A Review on Stability and Instability in Fluids and Solids

A criteria for the stability/instability of solid bodies in contact is given here. On the basis of criteria for stability/instability, the coefficient of stability/instability is derived. By using the equation (U-c)(D^Λ2-α^Λ2 )- U^Λ''=0 governing parallel two-dimensional inviscid parallel shear flows, if the basic study flow is of the form U=U(z)(z_1≤z≤z_2). Raleigh had proved that if c_i≠0 then c_r must lie in the range U_min<c_r<U_max, Howard (1961) proved that the value of c=c_r+ic_i must lie in the semicircle (0Λ2+c_i^Λ2≤{ (1/2)(U_max-U_min)}^Λ2. Further results for criteria of instability on the basis of Raleigh and Howard’s results are given in this paper.