Abstract
This paper investigates natural frequencies of free transverse vibrations of prestressed beams, and the governing equations and natural frequencies of the free vibration in related literatures are discussed and corrected. The differential quadrature methods (DQ) are applied directly to the corrected governing equations to get the the values of natural frequency numerically. Under the simple supported boundary conditions, the natural frequencies of model beam are numerically studied, and the physical parameters of the beam are analyzed respectively. The numerical results show that the natural frequency values increase with the growth of concrete strength and eccentricity of prestressed steels. But with the increase of the span length of beam and values of original prestressing force, the natural frequency values decrease.
Highlights
Prestressed concrete technique can effectively improve the cracking of concrete structure, improve the stiffness and durability of the structure, and give full play to the high strength performance of materials, which has been widely used in civil engineering[1,2,3]
For the vibration characteristics of prestressed beams, the formulas of different linear vibration frequencies are derived by applying the theory of material mechanics and structural dynamics[3,7], these formulas are based on simplified vibration control equations, and their accuracy is worth discussing
The differential equations are transformed to a generalize d eigenvalue problem, and the numerical solutions of natural frequency are obtained based on the method of differential quadrature (DQ)
Summary
Prestressed concrete technique can effectively improve the cracking of concrete structure, improve the stiffness and durability of the structure, and give full play to the high strength performance of materials, which has been widely used in civil engineering[1,2,3]. The differential quadrature (DQ) method is a powerful tool for dealing with dynamical problems. It was introduced for structural analysis by Bert et al.[4]. For the vibration characteristics of prestressed beams, the formulas of different linear vibration frequencies are derived by applying the theory of material mechanics and structural dynamics[3,7], these formulas are based on simplified vibration control equations, and their accuracy is worth discussing. The existing vibration control equations of prestressed beams are analyzed and corrected, and the differential quadrature method (DQ) is directly applied to the corrected equations.
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