained by Bolotin's and a "small parameter" method, respectively, with both solutions of the same form as functions of time, show considerable discrepancies between one another in the case of systems with more than one degree of freedom.…”

“…Recent noteworthy theoretical investigations in the area have been carried out by Bolotin [16], Hsu [18], Jakubovic and Stargincky [17], Valeev [19], Schmidt [15,20], Massa [21), and Nishikawa and Willems [22], and the basic concepts and earlier references can be found in the book by Cesari [23].…”

“…In the field of mechanics such equations appear and need particular attention in the study of dynamic stability of structures under periodic load, the stability of machines and mechanisms with periodically varying inertia and stiffness coefficients, the attitude stability of a spinning satellite in an elliptic orbit, the aeroelastic stability of helicopter blades, the stability of periodic response of vibrating non-linear systems, the stability of pipes conveying pulsating fluids, and others [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recent noteworthy theoretical investigations in the area have been carried out by Bolotin [16], Hsu [18], Jakubovic and Stargincky [17], Valeev [19], Schmidt [15,20], Massa [21), and Nishikawa and Willems [22], and the basic concepts and earlier references can be found in the book by Cesari [23].…”

Prediction of dynamic stability behavior of thin square plates subjected to constant compressive and periodic including constant compressive loads on perpendicular edges

“…Earlier studies on the dynamic stability of columns are briefly discussed (Timoshenko and Gere, 1961). The theory and application of the dynamic stability behavior of structures have been exhaustively given in the classic work of Bolotin (Bolotin, 1964). The first finite element (FE) studies on this topic for columns with various boundary conditions (Brown et al 1968).…”