Analytical Solutions

Abstract

A concentrated load acting on a continuous medium is usually described by a Dirac delta function. The point force or mass whose area of influence is limited, must be described in the entire spatial domain of the structure, for example 0≤ x ≤ l. Multiplication of the force by the Dirac delta function δ(x) leads to such an effect. Then we have the load terms δ(x − x ₀)P or δ(x − x ₀)md² w/dt ² described in the domain of the problem. Unfortunately, the mathematical treatment of the term of the first type is relatively simple. It does not contain the solution variable. The treatment of a term of the second type, which describes the inertial force induced by the material particle, is much more complex. It includes the acceleration of the selected point x ₀ as the second derivative of the solution of the differential equation w.