Abstract
The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.
Highlights
The development of rockets has led to larger values of thrust-to-weight and length-to-diameter ratios as required for longer range flights
To reduce the cost of the launching operation and initial handling and transportation, efforts are always made to reduce the rocket structural weight. These different requirements lead to a highly flexible structure, for which, dynamic response and vibrational characteristics are of great importance [1]
Forces acting on such a structure can be divided into conservative and non-conservative forces with the follower force a typical example of non-conservative forces
Summary
The development of rockets has led to larger values of thrust-to-weight and length-to-diameter ratios as required for longer range flights. The drag force is proportional to the square of the rocket diameter, and the preference is to vary the length as opposed to the diameter for a given range increase. To reduce the cost of the launching operation and initial handling and transportation, efforts are always made to reduce the rocket structural weight. These different requirements lead to a highly flexible structure, for which, dynamic response and vibrational characteristics are of great importance [1]. When a given structure is both under a constant follower force and whose direction changes according to the deformation of the structure, it can undergo static divergence whereby transverse natural frequencies merge into zero and flutter, where two natural frequencies coincide resulting in the amplitude of vibration growing without bound [2]
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