The beetle Oncideres cingulata is most likely the culprit. This insect is distributed throughout the eastern United States from New England to Florida and as far west as Kansas and Arizona. The larva are also cylindrical with a small head and shiny integument. Larvae can be up to one inch in length and are light brown to brownish-gray. Girdled twigs often remain on the tree until sufficient wind dislodges them.
Large infestations can result in a high percentage of twigs being girdled.
Though this may reduce the vigor and overall appearance of the tree, the overall effect on the tree's health is not severe. However, the twigs are unsightly and do not fall all at once so clean-up is a drawn out process. This beetle has a one year life cycle. Late in the growing season, the female deposits eggs in small scars chewed through the bark and then chews a continuous notch around the twig, girdling it. The notch is cut below the site of egg deposition apparently because the larva is unable to complete development in the presence of large amounts of sap.