This paper o!ers a survey of simple, #exible structural elements subjected to non-conservative follower loads, such as those caused by the thrust of rocket-and jet engines, and by dry friction in automotive disk-and drum-brake systems. Emphasis is on the &&canonical problems'', Beck's, Reut's, Leipholz's, and Hauger's columns. Beck's and Reut's columns have been realized experimentally, and very good agreement between theory and experiments has been found. Leipholz's column is basically realized in an automobile brake system, where noise due to dynamic or parametric instability (brake squeal) is a well-known environmental problem. It is attempted to give a broad overview, with emphasis on experimental works and the associated theoretical problems. Structural optimization is also included in the review, as many studies in that area have served an important purpose in the development of optimization techniques for practical, large-scale optimization problems with non-conservative forces, such as in aeroelasticity.
2000 Academic Press * *x EI *y *x #E*I * *t *y *x !gm *y *x #g *y *x * V m( ) d #(p#Mg) *y *x #C *y *t #m *y *t "0.
Here y"y(x, t) is the transverse displacement at position x, t is the time, m"m(x) is the mass per unit length, p is the mean thrust, EI"EI(x) is the #exural rigidity of the column (E is the modulus of elasticity and I is the area moment of inertia), E* is the coe$cient of dynamic visco-elastic resistance [25,26], M is the endmass, J is the corresponding rotatory inertia, g is the gravity acceleration, and C is the coe$cient of external viscous damping. This coe$cient is proportional to the width (or diameter) of the column [27]. If the column is clamped at x"0 and free at x"ΒΈ, the boundary conditions are y"0 and *y *x "0 at x"0, EI *y *x #E*I * *t *y *x !Mg *y *x a#M * *t y#a *y *x a#J * *t *y *x "0 and * *x EI *y *x #E*I * *t *y *x #Mg *y *x !M * *t y#a *y *x "0 at x"ΒΈ, (
where a is the distace from the column end to the center of gravity of the end-mass.