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In this article, we study a mathematical model for a one-dimensional suspension bridge problem with nonlinear damping. The model takes into consideration the vibration of the bridge deck in the vertical plane and main cable from which the bridge deck is suspended by the suspenders. We use the multiplier method to establish explicit and generalized decay results, without imposing restrictive growth assumption near the origin on the damping terms. Our results substantially improve, extend, and generalize some earlier related results in the literature.

In this study, a nonlinear damped wave equation within a bounded domain was considered. We began by demonstrating the global existence of solutions through the application of the well-depth method. Following this, a general decay rate for the solutions was established using the multiplier method alongside key properties of convex functions. Notably, these results were derived without the imposition of restrictive growth assumptions on the frictional damping, making this work an improvement and extension of previous findings in the field. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of solutions for unconstrained one dimensional suspension bridge model. We dissipate the system with two nonlinear dampings of variable exponents-type. We obtain exponential and polynomial decay results based on the range of the variable exponents by using the multiplier method. Our results built on, developed and generalized some earlier results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a piezoelectric beam model with nonlinear source terms and investigate the interaction between a viscoelastic damping and a nonlinear frictional damping. Under general assumptions on the relaxation function and the nonlinear feedback, we establish explicit formulae for the energy decay rates of this system and prove that the energy decays at a rate dictated by the weaker damping. Our results substantially improve some earlier related results in the literature. [ABSTRACT FROM AUTHOR]

Strong vibrations can cause considerable damage to structures and break materials apart. The main reason for the Tacoma Narrows Bridge collapse was the sudden transition from longitudinal to torsional oscillations caused by a resonance phenomenon. There exists evidence that several other bridges collapsed for the same reason. To overcome unwanted vibrations and prevent structures from resonating during earthquakes and winds, features and modifications such as dampers are used to stabilize these bridges. In this work, we study a nonlinear viscoelastic plate equation with variable exponents, which models the deformation of a suspension bridge. First, we establish explicit and general decay results of the system depending on the decay rate of the relaxation function and the nature of the variable‐exponents nonlinearity. Then, we perform several numerical tests to illustrate our theoretical decay results. Our results extend and generalize many earlier works in the literature. [ABSTRACT FROM AUTHOR]

This paper aims to establish a general stability result for a one-dimensional linear swelling porous-elastic system with infinite memory, irrespective of the wave speeds of the system. The proof is based on the multiplier method and some properties of convex functions. The kernel in our memory term is more general and of a broader class. Our output extends and improves some of the available results on swelling porous media in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a coupling non-linear system of two plate equations with logarithmic source terms. First, we study the local existence of solutions of the system using the Faedo-Galerkin method and Banach fixed point theorem. Second, we prove the global existence of solutions of the system by using the potential wells. Finally, using the multiplier method, we establish an exponential decay result for the energy of solutions of the system. Some conditions on the variable exponents that appear in the coupling functions and the involved constants that appear in the source terms are determined to ensure the existence and stability of solutions of the system. A series of lemmas and theorems have been proved and used to overcome the difficulties caused by the variable exponent and the logarithmic nonlinearities. Our result generalizes some earlier related results in the literature from the case of only constant exponent of the nonlinear internal forcing terms to the case of variable exponent and logarithmic source terms, which is more useful from the physical point of view and needed in several applications. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with a viscoelastic wave equation with infinite memory and nonlinear frictional damping of variable-exponent type. First, we establish explicit and general decay results with a very general assumption on the relaxation function. Then, we remove the constraint imposed on the boundedness condition on the initial data used in the earlier results in the literature. Finally, we perform several numerical tests to illustrate our theoretical findings. This study generalizes and improves previous literature outcomes. [ABSTRACT FROM AUTHOR]