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Empty soft-drink cans and mass-loaded rods: Analogous homework problems from acoustic and mechanical domains

Daniel A Russell1

  • 1Graduate Program in Acoustics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.

The Journal of the Acoustical Society of America
|July 1, 2026
PubMed

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Impact Loading01:19

Impact Loading

Impact loading occurs when a moving object collides with a stationary structure, such as a rod with a uniform cross-sectional area fixed at one end. Under these conditions, the rod absorbs the kinetic energy from the striking object, leading to deformation and subsequent stress development. As the rod returns to its original position and reaches maximum stress, the absorbed energy, initially manifested as kinetic energy, transforms entirely into strain energy.
In cases of elastic deformation,...
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
Applications of Stress01:04

Applications of Stress

Consider a structure made of a boom and a rod designed to support a load. These two components are connected by a pin and stabilized by brackets and pins. The boom and the rod are detached from their supports to assess the different stresses imposed on this structure, and a free-body diagram is drawn. Then, all the forces applied, including the load acting on the structure, are identified. The reaction forces exerted on both the boom and the rod are computed using the equilibrium equations.
The...
Temperature Dependent Deformation01:12

Temperature Dependent Deformation

In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
Internal Loadings in Structural Members: Problem Solving01:28

Internal Loadings in Structural Members: Problem Solving

When designing or analyzing a structural member, it is important to consider the internal loadings developed within the member. These internal loadings include normal force, shear force, and bending moment. Engineers can ensure that the structural member can support the applied external forces by calculating these internal loadings.
To illustrate this, let's consider a beam OC of 5 kN, inclined at an angle of 53.13° with the horizontal and supported at both ends. Determine the internal loadings...